library(tidyverse)
library(tidyr)
library(dplyr)
library(readr)
library(purrr)
library(ggplot2)
library(e1071)
library(emmeans)
library(lme4)
library(lmerTest)
library(patchwork)
library(brms)
library(bayesplot)
library(car)
library(effects)
library(glue)
library(scales)
library(data.table)
library(effects)
# Disable emmeans computation limits for large models
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)Group CoM Analysis 3
The used data here is mixed: the training blocks are cleaned of all trials that had a accuracy <0.8 and also the trials with xsens errors are deleted. The Test-Blocks (4 & 5) involve all trials except the ones with xsens errors.
# -------- Step-Level Step Counts --------
step_counts <- tibble(
Block = c(1, 2, 3, 4, 5),
Steps = c(6, 12, 18, 18, 18)
)
# -------- Assign Steps Helper Function --------
assign_steps_by_block <- function(df, steps_df = step_counts) {
df %>%
inner_join(steps_df, by = "Block") %>%
group_by(subject, Block, trial) %>%
mutate(Step = cut_number(row_number(), n = unique(Steps), labels = FALSE)) %>%
ungroup()
}
# -------- Tag Trial Phases Function (26 or 25 as end marker) --------
tag_trial_phases <- function(df) {
df %>%
group_by(subject, Block, trial) %>%
mutate(
start_ms = ms[which(Marker.Text == 27)[1]],
end_ms = {
end_candidates <- which(Marker.Text %in% c(26, 25))
if (length(end_candidates) > 0) ms[end_candidates[1]] else NA_real_
},
phase = case_when(
!is.na(start_ms) & !is.na(end_ms) & ms >= start_ms & ms <= end_ms ~ "Execution",
!is.na(start_ms) & ms >= (start_ms - 1500) & ms < start_ms ~ "Preparation",
TRUE ~ NA_character_
)
) %>%
ungroup() %>%
filter(!is.na(phase))
}# Load Data
mixed_files <- list.files("/Users/can/Documents/Uni/Thesis/Data/Xsens/cleaned_csv/merged/Cleaned", pattern = "_mixed\\.csv$", full.names = TRUE)
all_data_mixed <- map_dfr(mixed_files, read_csv)
# Tag trial phases once
tagged_data <- tag_trial_phases(all_data_mixed) %>% mutate(DataType = "Mixed")
tagged_data2 <- tag_trial_phases(all_data_mixed) %>% mutate(DataType = "Mixed")# Compute RMS Function
compute_rms <- function(df) {
df %>%
group_by(subject, Block, trial, phase) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
group_by(subject, Block, phase) %>%
arrange(trial) %>%
mutate(TrialInBlock = row_number()) %>%
ungroup()
}# Compute RMS per trial and phase (used throughout)
rms_data <- compute_rms(tagged_data) %>%
mutate(DataType = "Mixed")
group_rms_summary <- rms_data %>%
group_by(Block, TrialInBlock, phase) %>%
summarise(
mean_rms_x = mean(rms_x, na.rm = TRUE),
se_rms_x = sd(rms_x, na.rm = TRUE) / sqrt(n()),
mean_rms_y = mean(rms_y, na.rm = TRUE),
se_rms_y = sd(rms_y, na.rm = TRUE) / sqrt(n()),
mean_rms_z = mean(rms_z, na.rm = TRUE),
se_rms_z = sd(rms_z, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)# --- New Analysis: Average number of trials with trial.acc == 1 per block ---
trial_acc_summary <- tagged_data %>%
select(subject, Block, trial, trial.acc) %>%
distinct() %>%
filter(trial.acc == 1) %>%
group_by(subject, Block) %>%
summarise(n_trials_with_acc1 = n(), .groups = "drop") %>%
group_by(Block) %>%
summarise(mean_trials_with_acc1 = mean(n_trials_with_acc1),
sd_trials_with_acc1 = sd(n_trials_with_acc1),
n_subjects = n())
# Show result
print(trial_acc_summary)# A tibble: 5 × 4
Block mean_trials_with_acc1 sd_trials_with_acc1 n_subjects
<dbl> <dbl> <dbl> <int>
1 1 35.5 4.26 18
2 2 28.9 7.30 18
3 3 22.1 9.63 18
4 4 39.2 4.51 18
5 5 28.9 10.0 181 Acceleration in Blocks and phases
#1.1 RMS Acceleration Box Plots - Execution
# ----- Execution Phase RMS Boxplots -----
exec_data <- rms_data %>% filter(phase == "Execution")
for (axis in c("x", "y", "z")) {
axis_col <- paste0("rms_", axis)
gg <- ggplot(exec_data, aes(x = factor(Block), y = .data[[axis_col]], fill = phase)) +
geom_boxplot(alpha = 0.7, outlier.shape = NA) +
geom_jitter(width = 0.2, alpha = 0.4, size = 0.6) +
geom_vline(xintercept = 3.5, linetype = "dashed", color = "black") +
ylim(0, 2.5) +
labs(
title = paste("Execution Phase:", toupper(axis), "Axis"),
x = "Block",
y = "RMS Acceleration"
) +
theme_minimal() +
theme(text = element_text(size = 12),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),legend.position = "none")
print(gg)
}Warning: Removed 3 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).
Warning: Removed 16 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 16 rows containing missing values or values outside the scale range
(`geom_point()`).
Warning: Removed 175 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 175 rows containing missing values or values outside the scale range
(`geom_point()`).
#1.2 RMS Acceleration Box Plots - Preparation
# ----- Preparation Phase RMS Boxplots -----
# Extract 1500ms Preparation Window
prep_window_ms <- 1500
extract_preparation_phase <- function(df) {
df %>%
group_split(subject, Block, trial) %>%
map_dfr(function(trial_df) {
exec_start_row <- which(trial_df$Marker.Text == 27)[1]
if (!is.na(exec_start_row) && exec_start_row > 1) {
exec_start_ms <- trial_df$ms[exec_start_row]
trial_df %>%
filter(ms >= (exec_start_ms - prep_window_ms) & ms < exec_start_ms) %>%
mutate(phase = "Preparation")
} else {
NULL
}
})
}
prep_data <- extract_preparation_phase(tagged_data)
# Compute preparation phase RMS
prep_rms <- prep_data %>%
group_by(subject, Block, trial, phase) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
)
# Plot preparation boxplots
for (axis in c("x", "y", "z")) {
axis_col <- paste0("rms_", axis)
fill_color <- switch(axis,
"x" = "skyblue",
"y" = "salmon",
"z" = "seagreen")
gg <- ggplot(prep_rms, aes(x = factor(Block), y = .data[[axis_col]])) +
geom_boxplot(fill = fill_color, alpha = 0.7, outlier.shape = NA) +
geom_jitter(width = 0.2, alpha = 0.4, size = 0.6) +
geom_vline(xintercept = 3.5, linetype = "dashed", color = "black") +
ylim(0, 0.5) +
labs(
title = paste("Preparation Phase:", toupper(axis), "Axis"),
x = "Block",
y = "RMS Acceleration"
) +
theme_minimal() +
theme(text = element_text(size = 12),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),legend.position = "none")
print(gg)
}Warning: Removed 159 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 159 rows containing missing values or values outside the scale range
(`geom_point()`).
Warning: Removed 159 rows containing non-finite outside the scale range
(`stat_boxplot()`).
Removed 159 rows containing missing values or values outside the scale range
(`geom_point()`).
Warning: Removed 217 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 217 rows containing missing values or values outside the scale range
(`geom_point()`).
#1.3 LMM to assess whether block and phase significantly influence rms (per axis)
# Combine into one dataframe for modeling
rms_combined <- bind_rows(
prep_rms,
exec_data
) %>%
mutate(
phase = factor(phase, levels = c("Preparation", "Execution")),
Block = factor(Block),
Trial = factor(trial)
)
for (axis in c("x", "y", "z")) {
cat("\n\n-----------------------------\n")
cat(paste("Axis:", axis, "\n"))
axis_col <- paste0("rms_", axis)
formula <- as.formula(paste(axis_col, "~ Block * phase + (1 | subject) + (1 | Trial)"))
model <- lmer(formula, data = rms_combined)
summary(model) # Fixed effects and model info
# Estimated marginal means and pairwise comparisons
emms <- emmeans(model, ~ Block * phase)
print(emms)
# Pairwise comparisons within each phase
cat("\nPairwise comparisons between blocks within each phase:\n")
print(contrast(emms, method = "pairwise", by = "phase", adjust = "tukey"))
# Interaction significance
# Use Type II Chi-square ANOVA from 'car' package
cat("\nType II Chi-square ANOVA:\n")
print(car::Anova(model, type = 2, test.statistic = "Chisq"))
}
-----------------------------
Axis: x boundary (singular) fit: see help('isSingular') Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.066 0.0343 20.1 -0.00565 0.138
2 Preparation 0.119 0.0346 20.6 0.04701 0.191
3 Preparation 0.169 0.0350 21.6 0.09682 0.242
4 Preparation 0.126 0.0340 19.4 0.05508 0.197
5 Preparation 0.129 0.0340 19.3 0.05759 0.200
1 Execution 0.855 0.0343 20.1 0.78328 0.926
2 Execution 0.795 0.0346 20.6 0.72318 0.867
3 Execution 0.666 0.0350 21.6 0.59381 0.739
4 Execution 0.738 0.0340 19.4 0.66726 0.810
5 Execution 0.585 0.0340 19.3 0.51372 0.656
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise comparisons between blocks within each phase:
phase = Preparation:
contrast estimate SE df t.ratio p.value
Block1 - Block2 -0.05302 0.0149 6400 -3.547 0.0036
Block1 - Block3 -0.10350 0.0159 6424 -6.508 <.0001
Block1 - Block4 -0.06026 0.0137 6404 -4.408 0.0001
Block1 - Block5 -0.06273 0.0136 6403 -4.607 <.0001
Block2 - Block3 -0.05048 0.0164 6422 -3.085 0.0175
Block2 - Block4 -0.00724 0.0142 6398 -0.508 0.9866
Block2 - Block5 -0.00971 0.0142 6398 -0.684 0.9599
Block3 - Block4 0.04324 0.0152 6418 2.838 0.0368
Block3 - Block5 0.04077 0.0152 6421 2.684 0.0564
Block4 - Block5 -0.00247 0.0128 6383 -0.193 0.9997
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.05975 0.0149 6400 3.997 0.0006
Block1 - Block3 0.18845 0.0159 6424 11.851 <.0001
Block1 - Block4 0.11650 0.0137 6404 8.522 <.0001
Block1 - Block5 0.27007 0.0136 6403 19.837 <.0001
Block2 - Block3 0.12870 0.0164 6422 7.865 <.0001
Block2 - Block4 0.05675 0.0142 6398 3.985 0.0007
Block2 - Block5 0.21032 0.0142 6398 14.827 <.0001
Block3 - Block4 -0.07195 0.0152 6418 -4.723 <.0001
Block3 - Block5 0.08162 0.0152 6421 5.374 <.0001
Block4 - Block5 0.15357 0.0128 6383 11.973 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
Type II Chi-square ANOVA:
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: rms_x
Chisq Df Pr(>Chisq)
Block 155.99 4 < 2.2e-16 ***
phase 8927.26 1 < 2.2e-16 ***
Block:phase 359.97 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
-----------------------------
Axis: y boundary (singular) fit: see help('isSingular') Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.0644 0.0391 20.4 -0.0170 0.146
2 Preparation 0.1307 0.0394 21.0 0.0488 0.213
3 Preparation 0.1767 0.0399 22.1 0.0940 0.259
4 Preparation 0.1231 0.0387 19.6 0.0423 0.204
5 Preparation 0.1228 0.0387 19.5 0.0421 0.204
1 Execution 0.9022 0.0391 20.4 0.8208 0.984
2 Execution 0.8438 0.0394 21.0 0.7619 0.926
3 Execution 0.6963 0.0399 22.1 0.6136 0.779
4 Execution 0.7693 0.0387 19.6 0.6885 0.850
5 Execution 0.6083 0.0387 19.5 0.5275 0.689
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise comparisons between blocks within each phase:
phase = Preparation:
contrast estimate SE df t.ratio p.value
Block1 - Block2 -0.066293 0.0177 6400 -3.740 0.0017
Block1 - Block3 -0.112259 0.0189 6424 -5.953 <.0001
Block1 - Block4 -0.058741 0.0162 6404 -3.623 0.0027
Block1 - Block5 -0.058438 0.0161 6403 -3.619 0.0028
Block2 - Block3 -0.045966 0.0194 6422 -2.368 0.1241
Block2 - Block4 0.007552 0.0169 6398 0.447 0.9917
Block2 - Block5 0.007855 0.0168 6398 0.467 0.9903
Block3 - Block4 0.053518 0.0181 6418 2.962 0.0255
Block3 - Block5 0.053820 0.0180 6421 2.988 0.0236
Block4 - Block5 0.000303 0.0152 6383 0.020 1.0000
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.058482 0.0177 6400 3.299 0.0087
Block1 - Block3 0.205943 0.0189 6424 10.920 <.0001
Block1 - Block4 0.132968 0.0162 6404 8.201 <.0001
Block1 - Block5 0.293955 0.0161 6403 18.205 <.0001
Block2 - Block3 0.147461 0.0194 6422 7.598 <.0001
Block2 - Block4 0.074486 0.0169 6398 4.410 0.0001
Block2 - Block5 0.235473 0.0168 6398 13.997 <.0001
Block3 - Block4 -0.072975 0.0181 6418 -4.039 0.0005
Block3 - Block5 0.088011 0.0180 6421 4.887 <.0001
Block4 - Block5 0.160986 0.0152 6383 10.583 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
Type II Chi-square ANOVA:
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: rms_y
Chisq Df Pr(>Chisq)
Block 149.37 4 < 2.2e-16 ***
phase 7098.30 1 < 2.2e-16 ***
Block:phase 289.17 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
-----------------------------
Axis: z
Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.0673 0.0647 20.2 -0.0675 0.202
2 Preparation 0.1724 0.0651 20.8 0.0369 0.308
3 Preparation 0.2493 0.0659 21.8 0.1125 0.386
4 Preparation 0.1633 0.0641 19.5 0.0295 0.297
5 Preparation 0.1609 0.0640 19.4 0.0271 0.295
1 Execution 1.4002 0.0647 20.2 1.2654 1.535
2 Execution 1.3895 0.0651 20.8 1.2540 1.525
3 Execution 1.1906 0.0659 21.8 1.0538 1.327
4 Execution 1.2872 0.0641 19.5 1.1533 1.421
5 Execution 1.0224 0.0640 19.4 0.8885 1.156
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise comparisons between blocks within each phase:
phase = Preparation:
contrast estimate SE df t.ratio p.value
Block1 - Block2 -0.10503 0.0286 6398 -3.673 0.0023
Block1 - Block3 -0.18195 0.0304 6423 -5.979 <.0001
Block1 - Block4 -0.09599 0.0262 6403 -3.670 0.0023
Block1 - Block5 -0.09354 0.0260 6401 -3.591 0.0031
Block2 - Block3 -0.07692 0.0313 6421 -2.456 0.1009
Block2 - Block4 0.00904 0.0272 6396 0.332 0.9974
Block2 - Block5 0.01149 0.0271 6396 0.423 0.9933
Block3 - Block4 0.08596 0.0292 6416 2.949 0.0266
Block3 - Block5 0.08841 0.0291 6420 3.042 0.0199
Block4 - Block5 0.00245 0.0245 6383 0.100 1.0000
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.01063 0.0286 6398 0.372 0.9959
Block1 - Block3 0.20954 0.0304 6423 6.886 <.0001
Block1 - Block4 0.11298 0.0262 6403 4.320 0.0002
Block1 - Block5 0.37780 0.0260 6401 14.504 <.0001
Block2 - Block3 0.19891 0.0313 6421 6.352 <.0001
Block2 - Block4 0.10235 0.0272 6396 3.757 0.0016
Block2 - Block5 0.36717 0.0271 6396 13.529 <.0001
Block3 - Block4 -0.09656 0.0292 6416 -3.312 0.0083
Block3 - Block5 0.16826 0.0291 6420 5.790 <.0001
Block4 - Block5 0.26482 0.0245 6383 10.793 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
Type II Chi-square ANOVA:
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: rms_z
Chisq Df Pr(>Chisq)
Block 119.90 4 < 2.2e-16 ***
phase 7973.86 1 < 2.2e-16 ***
Block:phase 206.08 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Combine into one dataframe for modeling
rms_combined <- bind_rows(
prep_rms,
exec_data
) %>%
mutate(
phase = factor(phase, levels = c("Preparation", "Execution")),
Block = factor(Block),
Trial = factor(trial)
)
# Loop through x, y, z axes
for (axis in c("x", "y", "z")) {
cat("\n\n=============================\n")
cat(paste("Axis:", toupper(axis), "\n"))
cat("=============================\n")
axis_col <- paste0("rms_", axis)
formula <- as.formula(paste(axis_col, "~ Block * phase + (1 | subject) + (1 | Trial)"))
model <- lmer(formula, data = rms_combined)
cat("\nModel Summary:\n")
print(summary(model))
# Estimated marginal means
emms <- emmeans(model, ~ Block * phase)
cat("\nEstimated Marginal Means:\n")
print(emms)
# Pairwise block comparisons within each phase
cat("\nPairwise Block Comparisons within Each Phase (Axis:", toupper(axis), ")\n")
pairwise_block <- contrast(emms, method = "pairwise", by = "phase", adjust = "tukey")
print(pairwise_block)
# Type II chi-square ANOVA
cat("\nType II Chi-square ANOVA Table (Axis:", toupper(axis), ")\n")
print(car::Anova(model, type = 2, test.statistic = "Chisq"))
}
=============================
Axis: X
=============================boundary (singular) fit: see help('isSingular')
Model Summary:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: formula
Data: rms_combined
REML criterion at convergence: 882.4
Scaled residuals:
Min 1Q Median 3Q Max
-4.2111 -0.5306 -0.0978 0.3164 8.6631
Random effects:
Groups Name Variance Std.Dev.
Trial (Intercept) 0.00000 0.0000
subject (Intercept) 0.01935 0.1391
Residual 0.06567 0.2563
Number of obs: 6450, groups: Trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.06596 0.03433 20.04918 1.921 0.069054 .
Block2 0.05302 0.01495 6423.27588 3.547 0.000392 ***
Block3 0.10350 0.01590 6423.55433 6.510 8.07e-11 ***
Block4 0.06026 0.01367 6423.07386 4.408 1.06e-05 ***
Block5 0.06273 0.01361 6423.08045 4.608 4.15e-06 ***
phaseExecution 0.78893 0.01440 6422.99243 54.772 < 2e-16 ***
Block2:phaseExecution -0.11277 0.02111 6422.99243 -5.341 9.58e-08 ***
Block3:phaseExecution -0.29195 0.02243 6422.99243 -13.014 < 2e-16 ***
Block4:phaseExecution -0.17676 0.01933 6422.99243 -9.146 < 2e-16 ***
Block5:phaseExecution -0.33280 0.01925 6422.99243 -17.292 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Block2 Block3 Block4 Block5 phsExc Blc2:E Blc3:E Blc4:E
Block2 -0.202
Block3 -0.190 0.439
Block4 -0.221 0.508 0.478
Block5 -0.222 0.510 0.479 0.558
phaseExectn -0.210 0.482 0.453 0.527 0.529
Blck2:phsEx 0.143 -0.706 -0.309 -0.359 -0.361 -0.682
Blck3:phsEx 0.135 -0.309 -0.706 -0.338 -0.340 -0.642 0.438
Blck4:phsEx 0.156 -0.359 -0.338 -0.707 -0.394 -0.745 0.508 0.479
Blck5:phsEx 0.157 -0.361 -0.339 -0.394 -0.707 -0.748 0.511 0.481 0.558
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
Estimated Marginal Means:
Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.066 0.0343 20.1 -0.00565 0.138
2 Preparation 0.119 0.0346 20.6 0.04701 0.191
3 Preparation 0.169 0.0350 21.6 0.09682 0.242
4 Preparation 0.126 0.0340 19.4 0.05508 0.197
5 Preparation 0.129 0.0340 19.3 0.05759 0.200
1 Execution 0.855 0.0343 20.1 0.78328 0.926
2 Execution 0.795 0.0346 20.6 0.72318 0.867
3 Execution 0.666 0.0350 21.6 0.59381 0.739
4 Execution 0.738 0.0340 19.4 0.66726 0.810
5 Execution 0.585 0.0340 19.3 0.51372 0.656
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Block Comparisons within Each Phase (Axis: X )
phase = Preparation:
contrast estimate SE df t.ratio p.value
Block1 - Block2 -0.05302 0.0149 6400 -3.547 0.0036
Block1 - Block3 -0.10350 0.0159 6424 -6.508 <.0001
Block1 - Block4 -0.06026 0.0137 6404 -4.408 0.0001
Block1 - Block5 -0.06273 0.0136 6403 -4.607 <.0001
Block2 - Block3 -0.05048 0.0164 6422 -3.085 0.0175
Block2 - Block4 -0.00724 0.0142 6398 -0.508 0.9866
Block2 - Block5 -0.00971 0.0142 6398 -0.684 0.9599
Block3 - Block4 0.04324 0.0152 6418 2.838 0.0368
Block3 - Block5 0.04077 0.0152 6421 2.684 0.0564
Block4 - Block5 -0.00247 0.0128 6383 -0.193 0.9997
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.05975 0.0149 6400 3.997 0.0006
Block1 - Block3 0.18845 0.0159 6424 11.851 <.0001
Block1 - Block4 0.11650 0.0137 6404 8.522 <.0001
Block1 - Block5 0.27007 0.0136 6403 19.837 <.0001
Block2 - Block3 0.12870 0.0164 6422 7.865 <.0001
Block2 - Block4 0.05675 0.0142 6398 3.985 0.0007
Block2 - Block5 0.21032 0.0142 6398 14.827 <.0001
Block3 - Block4 -0.07195 0.0152 6418 -4.723 <.0001
Block3 - Block5 0.08162 0.0152 6421 5.374 <.0001
Block4 - Block5 0.15357 0.0128 6383 11.973 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
Type II Chi-square ANOVA Table (Axis: X )
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: rms_x
Chisq Df Pr(>Chisq)
Block 155.99 4 < 2.2e-16 ***
phase 8927.26 1 < 2.2e-16 ***
Block:phase 359.97 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
=============================
Axis: Y
=============================boundary (singular) fit: see help('isSingular')
Model Summary:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: formula
Data: rms_combined
REML criterion at convergence: 3077.5
Scaled residuals:
Min 1Q Median 3Q Max
-3.6792 -0.5190 -0.0701 0.3330 22.7211
Random effects:
Groups Name Variance Std.Dev.
Trial (Intercept) 0.00000 0.0000
subject (Intercept) 0.02484 0.1576
Residual 0.09236 0.3039
Number of obs: 6450, groups: Trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.06440 0.03907 20.34777 1.648 0.114612
Block2 0.06629 0.01773 6423.29983 3.740 0.000186 ***
Block3 0.11226 0.01885 6423.60420 5.954 2.75e-09 ***
Block4 0.05874 0.01621 6423.07883 3.623 0.000293 ***
Block5 0.05844 0.01615 6423.08604 3.620 0.000297 ***
phaseExecution 0.83784 0.01708 6422.98972 49.047 < 2e-16 ***
Block2:phaseExecution -0.12477 0.02504 6422.98972 -4.983 6.43e-07 ***
Block3:phaseExecution -0.31820 0.02661 6422.98972 -11.960 < 2e-16 ***
Block4:phaseExecution -0.19171 0.02292 6422.98972 -8.364 < 2e-16 ***
Block5:phaseExecution -0.35239 0.02283 6422.98972 -15.439 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Block2 Block3 Block4 Block5 phsExc Blc2:E Blc3:E Blc4:E
Block2 -0.211
Block3 -0.198 0.439
Block4 -0.231 0.508 0.478
Block5 -0.232 0.510 0.479 0.558
phaseExectn -0.219 0.482 0.453 0.527 0.529
Blck2:phsEx 0.149 -0.706 -0.309 -0.359 -0.361 -0.682
Blck3:phsEx 0.140 -0.309 -0.706 -0.338 -0.340 -0.642 0.438
Blck4:phsEx 0.163 -0.359 -0.338 -0.707 -0.394 -0.745 0.508 0.479
Blck5:phsEx 0.164 -0.361 -0.339 -0.394 -0.707 -0.748 0.511 0.481 0.558
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see help('isSingular')
Estimated Marginal Means:
Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.0644 0.0391 20.4 -0.0170 0.146
2 Preparation 0.1307 0.0394 21.0 0.0488 0.213
3 Preparation 0.1767 0.0399 22.1 0.0940 0.259
4 Preparation 0.1231 0.0387 19.6 0.0423 0.204
5 Preparation 0.1228 0.0387 19.5 0.0421 0.204
1 Execution 0.9022 0.0391 20.4 0.8208 0.984
2 Execution 0.8438 0.0394 21.0 0.7619 0.926
3 Execution 0.6963 0.0399 22.1 0.6136 0.779
4 Execution 0.7693 0.0387 19.6 0.6885 0.850
5 Execution 0.6083 0.0387 19.5 0.5275 0.689
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Block Comparisons within Each Phase (Axis: Y )
phase = Preparation:
contrast estimate SE df t.ratio p.value
Block1 - Block2 -0.066293 0.0177 6400 -3.740 0.0017
Block1 - Block3 -0.112259 0.0189 6424 -5.953 <.0001
Block1 - Block4 -0.058741 0.0162 6404 -3.623 0.0027
Block1 - Block5 -0.058438 0.0161 6403 -3.619 0.0028
Block2 - Block3 -0.045966 0.0194 6422 -2.368 0.1241
Block2 - Block4 0.007552 0.0169 6398 0.447 0.9917
Block2 - Block5 0.007855 0.0168 6398 0.467 0.9903
Block3 - Block4 0.053518 0.0181 6418 2.962 0.0255
Block3 - Block5 0.053820 0.0180 6421 2.988 0.0236
Block4 - Block5 0.000303 0.0152 6383 0.020 1.0000
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.058482 0.0177 6400 3.299 0.0087
Block1 - Block3 0.205943 0.0189 6424 10.920 <.0001
Block1 - Block4 0.132968 0.0162 6404 8.201 <.0001
Block1 - Block5 0.293955 0.0161 6403 18.205 <.0001
Block2 - Block3 0.147461 0.0194 6422 7.598 <.0001
Block2 - Block4 0.074486 0.0169 6398 4.410 0.0001
Block2 - Block5 0.235473 0.0168 6398 13.997 <.0001
Block3 - Block4 -0.072975 0.0181 6418 -4.039 0.0005
Block3 - Block5 0.088011 0.0180 6421 4.887 <.0001
Block4 - Block5 0.160986 0.0152 6383 10.583 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
Type II Chi-square ANOVA Table (Axis: Y )
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: rms_y
Chisq Df Pr(>Chisq)
Block 149.37 4 < 2.2e-16 ***
phase 7098.30 1 < 2.2e-16 ***
Block:phase 289.17 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
=============================
Axis: Z
=============================
Model Summary:
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: formula
Data: rms_combined
REML criterion at convergence: 9241.3
Scaled residuals:
Min 1Q Median 3Q Max
-3.7337 -0.5480 -0.1334 0.3796 11.1043
Random effects:
Groups Name Variance Std.Dev.
Trial (Intercept) 0.0001909 0.01382
subject (Intercept) 0.0683512 0.26144
Residual 0.2403028 0.49021
Number of obs: 6450, groups: Trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 0.06735 0.06467 20.19820 1.041 0.309955
Block2 0.10503 0.02860 6396.94989 3.673 0.000242 ***
Block3 0.18195 0.03042 6423.29337 5.981 2.34e-09 ***
Block4 0.09599 0.02615 6402.26087 3.670 0.000244 ***
Block5 0.09354 0.02605 6400.39890 3.591 0.000332 ***
phaseExecution 1.33280 0.02755 6375.73377 48.370 < 2e-16 ***
Block2:phaseExecution -0.11566 0.04039 6375.73377 -2.863 0.004204 **
Block3:phaseExecution -0.39149 0.04291 6375.73377 -9.122 < 2e-16 ***
Block4:phaseExecution -0.20897 0.03697 6375.73377 -5.652 1.65e-08 ***
Block5:phaseExecution -0.47134 0.03682 6375.73377 -12.802 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) Block2 Block3 Block4 Block5 phsExc Blc2:E Blc3:E Blc4:E
Block2 -0.205
Block3 -0.193 0.439
Block4 -0.225 0.508 0.478
Block5 -0.226 0.510 0.479 0.558
phaseExectn -0.213 0.482 0.453 0.527 0.529
Blck2:phsEx 0.145 -0.706 -0.309 -0.359 -0.361 -0.682
Blck3:phsEx 0.137 -0.309 -0.705 -0.338 -0.340 -0.642 0.438
Blck4:phsEx 0.159 -0.359 -0.338 -0.707 -0.394 -0.745 0.508 0.479
Blck5:phsEx 0.159 -0.361 -0.339 -0.394 -0.707 -0.748 0.511 0.481 0.558
Estimated Marginal Means:
Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.0673 0.0647 20.2 -0.0675 0.202
2 Preparation 0.1724 0.0651 20.8 0.0369 0.308
3 Preparation 0.2493 0.0659 21.8 0.1125 0.386
4 Preparation 0.1633 0.0641 19.5 0.0295 0.297
5 Preparation 0.1609 0.0640 19.4 0.0271 0.295
1 Execution 1.4002 0.0647 20.2 1.2654 1.535
2 Execution 1.3895 0.0651 20.8 1.2540 1.525
3 Execution 1.1906 0.0659 21.8 1.0538 1.327
4 Execution 1.2872 0.0641 19.5 1.1533 1.421
5 Execution 1.0224 0.0640 19.4 0.8885 1.156
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Block Comparisons within Each Phase (Axis: Z )
phase = Preparation:
contrast estimate SE df t.ratio p.value
Block1 - Block2 -0.10503 0.0286 6398 -3.673 0.0023
Block1 - Block3 -0.18195 0.0304 6423 -5.979 <.0001
Block1 - Block4 -0.09599 0.0262 6403 -3.670 0.0023
Block1 - Block5 -0.09354 0.0260 6401 -3.591 0.0031
Block2 - Block3 -0.07692 0.0313 6421 -2.456 0.1009
Block2 - Block4 0.00904 0.0272 6396 0.332 0.9974
Block2 - Block5 0.01149 0.0271 6396 0.423 0.9933
Block3 - Block4 0.08596 0.0292 6416 2.949 0.0266
Block3 - Block5 0.08841 0.0291 6420 3.042 0.0199
Block4 - Block5 0.00245 0.0245 6383 0.100 1.0000
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.01063 0.0286 6398 0.372 0.9959
Block1 - Block3 0.20954 0.0304 6423 6.886 <.0001
Block1 - Block4 0.11298 0.0262 6403 4.320 0.0002
Block1 - Block5 0.37780 0.0260 6401 14.504 <.0001
Block2 - Block3 0.19891 0.0313 6421 6.352 <.0001
Block2 - Block4 0.10235 0.0272 6396 3.757 0.0016
Block2 - Block5 0.36717 0.0271 6396 13.529 <.0001
Block3 - Block4 -0.09656 0.0292 6416 -3.312 0.0083
Block3 - Block5 0.16826 0.0291 6420 5.790 <.0001
Block4 - Block5 0.26482 0.0245 6383 10.793 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
Type II Chi-square ANOVA Table (Axis: Z )
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: rms_z
Chisq Df Pr(>Chisq)
Block 119.90 4 < 2.2e-16 ***
phase 7973.86 1 < 2.2e-16 ***
Block:phase 206.08 4 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- Descriptive Statistics: Mean and SD of RMS per Axis, Block, and Phase ---
# Per Block and Phase
rms_summary_blockwise <- rms_combined %>%
group_by(phase, Block) %>%
summarise(
mean_rms_x = mean(rms_x, na.rm = TRUE),
sd_rms_x = sd(rms_x, na.rm = TRUE),
mean_rms_y = mean(rms_y, na.rm = TRUE),
sd_rms_y = sd(rms_y, na.rm = TRUE),
mean_rms_z = mean(rms_z, na.rm = TRUE),
sd_rms_z = sd(rms_z, na.rm = TRUE),
.groups = "drop"
)
# All Blocks Combined per Phase
rms_summary_allblocks <- rms_combined %>%
group_by(phase) %>%
summarise(
mean_rms_x = mean(rms_x, na.rm = TRUE),
sd_rms_x = sd(rms_x, na.rm = TRUE),
mean_rms_y = mean(rms_y, na.rm = TRUE),
sd_rms_y = sd(rms_y, na.rm = TRUE),
mean_rms_z = mean(rms_z, na.rm = TRUE),
sd_rms_z = sd(rms_z, na.rm = TRUE),
.groups = "drop"
) %>%
mutate(Block = "All") %>%
select(phase, Block, everything()) # Reorder columns to match
# Combine both summaries
rms_summary_stats <- bind_rows(rms_summary_blockwise, rms_summary_allblocks)
# Display the combined summary
print(rms_summary_stats)# A tibble: 12 × 8
phase Block mean_rms_x sd_rms_x mean_rms_y sd_rms_y mean_rms_z sd_rms_z
<fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Preparation 1 0.0606 0.0587 0.0579 0.0548 0.0573 0.0857
2 Preparation 2 0.119 0.242 0.131 0.334 0.178 0.514
3 Preparation 3 0.174 0.290 0.186 0.313 0.268 0.556
4 Preparation 4 0.127 0.219 0.124 0.223 0.164 0.379
5 Preparation 5 0.129 0.189 0.122 0.181 0.160 0.330
6 Execution 1 0.850 0.400 0.896 0.504 1.39 0.764
7 Execution 2 0.795 0.420 0.844 0.469 1.39 0.761
8 Execution 3 0.671 0.309 0.705 0.317 1.21 0.579
9 Execution 4 0.739 0.377 0.770 0.432 1.29 0.682
10 Execution 5 0.585 0.241 0.608 0.345 1.02 0.569
11 Preparation All 0.119 0.210 0.120 0.234 0.159 0.394
12 Execution All 0.722 0.365 0.758 0.433 1.25 0.689 # ------------------ Grouped RMS Boxplots by Phase and Block ------------------
# Ensure Block is a factor for consistent plotting
rms_combined$Block <- factor(rms_combined$Block, levels = c("1", "2", "3", "4", "5"))
# Helper function with dynamic ylim based on phase
plot_rms_by_phase_block <- function(data, target_phase, target_blocks, plot_title) {
df <- data %>%
filter(phase == target_phase, Block %in% target_blocks)
df_long <- df %>%
select(subject, Block, phase, starts_with("rms_")) %>%
pivot_longer(cols = starts_with("rms_"),
names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = case_when(
Axis == "rms_x" ~ "X",
Axis == "rms_y" ~ "Y",
Axis == "rms_z" ~ "Z",
TRUE ~ Axis
)
)
# Choose ylim based on phase
y_limit <- if (target_phase == "Preparation") c(0, 0.3) else c(0, 2.75)
# Plot
ggplot(df_long, aes(x = Block, y = RMS)) +
geom_boxplot(aes(fill = Block), outlier.shape = NA, alpha = 0.6) +
geom_jitter(width = 0.2, alpha = 0.3, size = 0.7) +
facet_wrap(~ Axis, ncol = 3, scales = "free_y") +
ylim(y_limit) +
labs(
title = plot_title,
x = "Block",
y = "RMS Acceleration"
) +
theme_minimal() +
theme(
text = element_text(size = 12),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
strip.text = element_text(size = 13, face = "bold"),
legend.position = "none"
)
}
# ------------------ Generate the 4 Requested Plots ------------------
# Plot 1: Preparation Phase, Blocks 1–3
plot_rms_by_phase_block(rms_combined, "Preparation", c("1", "2", "3"),
"Preparation Phase – Blocks 1–3")Warning: Removed 381 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 381 rows containing missing values or values outside the scale range
(`geom_point()`).
# Plot 2: Execution Phase, Blocks 1–3
plot_rms_by_phase_block(rms_combined, "Execution", c("1", "2", "3"),
"Execution Phase – Blocks 1–3")Warning: Removed 91 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 91 rows containing missing values or values outside the scale range
(`geom_point()`).
# Plot 3: Preparation Phase, Blocks 4–5
plot_rms_by_phase_block(rms_combined, "Preparation", c("4", "5"),
"Preparation Phase – Blocks 4–5")Warning: Removed 410 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 410 rows containing missing values or values outside the scale range
(`geom_point()`).
# Plot 4: Execution Phase, Blocks 4–5
plot_rms_by_phase_block(rms_combined, "Execution", c("4", "5"),
"Execution Phase – Blocks 4–5")Warning: Removed 42 rows containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 42 rows containing missing values or values outside the scale range
(`geom_point()`).
#2. #2.1 6 steps Block 1,4 & 5 - preparation for rms analysis, skip completely to part 3
# --- Step-Wise RMS: Blocks 1, 4, 5 — First 6 Steps ---
plot_stepwise_rms_blocks_145_first6 <- function(tagged_data2) {
step_markers <- c(14, 15, 16, 17)
buffer <- 3
step_data <- tagged_data2 %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_block() %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup()
step_indices <- step_data %>%
select(subject, Block, trial, row_id, Step)
window_data <- map_dfr(1:nrow(step_indices), function(i) {
step <- step_indices[i, ]
rows <- (step$row_id - buffer):(step$row_id + buffer)
step_data %>%
filter(subject == step$subject,
Block == step$Block,
trial == step$trial,
row_id %in% rows) %>%
mutate(Step = step$Step)
})
step_summary <- window_data %>%
group_by(subject, Block, trial, Step) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = toupper(gsub("rms_", "", Axis)),
Step = factor(Step),
Block = factor(Block),
subject = factor(subject),
trial_id = interaction(subject, trial, drop = TRUE)
) %>%
filter(Block %in% c("1", "4", "5"), Step %in% 1:6)
plot_data <- step_summary %>%
group_by(Block, Step, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
se_rms = sd(RMS, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)
axis_labels <- unique(plot_data$Axis)
plots <- map(axis_labels, function(ax) {
axis_data <- filter(plot_data, Axis == ax)
ggplot(axis_data, aes(x = Step, y = mean_rms, fill = Block)) +
geom_col(position = position_dodge(width = 0.8), width = 0.7) +
geom_errorbar(
aes(ymin = mean_rms - se_rms, ymax = mean_rms + se_rms),
position = position_dodge(width = 0.8),
width = 0.3
) +
ylim(0, 3.25) +
labs(
title = paste("Step-wise CoM RMS — Axis", ax),
x = "Step Number ",
y = "RMS Acceleration (m/s²)",
fill = "Block"
) +
theme_minimal() +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
text = element_text(size = 12),
plot.title = element_text(face = "bold"),
axis.text.x = element_text(angle = 0, vjust = 0.5)
)
})
names(plots) <- axis_labels
return(list(
plots = plots,
step_summary = step_summary,
plot_data = plot_data,
window_data = window_data
))
}
# -------- Run the Analysis Pipeline --------
result <- plot_stepwise_rms_blocks_145_first6(tagged_data2)
stepwise_block145_plots <- result$plots
step_summary <- result$step_summary
plot_data <- result$plot_data
window_data <- result$window_data
# -------- Print Plots --------
for (plot_name in names(stepwise_block145_plots)) {
cat("\n\n==== Axis:", plot_name, "====\n\n")
print(stepwise_block145_plots[[plot_name]])
}
==== Axis: X ====
==== Axis: Y ====
==== Axis: Z ====
# -------- RMS LMMs: Blocks 1, 4, 5 --------
print_stepwise_lmm_diagnostics <- function(results_list, dataset_name = "Mixed") {
cat(glue::glue("\n=========== STEPWISE LMM DIAGNOSTICS: {dataset_name} ===========\n"))
for (key in names(results_list)) {
cat("\n---", key, "---\n")
cat("ANOVA:\n")
print(results_list[[key]]$ANOVA)
cat("\nEstimated Marginal Means (Step | Block):\n")
print(results_list[[key]]$EmmeansStepBlock)
cat("\nPairwise Comparisons:\n")
print(results_list[[key]]$Pairwise)
cat("\nFixed Effects:\n")
print(results_list[[key]]$FixedEffects)
cat("\nRandom Effects:\n")
print(results_list[[key]]$RandomEffects)
cat("\nSample Scaled Residuals:\n")
print(head(results_list[[key]]$ScaledResiduals))
cat("\n=============================================================\n")
}
}
rms_lmm_results_6step <- list()
axes <- c("X", "Y", "Z")
for (ax in axes) {
cat(glue("\n\n========== Running models for 6-step Axis: {ax} ==========\n\n"))
df_rms <- step_summary %>% filter(Axis == ax)
rms_model <- lmer(RMS ~ Block + Step + (1 | subject) + (1 | trial_id), data = df_rms)
emmeans_step_block <- emmeans(rms_model, ~ Step | Block)
rms_lmm_results_6step[[paste0("RMS_", ax)]] <- list(
Model = rms_model,
ANOVA = anova(rms_model, type = 3),
Pairwise = emmeans(rms_model, pairwise ~ Block)$contrasts,
EmmeansStepBlock = summary(emmeans_step_block),
FixedEffects = fixef(rms_model),
RandomEffects = ranef(rms_model),
ScaledResiduals = resid(rms_model, scaled = TRUE)
)
}
========== Running models for 6-step Axis: X ==========
========== Running models for 6-step Axis: Y ==========
========== Running models for 6-step Axis: Z ==========print_stepwise_lmm_diagnostics(rms_lmm_results_6step, dataset_name = "6-Step RMS Acceleration")=========== STEPWISE LMM DIAGNOSTICS: 6-Step RMS Acceleration ===========
--- RMS_X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 95.556 47.778 2 9758.5 369.5428 <2e-16 ***
Step 0.295 0.059 5 9344.7 0.4566 0.8087
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 1:
Step emmean SE df lower.CL upper.CL
1 0.844 0.0741 17.5 0.688 1.000
2 0.853 0.0741 17.6 0.697 1.009
3 0.855 0.0743 17.7 0.699 1.011
4 0.848 0.0741 17.5 0.692 1.004
5 0.859 0.0741 17.6 0.703 1.015
6 0.846 0.0743 17.7 0.689 1.002
Block = 4:
Step emmean SE df lower.CL upper.CL
1 0.695 0.0740 17.4 0.539 0.851
2 0.704 0.0742 17.6 0.548 0.860
3 0.706 0.0745 17.9 0.550 0.863
4 0.699 0.0740 17.4 0.543 0.855
5 0.710 0.0742 17.6 0.554 0.866
6 0.697 0.0745 17.9 0.540 0.853
Block = 5:
Step emmean SE df lower.CL upper.CL
1 0.594 0.0740 17.4 0.438 0.750
2 0.604 0.0742 17.6 0.447 0.760
3 0.605 0.0745 17.9 0.449 0.762
4 0.598 0.0740 17.4 0.442 0.754
5 0.609 0.0742 17.6 0.453 0.765
6 0.596 0.0745 17.9 0.439 0.752
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block1 - Block4 0.149 0.00926 9844 16.090 <.0001
Block1 - Block5 0.250 0.00925 9822 26.994 <.0001
Block4 - Block5 0.101 0.00933 9686 10.802 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
0.843703357 -0.149009353 -0.249748774 0.009610432 0.011513087 0.004198155
Step5 Step6
0.015092115 0.001937280
Random Effects:
$trial_id
(Intercept)
3.1 -0.2422485371
4.1 0.1665601188
5.1 0.0040796703
7.1 -0.0221494591
8.1 -0.1422793133
10.1 -0.0887999321
11.1 -0.5423133285
13.1 0.0638958041
14.1 0.1040226145
15.1 0.0723346523
16.1 0.0427365754
17.1 -0.0240787701
18.1 0.0010327475
19.1 0.1487967904
20.1 0.0501203097
22.1 0.1511697248
23.1 -0.3129587503
2.2 0.0185587619
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4.2 0.0840589302
5.2 -0.0272489593
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10.2 0.2445621236
11.2 -0.1726072429
13.2 0.0349961870
14.2 -0.1113606675
15.2 0.2560216920
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17.2 0.0158435567
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19.2 0.0494165142
20.2 -0.1410008957
22.2 0.1591766005
23.2 0.9399708184
2.3 0.1556953035
3.3 -0.1484241267
4.3 0.0126275157
5.3 -0.0287668302
7.3 0.0429892943
10.3 0.2168034755
11.3 -0.3340829507
13.3 0.1149074525
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16.3 0.0477317826
17.3 -0.1204963768
18.3 0.0264114170
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22.3 0.0634685103
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7.4 -0.1913619731
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10.4 -0.4698513704
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11.7 0.0805977911
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23.7 0.3310065258
2.8 -0.1876581233
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3.9 0.2188944543
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2.11 0.3318366394
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11.39 0.4905724382
13.39 -0.1226099119
14.39 0.1270668935
15.39 0.0076635415
16.39 0.0523274686
17.39 0.0968526563
18.39 -0.0283413249
19.39 0.0036925205
20.39 0.1353633528
22.39 -0.0262723559
23.39 -0.3674729437
2.40 0.2250082391
3.40 -0.0391937663
4.40 0.0772533973
5.40 0.0774316690
7.40 0.3751966841
8.40 0.2072082814
10.40 -0.2461649449
11.40 0.0514874913
13.40 -0.2594252189
14.40 0.2204149404
15.40 -0.0995701648
16.40 -0.2404671081
17.40 0.1340521783
18.40 -0.1235856730
19.40 -0.0393775943
20.40 -0.0215483099
22.40 0.0510214871
23.40 -0.3838674888
2.41 0.0037498612
3.41 -0.0822060296
4.41 -0.0887462758
5.41 0.0302206357
7.41 -0.0062464976
8.41 0.0821926344
10.41 -0.4036673937
11.41 -0.1791239454
13.41 -0.1850799174
14.41 -0.0938312092
15.41 0.1104296319
16.41 -0.0337167096
17.41 0.0604438918
18.41 0.2490500317
19.41 -0.0988925970
20.41 0.0528768436
22.41 0.0514949355
23.41 -0.0163240822
2.42 0.1219905473
3.42 0.2896982622
4.42 -0.0858038544
5.42 0.1129305367
7.42 0.1669360554
8.42 0.1392134763
10.42 -0.0032588534
11.42 -0.2000378908
13.42 -0.2892656488
14.42 0.1364264497
15.42 -0.2153067708
16.42 0.0734184636
17.42 -0.0648183576
18.42 0.0680158717
19.42 -0.0288038405
20.42 0.0769158286
22.42 -0.0528336248
23.42 -0.1606168076
2.43 -0.0878715452
3.43 -0.3052337797
4.43 -0.1717207828
5.43 0.0112618381
7.43 0.0552276230
8.43 -0.2488370438
10.43 -0.2255605103
11.43 -0.0832131283
13.43 -0.2468784407
14.43 0.1482643114
15.43 0.1689457797
16.43 -0.0371340647
17.43 -0.1725366800
18.43 0.1070009015
19.43 -0.0266243078
20.43 0.0826133614
22.43 -0.2394799714
23.43 -0.0108596878
2.44 -0.1879056771
3.44 0.0914582300
4.44 0.1037911407
5.44 0.0640205806
7.44 -0.0475481624
8.44 0.4489202803
10.44 -0.0633534644
11.44 0.4309773401
13.44 -0.0479943772
14.44 -0.2618879578
15.44 0.0787242783
16.44 -0.0205666463
17.44 0.1486484954
18.44 0.4543283140
19.44 -0.0718967020
20.44 -0.0124721271
22.44 -0.1635912703
23.44 -0.0437311182
2.45 0.5066808696
3.45 0.2037310140
4.45 -0.1147468904
5.45 0.0785646003
7.45 -0.0505675623
8.45 0.0659562231
10.45 -0.6189985830
11.45 0.2150225925
13.45 -0.0821802705
14.45 -0.0142962420
15.45 -0.1680096468
16.45 -0.1116607035
17.45 -0.1693285611
18.45 0.3060175049
19.45 0.0299478254
20.45 0.0594659534
22.45 -0.1674255685
23.45 0.0939231466
2.46 -0.2057082754
3.46 -0.1113115715
4.46 0.1517901319
5.46 0.0035278269
7.46 -0.0841969991
8.46 -0.4660838556
10.46 -0.4094211796
11.46 -0.1541061136
13.46 0.0119928579
14.46 -0.1747875876
15.46 -0.1109957930
16.46 -0.2193407908
17.46 -0.1560029478
18.46 -0.1440785982
19.46 0.2026337585
20.46 -0.0860298018
22.46 -0.0447936306
23.46 -0.0211584575
2.47 -0.2244673330
3.47 0.5023167387
4.47 -0.0739345520
5.47 -0.0231779338
7.47 -0.0414102469
8.47 -0.4213461455
10.47 -0.5328043598
11.47 -0.1703716150
13.47 -0.1562095863
14.47 -0.2867037588
15.47 -0.2538868468
16.47 -0.3561506464
17.47 -0.0541010926
18.47 -0.2066832452
19.47 -0.1860098929
20.47 -0.0776458937
22.47 -0.1752398300
23.47 -0.2502827839
2.48 -0.2183148308
5.48 0.0922480197
23.48 -0.0192926151
$subject
(Intercept)
2 -0.04108480
3 0.12334123
4 -0.23045720
5 -0.34794958
7 -0.15453173
8 0.38541068
10 0.70421693
11 0.56180134
13 -0.19830516
14 0.07508729
15 0.02857434
16 -0.10218127
17 -0.28447438
18 -0.11787434
19 -0.30205126
20 -0.25698797
22 -0.16215057
23 0.31961647
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.2474358 -0.1978208 -0.2560971 -0.2357535 -0.1494968 -0.2801900
=============================================================
--- RMS_Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 50.402 25.2009 2 9674.4 127.0965 <2e-16 ***
Step 1.148 0.2296 5 9345.5 1.1578 0.3274
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 1:
Step emmean SE df lower.CL upper.CL
1 0.837 0.0866 17.6 0.655 1.019
2 0.844 0.0867 17.6 0.661 1.026
3 0.837 0.0869 17.8 0.654 1.019
4 0.827 0.0866 17.6 0.645 1.010
5 0.825 0.0867 17.6 0.643 1.007
6 0.807 0.0869 17.8 0.624 0.990
Block = 4:
Step emmean SE df lower.CL upper.CL
1 0.801 0.0865 17.5 0.619 0.983
2 0.808 0.0867 17.7 0.625 0.990
3 0.800 0.0871 18.0 0.617 0.983
4 0.791 0.0865 17.5 0.609 0.973
5 0.789 0.0867 17.7 0.606 0.971
6 0.771 0.0871 18.0 0.588 0.954
Block = 5:
Step emmean SE df lower.CL upper.CL
1 0.663 0.0865 17.5 0.481 0.845
2 0.670 0.0867 17.7 0.487 0.852
3 0.662 0.0871 18.0 0.479 0.845
4 0.653 0.0865 17.5 0.471 0.835
5 0.651 0.0867 17.7 0.468 0.833
6 0.633 0.0871 18.0 0.450 0.816
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block1 - Block4 0.0362 0.0115 9743 3.143 0.0048
Block1 - Block5 0.1742 0.0115 9725 15.142 <.0001
Block4 - Block5 0.1380 0.0116 9612 11.917 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3
0.8371517380 -0.0361966738 -0.1742103616 0.0066161521 -0.0005467238
Step4 Step5 Step6
-0.0098333406 -0.0121150988 -0.0302241623
Random Effects:
$trial_id
(Intercept)
3.1 -0.0747720660
4.1 -0.0291511826
5.1 0.0416491345
7.1 -0.0008021772
8.1 -0.0176312079
10.1 -0.3075630154
11.1 -0.8151880276
13.1 -0.1166414637
14.1 -0.0486039973
15.1 -0.0406677600
16.1 -0.1291213826
17.1 0.0552034659
18.1 0.1222974306
19.1 0.0227066184
20.1 -0.0367377208
22.1 0.0397024924
23.1 -0.2618375437
2.2 -0.0254809478
3.2 -0.1157983172
4.2 -0.0014931885
5.2 0.0172002440
7.2 -0.2153924671
8.2 -0.2484283180
10.2 -0.1377735606
11.2 -0.5140231396
13.2 -0.0449319352
14.2 -0.0843426171
15.2 0.0075546309
16.2 0.0733381218
17.2 0.0499922357
18.2 -0.2348379635
19.2 0.1199548347
20.2 -0.0539715599
22.2 0.2432174936
23.2 4.5934039319
2.3 -0.1315917558
3.3 0.0071783424
4.3 -0.0179443510
5.3 0.0502717403
7.3 -0.0200427634
10.3 -0.3093637940
11.3 -0.1960498569
13.3 -0.1751774331
14.3 -0.1894752572
15.3 -0.0557103247
16.3 -0.0698851441
17.3 -0.1296314479
18.3 0.1058472489
19.3 -0.1042066664
22.3 0.0300299583
23.3 -0.1183873648
2.4 -0.1761147591
3.4 0.1475881197
4.4 -0.0017522821
5.4 0.0120573023
7.4 -0.0473477346
8.4 -0.0526970828
10.4 -0.5706905800
11.4 -0.7804695851
13.4 0.0124025223
14.4 -0.0188579104
15.4 0.0499117801
16.4 0.0419697255
17.4 -0.1158321355
18.4 0.0573826121
19.4 -0.0131499127
20.4 -0.1017953620
22.4 0.0575486960
23.4 -0.2540225779
2.5 0.2174891625
3.5 -0.2587765526
4.5 -0.1239176789
5.5 -0.1253650412
7.5 -0.0794159851
8.5 -0.2269462576
10.5 -0.1119314098
11.5 -0.6462073013
13.5 -0.0204313238
14.5 0.2826041268
15.5 0.1897931195
16.5 0.0384311929
17.5 0.1717462470
18.5 -0.1007798965
19.5 -0.0861029198
20.5 -0.0118835180
22.5 0.0326548229
23.5 -0.4846811574
2.6 0.0182790472
3.6 -0.1300854272
4.6 0.1291354985
5.6 -0.0238062852
7.6 0.1060446694
8.6 -0.0417307797
10.6 0.2509620880
11.6 -0.2801493653
13.6 0.0395692202
14.6 0.1122581315
15.6 -0.0933907983
16.6 -0.1936363146
17.6 -0.1635910689
18.6 -0.0984248367
19.6 -0.0495766491
20.6 -0.0125985798
22.6 -0.0752893864
23.6 -0.3071586694
2.7 -0.0852714438
3.7 -0.1939140500
4.7 -0.1185473317
5.7 -0.0580074104
7.7 0.2415831916
8.7 -0.2116242443
10.7 -0.0912413140
11.7 0.1355862576
13.7 0.0700119209
14.7 -0.2234668179
15.7 -0.1568941079
16.7 0.1029067926
17.7 -0.0525170603
18.7 -0.1381113050
19.7 -0.0525017371
20.7 -0.0873456060
22.7 0.0154270199
23.7 0.7318692032
2.8 -0.0415032307
3.8 -0.0945723365
4.8 -0.1289636150
5.8 -0.0804443882
7.8 -0.0421189592
8.8 -0.2749874947
10.8 0.2965776086
11.8 -0.1321856491
13.8 -0.1877487065
14.8 0.0999509009
15.8 0.0255989793
16.8 0.0230901623
17.8 -0.1852435882
18.8 0.0086791634
19.8 -0.0810706817
20.8 -0.0382966556
22.8 -0.0291957681
23.8 -0.4727041793
2.9 -0.0312475570
3.9 -0.2334113550
4.9 -0.0002820696
5.9 0.2302950533
7.9 -0.0201917972
8.9 -0.1901659318
10.9 -0.0631799006
11.9 -0.1281606503
13.9 -0.0115507819
14.9 0.1930617654
15.9 -0.0552827577
16.9 0.1949409385
17.9 -0.0991712927
18.9 -0.1027213861
19.9 -0.0760520916
20.9 -0.0384655516
22.9 -0.0554785578
23.9 -0.0436919895
2.10 -0.2108007693
3.10 0.1045786201
4.10 -0.0018679468
5.10 -0.0650464756
7.10 -0.1185655444
8.10 -0.0668419021
10.10 0.1195155775
11.10 0.3477945177
13.10 -0.1288175763
14.10 0.1126111862
15.10 0.0787524512
16.10 0.0638299399
17.10 0.0867117642
18.10 -0.0021870933
19.10 0.1187566624
20.10 0.0070214490
22.10 0.0620512622
23.10 -0.6290991948
2.11 0.4356802504
3.11 0.3302245155
4.11 -0.0499654192
5.11 0.0041422164
7.11 0.1180230152
8.11 0.2158807881
10.11 0.4773050835
11.11 -0.1697300614
13.11 -0.0741171822
14.11 0.0483006958
15.11 0.0101111639
16.11 0.0122292828
17.11 -0.0954722926
18.11 -0.0119428461
19.11 -0.0993555460
20.11 0.2275665824
22.11 0.0454611505
23.11 -0.0827659331
2.12 -0.1348052544
3.12 0.2753569101
4.12 -0.0414965239
5.12 0.0660598941
7.12 -0.0712359621
8.12 -0.2862323721
10.12 -0.1197708439
11.12 -0.4917010117
13.12 -0.0067796241
14.12 -0.0069404651
15.12 -0.1125723075
16.12 0.0322056669
17.12 -0.0402590412
18.12 -0.2225109060
19.12 0.0360856934
20.12 -0.0673578470
22.12 -0.0348746417
23.12 0.1229794310
2.13 0.0478546218
3.13 -0.0668919704
4.13 -0.1064543309
5.13 -0.0333098910
7.13 -0.0608477005
8.13 0.1209029413
10.13 -0.2673292514
11.13 -0.4729003240
13.13 -0.1970900543
14.13 0.2322074210
15.13 -0.1540791933
16.13 -0.0094718292
17.13 -0.1093886946
18.13 0.0981763269
19.13 -0.0289692699
20.13 0.0315907119
22.13 -0.0357839398
23.13 0.1902369251
2.14 -0.0773694490
3.14 -0.1663381821
4.14 -0.1192801029
5.14 -0.0551494615
7.14 -0.0776509044
8.14 0.5225526063
10.14 -0.0362000211
11.14 -0.2234396239
13.14 -0.0504317121
14.14 -0.0607469117
15.14 0.0683134219
16.14 -0.1657160955
17.14 -0.0658329024
18.14 0.1007254293
19.14 0.1409588187
20.14 -0.0696455825
22.14 -0.0782382362
23.14 -0.1523356887
2.15 -0.0891971808
3.15 0.1804075233
4.15 0.0043701463
5.15 0.0229348322
7.15 -0.0454556778
8.15 -0.0888367083
10.15 0.1813496235
11.15 -0.1602367082
13.15 0.0644250524
14.15 -0.2636698595
15.15 -0.0640991979
16.15 0.0611384551
17.15 -0.0118683138
18.15 -0.0110504421
19.15 -0.0574183165
20.15 -0.0680693186
22.15 -0.0395311667
23.15 -0.1621591915
2.16 -0.0259404834
3.16 -0.0892575146
4.16 -0.1836550708
5.16 -0.0289123537
7.16 -0.1196260643
8.16 -0.0297038049
10.16 -0.1486373246
11.16 -0.0578515047
13.16 -0.1114356145
14.16 -0.0347656049
15.16 0.1096201180
16.16 -0.0507644434
17.16 0.0975095095
18.16 0.1941858697
19.16 -0.0391498681
20.16 -0.1343195373
22.16 -0.0989527309
23.16 0.0797201488
2.17 0.2137287978
3.17 0.2103735717
4.17 -0.1321220018
5.17 -0.1190147400
7.17 -0.1686603519
8.17 -0.0518676433
10.17 0.1249406714
11.17 -0.5476789267
13.17 -0.0299794505
14.17 -0.0484318348
15.17 0.1356456732
16.17 -0.1914768667
17.17 -0.0766866945
18.17 -0.0383299071
19.17 -0.0808322888
20.17 -0.0625301028
22.17 -0.0412424373
23.17 -0.3007039723
2.18 -0.0760723505
3.18 0.1232510047
4.18 -0.0169504520
5.18 -0.1106482320
7.18 -0.0517678150
8.18 0.1134241779
10.18 -0.1383778235
11.18 -0.7526835939
13.18 -0.0881774725
14.18 -0.2465412784
15.18 0.0855402122
16.18 -0.0776888419
17.18 -0.0089232768
18.18 -0.1505462637
19.18 -0.0933163850
20.18 0.0412962845
22.18 0.0881213488
23.18 0.3895074584
2.19 0.2456933882
3.19 -0.0703796889
4.19 -0.1656992848
5.19 -0.1700907883
7.19 -0.0934045536
8.19 -0.1072493265
10.19 -0.3256385006
11.19 0.2070430214
13.19 -0.0815248234
14.19 -0.0066156654
15.19 0.0087940776
16.19 -0.1868436921
17.19 -0.0389699627
18.19 -0.0460718261
19.19 0.0415308741
20.19 -0.0800163312
22.19 -0.0673813070
23.19 -0.2635171095
2.20 0.3122384598
3.20 0.3517677053
4.20 -0.0648751250
5.20 0.0104056554
7.20 -0.0792885186
8.20 -0.0859293609
10.20 0.7368901066
11.20 -0.6525423053
13.20 0.0153512565
14.20 -0.1269929688
15.20 -0.0599983630
16.20 -0.2523327291
17.20 0.0270484309
18.20 -0.0423572909
19.20 -0.0724854486
20.20 -0.0365091290
22.20 -0.0013633085
23.20 -0.2583668662
2.21 0.0782572829
3.21 -0.0005502396
4.21 0.0136696130
5.21 -0.0527468944
7.21 0.0325556429
8.21 -0.0320171843
10.21 0.8819915652
11.21 -0.3553452393
13.21 -0.0522237197
14.21 -0.2247754719
15.21 -0.0671092875
16.21 -0.1589934657
17.21 -0.1109119529
18.21 0.0436315247
19.21 0.0028206169
20.21 0.0142179412
22.21 0.0062641459
23.21 0.5662646950
2.22 0.0186050148
3.22 0.0414290871
4.22 0.1961448725
5.22 0.1462874862
7.22 -0.1466086338
8.22 0.3604108360
10.22 0.2705309870
11.22 -0.2729380738
13.22 0.0486506816
14.22 0.0092517756
15.22 -0.1162981239
16.22 -0.0019169204
17.22 0.0131614758
18.22 -0.0081587669
19.22 -0.0245990640
20.22 -0.1120270445
22.22 0.0050388038
23.22 0.1598425075
2.23 -0.1856865870
3.23 0.4052230906
4.23 -0.0061041121
5.23 0.0894066052
7.23 -0.0498839599
8.23 0.2513388078
10.23 0.5693201936
11.23 0.1380789906
13.23 -0.0256915401
14.23 -0.3145036555
15.23 -0.0645270052
16.23 0.2905974290
17.23 -0.0162999843
18.23 0.0001546562
19.23 -0.0116091064
20.23 0.0175558570
22.23 -0.0369288927
23.23 -0.2529243011
2.24 -0.1420062984
3.24 0.0476675460
4.24 -0.0120411100
5.24 0.0430577853
7.24 -0.0574766901
8.24 0.4590127669
10.24 0.0665595682
11.24 -0.4620924361
13.24 0.0419827297
14.24 0.0640935701
15.24 -0.2256259571
16.24 -0.1209552135
17.24 0.0202390629
18.24 0.1094660962
19.24 0.0155997891
20.24 0.0031556079
22.24 -0.0579164664
23.24 0.0557724296
2.25 0.2977883107
3.25 -0.0688289666
4.25 -0.0518805291
5.25 -0.0101034716
7.25 -0.0295421987
8.25 0.0578377076
10.25 -0.2095193288
11.25 0.4775318738
13.25 0.0326067798
14.25 -0.0548543800
15.25 -0.0889790676
16.25 0.1458271856
17.25 -0.1871074588
18.25 0.1105160172
19.25 -0.0867861664
20.25 -0.0569788736
22.25 -0.0812481214
23.25 0.0531481886
2.26 -0.1320312472
3.26 -0.1435549144
4.26 -0.0458504394
5.26 -0.0166267630
7.26 -0.1534638627
8.26 -0.1851101889
10.26 0.6597949585
11.26 0.0710791966
13.26 0.0315178640
14.26 0.1315350688
15.26 0.0867652131
16.26 0.1470802082
17.26 0.0617552192
18.26 -0.0953857627
19.26 -0.0472548386
20.26 0.0579368128
22.26 -0.0058925205
23.26 -0.4776419921
2.27 -0.0264879778
3.27 -0.1050854950
4.27 -0.1125777497
5.27 0.0189410965
7.27 -0.0581423276
8.27 -0.0064008348
10.27 0.0875621369
11.27 -0.2257119577
13.27 -0.0118575168
14.27 -0.0748667400
15.27 -0.1614447484
16.27 0.0205951330
17.27 -0.0999013635
18.27 0.1118363865
19.27 0.0520449911
20.27 0.0068645494
22.27 0.0076162045
23.27 0.2334561162
2.28 -0.1925172190
3.28 -0.0955071585
4.28 -0.1467129131
5.28 0.0202062034
7.28 -0.0390955617
8.28 0.9998782632
10.28 -0.1584398517
11.28 -0.2198201464
13.28 0.3099484121
14.28 -0.2474688071
15.28 0.0238770352
16.28 -0.0897609663
17.28 -0.1927664988
18.28 -0.1045321207
19.28 -0.0410003109
20.28 -0.0472010486
22.28 0.0238849355
23.28 -0.1722676362
2.29 -0.0095994298
3.29 0.1706675515
4.29 0.0048872693
5.29 -0.1020920008
7.29 -0.2014540553
8.29 -0.0555710829
10.29 -0.0350375337
11.29 -0.6472118167
13.29 0.1064089416
14.29 0.1647982852
15.29 0.0390511032
16.29 0.0407156603
17.29 0.0743028021
18.29 0.0171548456
19.29 0.2191662660
20.29 -0.1010098836
22.29 -0.0833933012
23.29 -0.3010408018
2.30 -0.1415429219
3.30 0.0423761545
4.30 0.1019175473
5.30 -0.0029900600
7.30 0.0384458875
8.30 0.2780510163
10.30 0.6621008990
11.30 0.3922583684
13.30 0.1024180061
14.30 0.0778865101
15.30 0.0097096580
16.30 0.5612100069
17.30 0.1584340005
18.30 -0.0471685075
19.30 0.0092963566
20.30 -0.0681486002
22.30 -0.1108905266
23.30 -0.0825340229
2.31 0.2331952431
3.31 0.2860842875
4.31 0.0799054787
5.31 0.0179759613
7.31 -0.1873073976
8.31 -0.0206649954
10.31 0.1873660928
11.31 1.8396992406
13.31 -0.0886149356
14.31 0.1381967145
15.31 -0.1970035391
16.31 0.1449614911
17.31 0.2347840411
18.31 0.0776836015
19.31 -0.0373422425
20.31 0.0074792745
22.31 -0.0210955944
23.31 0.3431769652
2.32 -0.0763340326
3.32 0.1740065549
4.32 0.2419067245
5.32 0.0978708604
7.32 0.3020549639
8.32 0.4003212876
10.32 -0.0232408165
11.32 1.6228245011
13.32 -0.1689108541
14.32 -0.1262641077
15.32 0.0832388122
16.32 0.2009530311
17.32 0.1467257497
18.32 -0.0455488386
19.32 -0.0231524238
20.32 -0.1219743181
22.32 0.0712473020
23.32 0.2404400863
2.33 -0.1017751930
3.33 -0.0099523267
4.33 -0.0930147290
5.33 -0.0167340577
7.33 0.1329631185
8.33 0.4255882465
10.33 -0.1799356756
11.33 1.6906372506
13.33 0.0318543680
14.33 -0.3129813226
15.33 -0.1333413081
16.33 -0.1717190878
17.33 -0.0492588386
18.33 0.0327461159
19.33 0.0161509338
20.33 0.0318240379
22.33 -0.0799321359
23.33 -0.0354950549
2.34 0.0737433757
3.34 0.1203255075
4.34 -0.1560257792
5.34 -0.0094285426
7.34 0.0772302705
8.34 0.4096521234
10.34 1.5289931652
11.34 0.6562039486
13.34 0.4582397202
14.34 -0.1485452631
15.34 -0.0098109345
16.34 0.0770602805
17.34 0.1240286218
18.34 0.0651120154
19.34 0.0209877674
20.34 0.1036742039
22.34 0.0273323591
23.34 -0.2377825802
2.35 0.1872218080
3.35 -0.3210394810
4.35 -0.0956326925
5.35 -0.0589436855
7.35 -0.0194798878
8.35 -0.3141003065
10.35 0.6059555946
11.35 0.4248476845
13.35 0.2954222888
14.35 0.3725498381
15.35 0.2227529741
16.35 0.0745751471
17.35 0.0512735174
18.35 0.0554965503
19.35 -0.0595232594
20.35 0.0122151007
22.35 0.0422235954
23.35 -0.4280524064
2.36 -0.0149385432
3.36 0.0468926894
4.36 0.1156902499
5.36 -0.0232607115
7.36 0.1356940231
8.36 -0.3008030505
10.36 0.0224905658
11.36 0.1341509682
13.36 0.2059342132
14.36 0.0819582583
15.36 0.0523170602
16.36 0.5767252208
17.36 0.0226601532
18.36 0.0364777536
19.36 0.1070329005
20.36 -0.0205331915
22.36 0.2977811914
23.36 0.1762999871
2.37 0.3928032047
3.37 -0.0379275738
4.37 0.1206786108
5.37 -0.0439390180
7.37 0.1375228200
8.37 0.9197467111
10.37 -0.7173379797
11.37 -0.2638465159
13.37 -0.1585226311
14.37 0.0666157346
15.37 -0.0099331540
16.37 0.0467414672
17.37 0.1009756822
18.37 0.2569422452
19.37 0.0899198449
20.37 0.0166364954
22.37 0.0791212472
23.37 -0.0757342903
2.38 0.3141781453
3.38 0.0483326068
4.38 -0.0676834084
5.38 -0.0981792783
7.38 0.2110154487
8.38 -0.1832478523
10.38 -0.8953600345
11.38 0.4650340430
13.38 -0.3106434257
14.38 -0.0849606040
15.38 0.0767003631
16.38 -0.0742953691
17.38 0.0067421959
18.38 0.0837433210
19.38 -0.0119889905
20.38 -0.0498671893
22.38 -0.0811244879
23.38 -0.2607317762
2.39 0.3592098317
3.39 -0.1909201609
4.39 0.0088667894
5.39 0.0267637998
7.39 0.1138121144
8.39 -0.4647778497
10.39 0.3255144877
11.39 0.6699376063
13.39 -0.0201812601
14.39 0.3709694971
15.39 0.0987408428
16.39 -0.2359549742
17.39 0.0314005215
18.39 -0.0061436342
19.39 -0.1284635350
20.39 0.1679044581
22.39 0.0942859535
23.39 -0.4000667775
2.40 -0.1268129998
3.40 -0.1249666002
4.40 0.1719539374
5.40 -0.0040823430
7.40 0.4910456918
8.40 0.4374432275
10.40 -0.0157060337
11.40 0.8133419744
13.40 -0.3488015852
14.40 0.1517070901
15.40 -0.0558105540
16.40 0.0470140635
17.40 0.0332788016
18.40 0.1722675965
19.40 -0.0318983344
20.40 0.1164891790
22.40 -0.0305631932
23.40 -0.4245129791
2.41 -0.0146962287
3.41 0.0388394750
4.41 0.1182072956
5.41 -0.0890039509
7.41 -0.0696480621
8.41 -0.1798787154
10.41 -0.2083254988
11.41 -0.3081448404
13.41 -0.3085665526
14.41 0.1434034224
15.41 -0.1148072052
16.41 -0.0648460541
17.41 0.2727966485
18.41 -0.0752698116
19.41 0.0883707352
20.41 -0.0890186953
22.41 0.1590251577
23.41 -0.4098739584
2.42 0.1062364811
3.42 0.1106915578
4.42 0.3495848964
5.42 0.2327575294
7.42 0.1043858672
8.42 -0.1393794574
10.42 -0.2364372092
11.42 -0.5542321982
13.42 -0.3154739527
14.42 0.1278515457
15.42 -0.1370561680
16.42 0.1833148213
17.42 -0.0708678463
18.42 0.2969305344
19.42 0.0970807014
20.42 -0.0460157323
22.42 0.0511541096
23.42 0.8463862910
2.43 0.1511460611
3.43 -0.0967948175
4.43 0.0206377873
5.43 -0.0201525297
7.43 0.0790190828
8.43 -0.3295143216
10.43 -0.6134676000
11.43 0.3140805151
13.43 -0.3451375455
14.43 0.2754575451
15.43 0.0235964811
16.43 -0.1427241346
17.43 -0.1325913613
18.43 0.0442883406
19.43 -0.0015661795
20.43 0.2423447904
22.43 -0.1705496200
23.43 -0.3927203663
2.44 -0.3114548922
3.44 -0.0758087144
4.44 -0.0018867917
5.44 -0.0428804466
7.44 0.0612954246
8.44 -0.3757452193
10.44 -0.0016296657
11.44 0.1084402383
13.44 0.1107204877
14.44 0.1074974110
15.44 0.4009769681
16.44 -0.2431852968
17.44 0.0497201799
18.44 0.0843620431
19.44 0.1096528585
20.44 0.1454081977
22.44 -0.0572622096
23.44 -0.2104338834
2.45 0.0071252638
3.45 0.1156659502
4.45 0.1986036660
5.45 0.0870250362
7.45 -0.1529461932
8.45 -0.5604468305
10.45 -0.8470201371
11.45 -0.3536834295
13.45 0.2819114285
14.45 -0.1516531837
15.45 -0.0150081601
16.45 -0.1370423808
17.45 0.2888468658
18.45 -0.1559571599
19.45 -0.0311965023
20.45 0.1471612147
22.45 -0.0414297265
23.45 -0.5294271457
2.46 -0.1916280854
3.46 -0.3355493341
4.46 0.1187662608
5.46 0.0152980194
7.46 -0.0062930407
8.46 -0.0459146233
10.46 0.2081862915
11.46 -0.3512396582
13.46 -0.0291241385
14.46 -0.1097175021
15.46 -0.0222828572
16.46 -0.2918146539
17.46 -0.1759185341
18.46 -0.3308109314
19.46 -0.0752899956
20.46 0.0743584622
22.46 -0.2173855989
23.46 -0.4607858137
2.47 -0.3859922339
3.47 -0.1542085715
4.47 -0.1393638084
5.47 -0.0541220723
7.47 -0.0793229767
8.47 -0.5152250443
10.47 -0.7757054869
11.47 0.9425069714
13.47 1.1055007560
14.47 -0.0652023777
15.47 0.1891069536
16.47 -0.2272546708
17.47 -0.1573957333
18.47 -0.2723464898
19.47 -0.0483394540
20.47 -0.0779592322
22.47 -0.1311358915
23.47 0.2107969546
2.48 -0.4041030773
5.48 -0.0126962806
23.48 0.2829466379
$subject
(Intercept)
2 0.18389241
3 0.15466965
4 -0.29710936
5 -0.34562309
7 -0.22419067
8 0.35210832
10 0.89662888
11 0.51825649
13 -0.17919952
14 0.11163096
15 -0.16866965
16 -0.10717580
17 -0.25820991
18 -0.06869581
19 -0.35673383
20 -0.27130912
22 -0.35524943
23 0.41497948
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-1.443951 -1.375905 -1.304274 -1.283419 -1.268344 -1.210523
=============================================================
--- RMS_Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 268.68 134.34 2 9700.9 278.4811 <2e-16 ***
Step 4.00 0.80 5 9340.3 1.6583 0.141
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 1:
Step emmean SE df lower.CL upper.CL
1 1.76 0.163 17.4 1.421 2.11
2 1.80 0.163 17.4 1.458 2.14
3 1.79 0.163 17.6 1.444 2.13
4 1.76 0.163 17.4 1.417 2.10
5 1.77 0.163 17.4 1.429 2.11
6 1.73 0.163 17.6 1.388 2.07
Block = 4:
Step emmean SE df lower.CL upper.CL
1 1.63 0.163 17.4 1.285 1.97
2 1.66 0.163 17.5 1.322 2.01
3 1.65 0.163 17.7 1.307 1.99
4 1.62 0.163 17.4 1.280 1.97
5 1.64 0.163 17.5 1.293 1.98
6 1.60 0.163 17.7 1.251 1.94
Block = 5:
Step emmean SE df lower.CL upper.CL
1 1.35 0.163 17.3 1.006 1.69
2 1.39 0.163 17.5 1.043 1.73
3 1.37 0.163 17.7 1.028 1.72
4 1.34 0.163 17.3 1.002 1.69
5 1.36 0.163 17.5 1.014 1.70
6 1.32 0.163 17.7 0.973 1.66
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block1 - Block4 0.137 0.0179 9778 7.611 <.0001
Block1 - Block5 0.415 0.0179 9759 23.184 <.0001
Block4 - Block5 0.279 0.0180 9637 15.456 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
1.764024497 -0.136534990 -0.415469325 0.037007987 0.023266920 -0.004502529
Step5 Step6
0.008011831 -0.032360684
Random Effects:
$trial_id
(Intercept)
3.1 -6.734647e-02
4.1 -4.340312e-02
5.1 2.627693e-01
7.1 3.687433e-01
8.1 -1.868739e-01
10.1 3.383499e-01
11.1 -3.951901e-01
13.1 -2.749718e-01
14.1 8.202932e-02
15.1 -2.275977e-02
16.1 -5.842531e-02
17.1 1.942368e-01
18.1 3.966266e-01
19.1 -2.208507e-02
20.1 1.491734e-01
22.1 1.937104e-01
23.1 -4.575966e-01
2.2 2.877592e-01
3.2 -5.349266e-01
4.2 -2.067404e-02
5.2 1.355011e-01
7.2 2.813439e-01
8.2 -3.496384e-01
10.2 -2.254852e-01
11.2 -1.017973e+00
13.2 1.589128e-01
14.2 1.669277e-01
15.2 6.446999e-02
16.2 2.077812e-01
17.2 1.978077e-01
18.2 -1.259568e+00
19.2 -4.440017e-02
20.2 -9.662948e-02
22.2 7.900167e-02
23.2 9.241357e-01
2.3 4.686837e-01
3.3 -8.619428e-02
4.3 1.296488e-01
5.3 -1.660622e-01
7.3 2.660280e-01
10.3 3.387398e-01
11.3 -3.568346e-01
13.3 -1.686166e-01
14.3 6.312426e-02
15.3 2.397034e-01
16.3 -1.993420e-01
17.3 -1.864477e-02
18.3 -5.885038e-02
19.3 8.571670e-02
22.3 6.200153e-02
23.3 -7.342200e-01
2.4 -4.373061e-01
3.4 -3.451696e-01
4.4 -1.103931e-01
5.4 5.504223e-02
7.4 1.115995e-01
8.4 -6.566528e-01
10.4 1.185385e+00
11.4 -6.500700e-01
13.4 -6.347131e-02
14.4 2.306236e-01
15.4 3.104884e-01
16.4 1.708304e-01
17.4 -7.795399e-02
18.4 3.335372e-01
19.4 2.143843e-02
20.4 -2.869241e-01
22.4 1.104226e-01
23.4 -6.392681e-01
2.5 1.024552e-01
3.5 -4.988836e-01
4.5 -1.582336e-01
5.5 -1.617113e-01
7.5 2.896266e-01
8.5 -5.903034e-01
10.5 4.557020e-01
11.5 -7.082031e-01
13.5 2.688752e-01
14.5 -5.562277e-02
15.5 3.612557e-01
16.5 3.727609e-01
17.5 3.473906e-01
18.5 -1.816657e-01
19.5 -4.125548e-01
20.5 -3.023728e-01
22.5 -9.007757e-02
23.5 -8.370615e-01
2.6 -2.573757e-01
3.6 -1.197564e-01
4.6 2.238582e-04
5.6 -3.709287e-03
7.6 4.967813e-01
8.6 9.289814e-01
10.6 -3.431727e-02
11.6 -4.040544e-01
13.6 6.643263e-02
14.6 2.002523e-02
15.6 -1.966388e-01
16.6 -4.787397e-01
17.6 -3.370657e-01
18.6 1.059997e-01
19.6 -1.296020e-01
20.6 -2.751773e-01
22.6 -7.584439e-02
23.6 -3.826139e-01
2.7 -2.076631e-01
3.7 -2.395399e-01
4.7 8.018129e-02
5.7 -7.848165e-02
7.7 -9.119282e-02
8.7 -5.389728e-01
10.7 1.126476e-01
11.7 -7.717728e-01
13.7 1.172328e+00
14.7 4.917879e-01
15.7 -1.559337e-01
16.7 1.257269e-01
17.7 -2.195657e-01
18.7 -2.573297e-01
19.7 -2.059414e-02
20.7 -2.452917e-01
22.7 1.990007e-02
23.7 3.932047e-01
2.8 8.612976e-05
3.8 7.418105e-02
4.8 -1.494669e-01
5.8 -1.591011e-01
7.8 5.037797e-01
8.8 -9.033086e-01
10.8 1.424437e+00
11.8 1.170315e+00
13.8 2.990133e-01
14.8 1.814116e-02
15.8 5.481221e-02
16.8 -1.546727e-01
17.8 -1.510448e-01
18.8 -1.923686e-02
19.8 -1.478375e-01
20.8 -4.071023e-02
22.8 -6.502255e-02
23.8 -7.845598e-01
2.9 -6.108042e-02
3.9 -9.673508e-02
4.9 -6.776792e-02
5.9 -5.160550e-02
7.9 3.842239e-01
8.9 -4.139613e-01
10.9 2.636409e-01
11.9 -2.814188e-01
13.9 1.708920e-01
14.9 -2.078020e-01
15.9 6.239317e-02
16.9 -1.284020e-02
17.9 5.299747e-02
18.9 -2.844631e-01
19.9 -4.178232e-02
20.9 -3.266780e-01
22.9 -1.915684e-02
23.9 -3.840258e-01
2.10 -2.423852e-01
3.10 3.284991e-01
4.10 2.390514e-01
5.10 -2.639558e-01
7.10 2.471425e-01
8.10 -4.091327e-01
10.10 2.039485e+00
11.10 -4.365449e-01
13.10 -3.734353e-01
14.10 -5.079546e-02
15.10 4.471460e-01
16.10 2.620310e-01
17.10 2.527789e-02
18.10 7.267870e-02
19.10 3.603659e-02
20.10 1.033174e-01
22.10 2.072848e-01
23.10 -8.579295e-01
2.11 2.251617e-02
3.11 -1.268743e-01
4.11 -8.621554e-03
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19.45 4.984070e-01
20.45 8.847132e-02
22.45 -5.942079e-01
23.45 -1.176079e+00
2.46 -9.626070e-02
3.46 -6.874577e-01
4.46 9.701088e-02
5.46 9.959214e-02
7.46 -6.762635e-01
8.46 -4.815281e-01
10.46 -1.721598e+00
11.46 -8.238979e-01
13.46 -5.081294e-01
14.46 -4.996988e-01
15.46 -4.750416e-01
16.46 -7.780598e-01
17.46 -8.951590e-02
18.46 4.203109e-01
19.46 -2.254788e-01
20.46 -6.129208e-02
22.46 -9.885504e-02
23.46 -1.011122e+00
2.47 -5.984065e-01
3.47 3.805718e-01
4.47 -1.568450e-01
5.47 -1.247052e-01
7.47 -2.477900e-01
8.47 -3.198929e-01
10.47 -1.323333e+00
11.47 -5.624013e-01
13.47 -1.075371e-01
14.47 -5.903209e-01
15.47 -2.719422e-01
16.47 -1.550460e-01
17.47 -2.143024e-01
18.47 -2.041255e-02
19.47 -3.031220e-02
20.47 -1.329407e-01
22.47 -1.800124e-01
23.47 3.025542e-01
2.48 -4.869513e-01
5.48 -2.491299e-01
23.48 -2.966408e-01
$subject
(Intercept)
2 -0.28069995
3 0.51939457
4 -0.56468289
5 -0.84139260
7 0.30330350
8 0.66185221
10 1.44977223
11 0.87900390
13 0.14983097
14 -0.48709647
15 0.04390682
16 -0.17924635
17 -0.81171912
18 0.27432234
19 -0.76418929
20 -0.58533061
22 -0.60902037
23 0.84199112
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.3910858 -0.5386600 -0.5396268 -0.4996448 -0.4546655 -0.2833216
=============================================================# -------- Identify Stepwise EMM Outliers vs. Overall Mean (per Axis × Block) --------
# Bind all EMMs into one dataframe
all_emm_6step <- bind_rows(lapply(rms_lmm_results_6step, function(res) res$EmmeansStepBlock), .id = "AxisLabel")
# Extract axis from label (e.g., "RMS_X" -> "X")
all_emm_6step <- all_emm_6step %>%
mutate(
Axis = gsub("RMS_", "", AxisLabel),
Step = as.numeric(as.character(Step)),
Block = as.factor(Block)
)
# Compute overall mean ± 1.96*SE per Block × Axis
overall_stats_6step <- all_emm_6step %>%
group_by(Block, Axis) %>%
summarise(
overall_mean = mean(emmean, na.rm = TRUE),
overall_se = sd(emmean, na.rm = TRUE) / sqrt(n()),
lower_bound = overall_mean - 1.96 * overall_se,
upper_bound = overall_mean + 1.96 * overall_se,
.groups = "drop"
)
# Join back and flag outliers
emm_outliers_6step <- left_join(all_emm_6step, overall_stats_6step, by = c("Block", "Axis")) %>%
mutate(
is_outlier = emmean < lower_bound | emmean > upper_bound
) %>%
filter(is_outlier)
# View flagged outlier steps
print(emm_outliers_6step) AxisLabel Step Block emmean SE df lower.CL upper.CL Axis
1 RMS_X 1 1 0.8437034 0.07406303 17.50140 0.6877844 0.9996224 X
2 RMS_X 5 1 0.8587955 0.07413965 17.57393 0.7027627 1.0148282 X
3 RMS_X 6 1 0.8456406 0.07430551 17.73171 0.6893611 1.0019202 X
4 RMS_X 1 4 0.6946940 0.07400917 17.45059 0.5388549 0.8505331 X
5 RMS_X 5 4 0.7097861 0.07416780 17.60066 0.5537116 0.8658607 X
6 RMS_X 6 4 0.6966313 0.07447367 17.89277 0.5401007 0.8531619 X
7 RMS_X 1 5 0.5939546 0.07400382 17.44555 0.4381234 0.7497858 X
8 RMS_X 5 5 0.6090467 0.07416782 17.60068 0.4529721 0.7651213 X
9 RMS_X 6 5 0.5958919 0.07447870 17.89761 0.4393537 0.7524300 X
10 RMS_Y 2 1 0.8437679 0.08666179 17.64793 0.6614375 1.0260983 Y
11 RMS_Y 6 1 0.8069276 0.08688169 17.82773 0.6242694 0.9895857 Y
12 RMS_Y 2 4 0.8075712 0.08669749 17.67706 0.6251877 0.9899547 Y
13 RMS_Y 6 4 0.7707309 0.08710140 18.00876 0.5877440 0.9537178 Y
14 RMS_Y 2 5 0.6695575 0.08669761 17.67716 0.4871739 0.8519412 Y
15 RMS_Y 6 5 0.6327172 0.08710762 18.01390 0.4497210 0.8157134 Y
16 RMS_Z 2 1 1.8010325 0.16280504 17.44198 1.4582057 2.1438593 Z
17 RMS_Z 6 1 1.7316638 0.16308976 17.56431 1.3884147 2.0749129 Z
18 RMS_Z 2 4 1.6644975 0.16285206 17.46215 1.3216011 2.0073939 Z
19 RMS_Z 6 4 1.5951288 0.16337503 17.68752 1.2514555 1.9388022 Z
20 RMS_Z 2 5 1.3855632 0.16285235 17.46228 1.0426663 1.7284600 Z
21 RMS_Z 6 5 1.3161945 0.16338325 17.69109 0.9725089 1.6598801 Z
overall_mean overall_se lower_bound upper_bound is_outlier
1 0.8507619 0.002416096 0.8460263 0.8554974 TRUE
2 0.8507619 0.002416096 0.8460263 0.8554974 TRUE
3 0.8507619 0.002416096 0.8460263 0.8554974 TRUE
4 0.7017525 0.002416096 0.6970170 0.7064881 TRUE
5 0.7017525 0.002416096 0.6970170 0.7064881 TRUE
6 0.7017525 0.002416096 0.6970170 0.7064881 TRUE
7 0.6010131 0.002416096 0.5962775 0.6057486 TRUE
8 0.6010131 0.002416096 0.5962775 0.6057486 TRUE
9 0.6010131 0.002416096 0.5962775 0.6057486 TRUE
10 0.8294679 0.005312853 0.8190547 0.8398811 TRUE
11 0.8294679 0.005312853 0.8190547 0.8398811 TRUE
12 0.7932712 0.005312853 0.7828580 0.8036844 TRUE
13 0.7932712 0.005312853 0.7828580 0.8036844 TRUE
14 0.6552575 0.005312853 0.6448443 0.6656707 TRUE
15 0.6552575 0.005312853 0.6448443 0.6656707 TRUE
16 1.7692618 0.009794631 1.7500643 1.7884592 TRUE
17 1.7692618 0.009794631 1.7500643 1.7884592 TRUE
18 1.6327268 0.009794631 1.6135293 1.6519242 TRUE
19 1.6327268 0.009794631 1.6135293 1.6519242 TRUE
20 1.3537924 0.009794631 1.3345949 1.3729899 TRUE
21 1.3537924 0.009794631 1.3345949 1.3729899 TRUE#2.2 12 steps Block 2,4 & 5 - preparation for rms analysis, skip completely to part 3
# --- Step-Wise RMS: Blocks 2, 4, 5 — First 12 Steps ---
plot_stepwise_rms_blocks_245_12steps <- function(tagged_data2) {
step_markers <- c(14, 15, 16, 17)
buffer <- 3
step_data <- tagged_data2 %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_block() %>%
filter(Block %in% c(2, 4, 5)) %>%
mutate(Step = as.numeric(Step)) %>%
group_by(subject, Block, trial) %>%
mutate(step_count = max(Step, na.rm = TRUE)) %>%
ungroup() %>%
filter(step_count %in% c(12, 18)) %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup() %>%
filter(Step <= 12)
step_indices <- step_data %>%
select(subject, Block, trial, row_id, Step)
window_data <- map_dfr(1:nrow(step_indices), function(i) {
step <- step_indices[i, ]
rows <- (step$row_id - buffer):(step$row_id + buffer)
step_data %>%
filter(subject == step$subject,
Block == step$Block,
trial == step$trial,
row_id %in% rows) %>%
mutate(Step = step$Step)
})
step_summary <- window_data %>%
group_by(subject, Block, trial, Step) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = toupper(gsub("rms_", "", Axis)),
Step = factor(Step),
Block = factor(Block),
subject = factor(subject),
trial_id = interaction(subject, trial, drop = TRUE)
) %>%
filter(Step %in% 1:12)
plot_data <- step_summary %>%
group_by(Block, Step, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
se_rms = sd(RMS, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)
axis_labels <- unique(plot_data$Axis)
plots <- map(axis_labels, function(ax) {
axis_data <- filter(plot_data, Axis == ax)
ggplot(axis_data, aes(x = Step, y = mean_rms, fill = Block)) +
geom_col(position = position_dodge(width = 0.8), width = 0.7) +
geom_errorbar(
aes(ymin = mean_rms - se_rms, ymax = mean_rms + se_rms),
position = position_dodge(width = 0.8),
width = 0.3
) +
ylim(0, 3.25) +
labs(
title = paste("Step-wise CoM RMS — Axis", ax),
x = "Step Number",
y = "RMS Acceleration (m/s²)",
fill = "Block"
) +
theme_minimal() +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
text = element_text(size = 12),
plot.title = element_text(face = "bold"),
axis.text.x = element_text(angle = 0, vjust = 0.5)
)
})
names(plots) <- axis_labels
return(list(
plots = plots,
step_summary = step_summary,
plot_data = plot_data,
window_data = window_data
))
}
# --- Run function and extract results ---
result <- plot_stepwise_rms_blocks_245_12steps(tagged_data2)
stepwise_block245_plots <- result$plots
step_summary <- result$step_summary
plot_data <- result$plot_data
window_data <- result$window_data
# --- Print plots ---
for (plot_name in names(stepwise_block245_plots)) {
cat("\n\n==== Axis:", plot_name, "====\n\n")
print(stepwise_block245_plots[[plot_name]])
}
==== Axis: X ====
==== Axis: Y ====
==== Axis: Z ====
# --- RMS LMMs: Blocks 2, 4, 5 --------
print_stepwise_lmm_diagnostics <- function(results_list, dataset_name = "Mixed") {
cat(glue::glue("\n=========== STEPWISE LMM DIAGNOSTICS: {dataset_name} ===========\n"))
for (key in names(results_list)) {
cat("\n---", key, "---\n")
cat("ANOVA:\n")
print(results_list[[key]]$ANOVA)
cat("\nEstimated Marginal Means (Step | Block):\n")
print(results_list[[key]]$EmmeansStepBlock)
cat("\nPairwise Comparisons:\n")
print(results_list[[key]]$Pairwise)
cat("\nFixed Effects:\n")
print(results_list[[key]]$FixedEffects)
cat("\nRandom Effects:\n")
print(results_list[[key]]$RandomEffects)
cat("\nSample Scaled Residuals:\n")
print(head(results_list[[key]]$ScaledResiduals))
cat("\n=============================================================\n")
}
}
rms_lmm_results <- list()
axes <- c("X", "Y", "Z")
for (ax in axes) {
cat(glue("\n\n========== Running models for Axis: {ax} ==========\n\n"))
df_rms <- step_summary %>% filter(Axis == ax)
rms_model <- lmer(RMS ~ Block + Step + (1 | subject) + (1 | trial_id), data = df_rms)
emmeans_step_block <- emmeans(rms_model, ~ Step | Block)
rms_lmm_results[[paste0("RMS_", ax)]] <- list(
Model = rms_model,
ANOVA = anova(rms_model, type = 3),
Pairwise = emmeans(rms_model, pairwise ~ Block)$contrasts,
EmmeansStepBlock = summary(emmeans_step_block),
FixedEffects = fixef(rms_model),
RandomEffects = ranef(rms_model),
ScaledResiduals = resid(rms_model, scaled = TRUE)
)
}
========== Running models for Axis: X ==========
========== Running models for Axis: Y ==========
========== Running models for Axis: Z ==========print_stepwise_lmm_diagnostics(rms_lmm_results, dataset_name = "12-Step RMS Acceleration")=========== STEPWISE LMM DIAGNOSTICS: 12-Step RMS Acceleration ===========
--- RMS_X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 45.310 22.6551 2 19014 184.3048 < 2.2e-16 ***
Step 13.019 1.1835 11 18552 9.6284 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 2:
Step emmean SE df lower.CL upper.CL
1 0.718 0.0617 17.6 0.588 0.848
2 0.731 0.0619 17.8 0.601 0.861
3 0.752 0.0621 18.1 0.621 0.882
4 0.724 0.0617 17.6 0.594 0.854
5 0.731 0.0619 17.8 0.601 0.861
6 0.719 0.0621 18.1 0.589 0.850
7 0.707 0.0619 17.8 0.577 0.837
8 0.697 0.0619 17.8 0.567 0.827
9 0.686 0.0619 17.8 0.556 0.817
10 0.675 0.0619 17.8 0.545 0.805
11 0.670 0.0619 17.8 0.540 0.800
12 0.661 0.0619 17.8 0.531 0.791
Block = 4:
Step emmean SE df lower.CL upper.CL
1 0.705 0.0617 17.6 0.575 0.835
2 0.718 0.0618 17.8 0.588 0.848
3 0.739 0.0622 18.2 0.608 0.869
4 0.711 0.0617 17.6 0.581 0.841
5 0.718 0.0618 17.8 0.588 0.848
6 0.706 0.0622 18.2 0.576 0.837
7 0.694 0.0618 17.8 0.564 0.824
8 0.684 0.0618 17.8 0.554 0.814
9 0.673 0.0618 17.8 0.543 0.804
10 0.662 0.0618 17.8 0.532 0.792
11 0.657 0.0618 17.8 0.527 0.787
12 0.648 0.0618 17.8 0.518 0.778
Block = 5:
Step emmean SE df lower.CL upper.CL
1 0.603 0.0617 17.6 0.473 0.733
2 0.616 0.0618 17.8 0.486 0.746
3 0.637 0.0622 18.2 0.506 0.767
4 0.609 0.0617 17.6 0.479 0.739
5 0.616 0.0618 17.8 0.486 0.746
6 0.604 0.0622 18.2 0.474 0.735
7 0.592 0.0618 17.8 0.462 0.722
8 0.582 0.0618 17.8 0.452 0.712
9 0.571 0.0618 17.8 0.441 0.702
10 0.560 0.0618 17.8 0.430 0.690
11 0.555 0.0618 17.8 0.425 0.685
12 0.546 0.0618 17.8 0.416 0.676
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block2 - Block4 0.013 0.00668 19078 1.948 0.1255
Block2 - Block5 0.115 0.00667 19086 17.239 <.0001
Block4 - Block5 0.102 0.00648 18923 15.745 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
0.717758146 -0.013007771 -0.115014938 0.012872078 0.033802008 0.006520064
Step5 Step6 Step7 Step8 Step9 Step10
0.012913655 0.001603176 -0.011128241 -0.020645452 -0.031261518 -0.042552604
Step11 Step12
-0.048039693 -0.056437266
Random Effects:
$trial_id
(Intercept)
3.1 -2.468751e-01
4.1 1.024657e-01
5.1 -5.584796e-02
7.1 4.183326e-02
8.1 -1.957584e-01
10.1 -1.342055e-01
11.1 -5.386706e-01
13.1 8.050233e-02
14.1 -2.225802e-01
15.1 1.174188e-01
16.1 -2.255247e-02
17.1 -1.554903e-01
18.1 -1.131007e-01
19.1 1.127393e-02
20.1 3.408906e-02
22.1 6.862464e-02
23.1 -5.283726e-03
2.2 3.489156e-02
3.2 -1.856873e-01
4.2 1.379374e-01
5.2 -5.700111e-02
7.2 -1.510064e-01
8.2 -2.245720e-01
10.2 3.945719e-01
11.2 -6.524696e-03
13.2 6.150733e-02
14.2 8.083234e-02
15.2 5.340765e-01
16.2 -6.176581e-02
17.2 -1.374549e-01
19.2 2.833108e-02
20.2 2.763554e-02
22.2 1.151475e-01
23.2 1.677737e+00
2.3 -1.533058e-02
3.3 1.850398e-02
4.3 -2.607371e-02
5.3 -5.660524e-02
7.3 5.952432e-02
10.3 4.831796e-01
11.3 -3.508192e-01
13.3 1.230211e-01
14.3 -1.119444e-01
15.3 5.483077e-02
16.3 3.914223e-02
17.3 -6.722175e-02
18.3 -1.005017e-01
19.3 -3.660073e-02
20.3 9.010507e-02
22.3 -2.192142e-02
23.3 2.060028e-01
2.4 -3.436818e-01
3.4 -1.103278e-01
4.4 -6.480357e-02
5.4 -6.830617e-02
7.4 -3.419831e-02
8.4 -6.923761e-02
10.4 1.011349e-03
11.4 -4.732885e-01
13.4 -9.447929e-03
14.4 5.867083e-02
15.4 -8.483914e-02
16.4 -5.853758e-02
17.4 -9.899702e-03
18.4 -1.338653e-01
19.4 -4.154879e-02
20.4 -7.973134e-02
22.4 1.878542e-02
23.4 1.146561e-01
2.5 -3.194843e-02
3.5 -4.978143e-02
4.5 5.156155e-02
5.5 -1.883256e-02
7.5 1.729399e-02
8.5 -1.222553e-01
10.5 8.885492e-02
11.5 -1.971838e-01
13.5 2.489148e-01
14.5 1.598379e-01
15.5 2.266137e-01
16.5 -8.552455e-02
17.5 -3.154001e-02
18.5 -8.367965e-02
19.5 -6.826474e-02
20.5 -3.061010e-02
22.5 5.189887e-02
23.5 -7.007147e-02
2.6 -1.379120e-01
3.6 5.987377e-02
4.6 -5.182350e-02
5.6 -2.173391e-02
7.6 1.780177e-01
8.6 -1.398396e-02
10.6 5.580913e-01
11.6 -1.674128e-02
13.6 5.945830e-02
14.6 1.224238e-01
15.6 -7.516571e-02
16.6 -4.689234e-02
17.6 -1.572497e-01
18.6 5.293448e-02
19.6 8.126654e-03
20.6 -1.998828e-02
22.6 4.858251e-02
23.6 4.483005e-01
2.7 -1.877337e-01
3.7 2.310604e-01
4.7 -1.880636e-02
5.7 -3.208055e-03
7.7 1.723597e-01
8.7 -5.780523e-02
10.7 -4.202827e-02
11.7 9.526421e-02
13.7 -4.070819e-02
14.7 7.420249e-02
15.7 -1.111688e-02
16.7 4.942945e-02
17.7 -9.158214e-02
18.7 -9.276125e-02
19.7 -3.843028e-02
20.7 6.647350e-03
22.7 -1.009542e-01
23.7 -7.850091e-02
2.8 -3.307173e-01
3.8 4.230682e-02
4.8 4.140049e-02
5.8 -1.608120e-02
7.8 -4.717953e-02
8.8 -3.823258e-02
10.8 8.234224e-02
11.8 -1.451589e-01
13.8 -2.391574e-02
14.8 2.258456e-01
15.8 -8.099153e-02
16.8 2.747550e-02
17.8 -1.237267e-01
18.8 -6.748546e-02
19.8 -2.506003e-03
20.8 -2.602943e-02
22.8 -3.257780e-02
23.8 -1.050611e-01
2.9 1.340269e-02
3.9 5.537559e-02
4.9 3.075692e-03
5.9 5.052772e-03
7.9 -2.631606e-02
8.9 -2.204693e-01
10.9 4.318613e-01
11.9 -3.218579e-01
13.9 -1.565215e-01
14.9 -7.019877e-02
15.9 1.556721e-04
16.9 -1.349004e-01
17.9 8.649978e-02
18.9 -1.364388e-01
19.9 4.933070e-02
20.9 -7.951358e-02
22.9 -4.223303e-03
23.9 -9.860677e-02
2.10 1.596400e-01
3.10 -9.436775e-02
4.10 5.863676e-02
5.10 -3.247379e-02
7.10 -1.304889e-01
8.10 -2.238137e-01
10.10 3.588058e-01
11.10 8.583326e-01
13.10 -1.114967e-02
14.10 7.959950e-02
15.10 -1.488175e-01
16.10 -9.291293e-02
17.10 -4.093862e-02
18.10 -3.547807e-02
19.10 -1.334951e-02
20.10 -1.256909e-01
22.10 1.378440e-02
23.10 -2.167830e-01
2.11 3.096896e-02
3.11 -9.908810e-02
4.11 -3.091801e-02
5.11 -3.552153e-02
7.11 -1.394151e-01
8.11 -1.190020e-01
10.11 2.905222e-01
11.11 -1.771284e-01
13.11 -1.048879e-01
14.11 -8.460636e-02
15.11 -6.736351e-02
16.11 1.188831e-01
17.11 -3.047865e-02
18.11 -1.162951e-01
19.11 -8.498870e-02
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11.46 -2.382881e-01
13.46 -3.392106e-01
14.46 -3.937027e-01
15.46 -2.032275e-01
16.46 -3.829473e-01
17.46 -3.137307e-01
18.46 -3.665283e-01
19.46 1.328775e-01
20.46 -4.687148e-02
22.46 -2.022548e-01
23.46 -4.400984e-01
2.47 -4.729630e-01
3.47 -4.543597e-01
4.47 -4.373815e-02
5.47 -2.057359e-01
7.47 -1.462395e-01
8.47 -7.750444e-01
10.47 -1.015136e+00
11.47 -5.507336e-01
13.47 -2.019484e-01
14.47 -3.922085e-01
15.47 -3.012417e-01
16.47 -4.163859e-01
17.47 -2.003197e-01
18.47 -3.900173e-01
19.47 -1.601447e-01
20.47 -1.008867e-01
22.47 -3.244284e-01
2.48 -4.269041e-01
$subject
(Intercept)
2 0.11242328
3 0.02714702
4 -0.21034139
5 -0.31203683
7 -0.11854082
8 0.29232920
10 0.71564423
11 0.39007704
13 -0.20693336
14 0.04124467
15 0.00517220
16 -0.04066873
17 -0.18779951
18 -0.04031469
19 -0.21237556
20 -0.21670502
22 -0.06996322
23 0.03164148
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.34841504 -0.35685139 -0.41824705 -0.15532180 -0.15324890 0.05888468
=============================================================
--- RMS_Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 64.280 32.140 2 18687 229.60 < 2.2e-16 ***
Step 28.456 2.587 11 18524 18.48 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 2:
Step emmean SE df lower.CL upper.CL
1 0.794 0.0698 17.6 0.647 0.941
2 0.800 0.0700 17.7 0.653 0.948
3 0.795 0.0702 18.0 0.647 0.942
4 0.788 0.0698 17.6 0.641 0.935
5 0.782 0.0700 17.7 0.634 0.929
6 0.755 0.0702 18.0 0.607 0.902
7 0.753 0.0700 17.7 0.606 0.900
8 0.744 0.0700 17.7 0.597 0.891
9 0.724 0.0700 17.7 0.576 0.871
10 0.710 0.0700 17.7 0.563 0.857
11 0.714 0.0700 17.7 0.567 0.861
12 0.681 0.0700 17.7 0.533 0.828
Block = 4:
Step emmean SE df lower.CL upper.CL
1 0.801 0.0698 17.5 0.654 0.948
2 0.808 0.0699 17.7 0.661 0.955
3 0.802 0.0703 18.0 0.654 0.950
4 0.795 0.0698 17.5 0.648 0.942
5 0.789 0.0699 17.7 0.642 0.936
6 0.762 0.0703 18.0 0.614 0.910
7 0.760 0.0699 17.7 0.613 0.907
8 0.751 0.0699 17.7 0.604 0.898
9 0.731 0.0699 17.7 0.584 0.878
10 0.717 0.0699 17.7 0.570 0.864
11 0.721 0.0699 17.7 0.574 0.868
12 0.688 0.0699 17.7 0.541 0.835
Block = 5:
Step emmean SE df lower.CL upper.CL
1 0.668 0.0698 17.5 0.521 0.815
2 0.674 0.0699 17.7 0.527 0.821
3 0.669 0.0703 18.0 0.521 0.816
4 0.661 0.0698 17.5 0.515 0.808
5 0.655 0.0699 17.7 0.508 0.802
6 0.629 0.0703 18.0 0.481 0.776
7 0.627 0.0699 17.7 0.480 0.774
8 0.618 0.0699 17.7 0.471 0.765
9 0.597 0.0699 17.7 0.450 0.745
10 0.584 0.0699 17.7 0.437 0.731
11 0.588 0.0699 17.7 0.441 0.735
12 0.554 0.0699 17.7 0.407 0.701
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block2 - Block4 -0.00726 0.00717 18721 -1.012 0.5695
Block2 - Block5 0.12616 0.00717 18729 17.601 <.0001
Block4 - Block5 0.13342 0.00694 18668 19.211 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3
0.7939634450 0.0072564416 -0.1261636600 0.0064892210 0.0008967414
Step4 Step5 Step6 Step7 Step8
-0.0064009251 -0.0124304230 -0.0392267387 -0.0409649191 -0.0499576135
Step9 Step10 Step11 Step12
-0.0703637070 -0.0840947760 -0.0799343941 -0.1134563308
Random Effects:
$trial_id
(Intercept)
3.1 -0.1661429660
4.1 -0.0364579522
5.1 -0.0333763718
7.1 0.1122530131
8.1 0.0192755731
10.1 0.1030479284
11.1 -0.6560372329
13.1 -0.1155720613
14.1 -0.1880989702
15.1 -0.0678287883
16.1 -0.1799599615
17.1 -0.1468943874
18.1 0.1639976312
19.1 -0.0077345874
20.1 -0.0757378811
22.1 0.0163223513
23.1 -0.2520055089
2.2 -0.1224673094
3.2 -0.2576678591
4.2 -0.0054664698
5.2 0.0358467610
7.2 -0.1523210320
8.2 -0.1882652758
10.2 0.1054131813
11.2 -0.4875127096
13.2 0.1031405553
14.2 0.3367014721
15.2 0.0925696142
16.2 0.0478492249
17.2 -0.1491546834
19.2 0.1838262122
20.2 0.2891196116
22.2 0.2327946092
23.2 11.5276076575
2.3 -0.1590897616
3.3 -0.1530492720
4.3 0.0500441347
5.3 0.1213521939
7.3 -0.1756057268
10.3 0.2142544899
11.3 -0.0307193751
13.3 -0.0944257940
14.3 -0.1253276870
15.3 -0.1245974203
16.3 0.1774193316
17.3 -0.0946362407
18.3 -0.0904714795
19.3 -0.1289862154
20.3 0.0863451639
22.3 0.0452258541
23.3 -0.1180636160
2.4 -0.2915940422
3.4 0.0441655492
4.4 -0.0653550097
5.4 0.0448411420
7.4 0.1036793174
8.4 0.0527328564
10.4 0.0290673049
11.4 -0.6415611575
13.4 -0.0522005070
14.4 0.1167890519
15.4 -0.1583601417
16.4 -0.1932795585
17.4 -0.2026138852
18.4 -0.0284229164
19.4 -0.0565312121
20.4 -0.0169683063
22.4 -0.0376805486
23.4 -0.2511104006
2.5 -0.0527986928
3.5 -0.1134811319
4.5 -0.1253991459
5.5 -0.0868298986
7.5 -0.0732245004
8.5 -0.1936561870
10.5 0.5507449746
11.5 -0.1770470964
13.5 0.1054381212
14.5 0.2021565810
15.5 0.1479345724
16.5 -0.0486161359
17.5 0.0495088233
18.5 -0.0789990719
19.5 -0.1969295646
20.5 0.1193221449
22.5 -0.0211438915
23.5 -0.4538973381
2.6 -0.0687048297
3.6 0.0509532445
4.6 0.1375308945
5.6 0.0232808317
7.6 0.1142763098
8.6 -0.0476133338
10.6 0.2707773530
11.6 0.1531986366
13.6 0.0043345023
14.6 0.1247763077
15.6 -0.1241090821
16.6 -0.0881810341
17.6 -0.1703335043
18.6 0.0510171742
19.6 -0.1015774925
20.6 0.0536238651
22.6 -0.0356141776
23.6 -0.2412143894
2.7 -0.2085321825
3.7 -0.1212004236
4.7 -0.1111667150
5.7 -0.0186650210
7.7 -0.0256645839
8.7 -0.1813201231
10.7 0.3924828509
11.7 0.3867049852
13.7 0.0550793469
14.7 0.2039795194
15.7 -0.0993556026
16.7 -0.0140071635
17.7 0.0626115386
18.7 0.0153298801
19.7 -0.1086082568
20.7 -0.0787419320
22.7 -0.0214532009
23.7 -0.0959819029
2.8 -0.1307460608
3.8 -0.0713213119
4.8 -0.0717829245
5.8 -0.1021190865
7.8 0.0336284833
8.8 -0.2155897489
10.8 0.0327288064
11.8 0.1680556505
13.8 -0.0668353622
14.8 0.1345188914
15.8 -0.0482592767
16.8 -0.1348349169
17.8 -0.1406208131
18.8 -0.0372114043
19.8 -0.0953249978
20.8 -0.0454507255
22.8 -0.1166422268
23.8 -0.4097487988
2.9 0.0330365871
3.9 0.0953719411
4.9 -0.0564547269
5.9 0.0449424050
7.9 -0.0245459971
8.9 -0.1216789420
10.9 0.4141209336
11.9 -0.3264493837
13.9 -0.1898291239
14.9 0.0636564886
15.9 -0.0035666786
16.9 -0.0997360288
17.9 -0.0206893059
18.9 -0.1648108194
19.9 -0.0844135533
20.9 -0.0113913652
22.9 -0.0812783357
23.9 -0.2904122333
2.10 -0.1522415501
3.10 0.1544918916
4.10 0.1343272890
5.10 -0.0182072877
7.10 -0.0356395380
8.10 -0.2004403557
10.10 0.6005109849
11.10 0.0137441577
13.10 0.0300893733
14.10 0.1100926530
15.10 -0.1244779353
16.10 -0.1483840411
17.10 0.0451507778
18.10 0.0656568655
19.10 0.0107891663
20.10 -0.0725021142
22.10 -0.0371623791
23.10 -0.4301097254
2.11 0.1503848955
3.11 0.3119306708
4.11 -0.0607835461
5.11 0.0373230287
7.11 0.0734471688
8.11 0.0233486592
10.11 0.0899437741
11.11 -0.2538808224
13.11 -0.0821334090
14.11 0.0104534198
15.11 0.0120325060
16.11 -0.0721634079
17.11 -0.0224595992
18.11 0.1051662289
19.11 -0.0676114966
20.11 0.0690234734
22.11 0.0073097134
23.11 -0.2589676525
2.12 -0.0469942605
3.12 0.2768982621
4.12 -0.0460718178
5.12 -0.0085225999
7.12 -0.1429020821
8.12 0.0688466424
10.12 0.2419271919
11.12 -0.3970757110
13.12 -0.0764628202
14.12 -0.3395367330
15.12 -0.0252811669
16.12 -0.1244123780
17.12 -0.0907009166
18.12 -0.1398026582
19.12 0.1666572989
20.12 -0.1163041406
22.12 -0.0887463042
23.12 -0.4669584980
2.13 -0.1678294814
3.13 -0.1997814758
4.13 0.0604814612
5.13 -0.0656251557
7.13 -0.0965675563
8.13 -0.0506935110
10.13 0.1379644179
11.13 0.0705220353
13.13 0.0004625212
14.13 0.0290603543
15.13 -0.1772669470
16.13 -0.1549402359
17.13 -0.0561368190
18.13 -0.0484990081
19.13 -0.0711290201
20.13 0.0421671640
22.13 0.1539917585
23.13 -0.3688157201
2.14 0.0230191367
3.14 -0.0138139676
4.14 -0.1741868926
5.14 -0.1038060210
7.14 -0.1636900796
8.14 0.2836081454
10.14 0.1913390504
11.14 -0.4801912646
13.14 -0.0790235878
14.14 -0.1762314312
15.14 0.0945272882
16.14 -0.0960809386
17.14 -0.0591734740
18.14 0.1315371347
19.14 0.0210735665
20.14 -0.1237038264
22.14 -0.0470460635
23.14 -0.4541119144
2.15 0.0203243479
3.15 0.0573615286
4.15 -0.1371212309
5.15 0.0430677250
7.15 -0.1177938057
8.15 0.0197124954
10.15 0.5818091803
11.15 -0.1451643355
13.15 -0.0519750662
14.15 -0.0167403093
15.15 -0.0387302446
16.15 0.1010526121
17.15 0.0434550298
18.15 -0.0197430538
19.15 -0.1364947202
20.15 -0.0444373732
22.15 -0.0784212506
23.15 -0.0800613835
2.16 -0.1209974158
3.16 0.0488388808
4.16 -0.1006043051
5.16 0.0619589080
7.16 -0.0956786532
8.16 0.0750975484
10.16 0.1300766720
11.16 0.0673349066
13.16 -0.1387672534
14.16 0.0975355778
15.16 0.0441668110
16.16 -0.0364028532
17.16 -0.0745523818
18.16 0.0858070775
19.16 -0.0481256705
20.16 -0.1458234470
22.16 -0.0424113637
23.16 -0.4177781232
2.17 0.1118454415
3.17 0.1208009731
4.17 -0.0290069072
5.17 -0.1273210419
7.17 -0.1999929566
8.17 0.4603101422
10.17 0.7235464314
11.17 -0.4275221598
13.17 -0.0536878856
14.17 0.0452629766
15.17 0.0173307969
16.17 0.0322814019
17.17 -0.0509279124
18.17 0.0410370712
19.17 -0.0256844439
20.17 0.0007366018
22.17 0.0069360896
23.17 -0.2080958096
2.18 0.1320760459
3.18 0.3810319480
4.18 -0.0323005252
5.18 -0.0202760908
7.18 0.0806185641
8.18 -0.0042187743
10.18 0.3920810257
11.18 -0.5373649632
13.18 -0.0520889333
14.18 -0.2525548517
15.18 -0.0163274007
16.18 -0.1276485873
17.18 -0.1348186292
18.18 0.2039938388
19.18 -0.0910215504
20.18 0.0438124567
22.18 0.0543566654
23.18 -0.2083008282
2.19 0.0553752298
3.19 -0.0462798070
4.19 -0.0705063972
5.19 -0.0793909308
7.19 0.1130836895
8.19 -0.2447656243
10.19 0.2608209678
11.19 0.6131283528
13.19 0.0385910642
14.19 0.0491089060
15.19 0.0251309516
16.19 -0.1631644055
17.19 -0.0783269658
18.19 -0.1865405554
19.19 0.0164723467
20.19 -0.0424420487
22.19 -0.1277994260
23.19 -0.4473808901
2.20 0.1840388060
3.20 0.0266083166
4.20 -0.0283580759
5.20 0.0252839423
7.20 0.0611708926
8.20 -0.2811770559
10.20 0.7392522519
11.20 0.2810649154
13.20 -0.0371962379
14.20 -0.1170292250
15.20 -0.0359905230
16.20 -0.1950891296
17.20 0.0984112370
18.20 -0.0890849764
19.20 0.0396799793
20.20 -0.0894549635
22.20 -0.0401422580
23.20 -0.2118234862
2.21 0.1888614358
3.21 0.0434320987
4.21 -0.0688310478
5.21 -0.0346845577
7.21 -0.0038689023
8.21 0.0982838860
10.21 0.7393748619
11.21 -0.4633275399
13.21 -0.0672719808
14.21 0.0395855159
15.21 0.0983336562
16.21 -0.0534762852
17.21 -0.1422806247
18.21 -0.0403224229
19.21 -0.1052922402
20.21 -0.1145681749
22.21 -0.0079879866
23.21 -0.2716362230
2.22 0.4727910016
3.22 0.2837332162
4.22 0.0805892365
5.22 0.0299765480
7.22 -0.0876520982
8.22 0.5703466547
10.22 0.3235002344
11.22 -0.4058693006
13.22 0.0286681308
14.22 0.0724667214
15.22 -0.0882695510
16.22 0.0467110027
17.22 0.0499132775
18.22 -0.0194773996
19.22 -0.0477067122
20.22 -0.0020030118
22.22 0.0613145684
23.22 -0.4631641485
2.23 0.4017997930
3.23 0.2824187937
4.23 -0.0429619925
5.23 0.0029979164
7.23 -0.0180336967
8.23 0.3775806262
10.23 0.8614192275
11.23 0.5074335064
13.23 -0.0554916341
14.23 -0.0834011921
15.23 0.1720763778
16.23 0.0774185364
17.23 0.0451516259
18.23 -0.0334526766
19.23 -0.0784360048
20.23 -0.0028843094
22.23 -0.0077213258
23.23 -0.0541414486
2.24 -0.0446495481
3.24 0.0430192163
4.24 -0.0386007601
5.24 0.0766645839
7.24 -0.1499723579
8.24 0.6272168104
10.24 0.2544441537
11.24 0.4128318931
13.24 -0.0330587846
14.24 -0.1581050961
15.24 -0.1967574146
16.24 -0.0321706908
17.24 0.0635255724
18.24 0.0026301378
19.24 0.0187248533
20.24 -0.0212766965
22.24 -0.0114347551
23.24 -0.1435638086
2.25 0.3117465325
3.25 0.4122278117
4.25 -0.0846694700
5.25 -0.0539744271
7.25 -0.0903525972
8.25 -0.0838199145
10.25 0.2350447603
11.25 0.7526817760
13.25 0.0735428309
14.25 -0.0627215877
15.25 -0.0474400990
16.25 0.0719987511
17.25 0.0797164187
18.25 0.1453806823
19.25 -0.1234666612
20.25 -0.1367401059
22.25 -0.0096488966
23.25 -0.0251985589
2.26 0.2050125268
3.26 0.0405968425
4.26 -0.0123646331
5.26 -0.0331543109
7.26 -0.1127189944
8.26 0.6643804003
10.26 0.7671975035
11.26 0.5554067853
13.26 0.0535992772
14.26 -0.0065032947
15.26 0.0557119475
16.26 0.1418498766
17.26 -0.0736041101
18.26 -0.0750398448
19.26 -0.0090985488
20.26 0.0588972842
22.26 -0.1022011063
23.26 -0.3673849818
2.27 0.1678815182
3.27 -0.0061176276
4.27 -0.1703693009
5.27 -0.0093598794
7.27 -0.1488512245
8.27 0.1892999630
10.27 0.3057587167
11.27 0.8879670686
13.27 0.1712483529
14.27 -0.1102102040
15.27 -0.0761038178
16.27 0.0903603308
17.27 -0.0923411283
18.27 0.0117624102
19.27 0.0193558470
20.27 -0.0521109661
22.27 -0.0237961522
23.27 -0.0611246168
2.28 0.1361830587
3.28 -0.1694444375
4.28 -0.1055629359
5.28 -0.0280583018
7.28 -0.0912366980
8.28 0.8044744981
10.28 -0.3493437160
11.28 -0.2888225326
13.28 0.1251131975
14.28 -0.0849481689
15.28 0.0672520139
16.28 0.1358218080
17.28 -0.0434045344
18.28 -0.2531197656
19.28 -0.0782873593
20.28 -0.0690103079
22.28 0.0273932362
23.28 0.0246571477
2.29 0.0906457863
3.29 0.4676439185
4.29 -0.0877755311
5.29 0.0038776091
7.29 -0.0096851687
8.29 0.2128688951
10.29 0.5029383562
11.29 -0.5474503926
13.29 0.2126836507
14.29 0.1188777706
15.29 -0.0013980224
16.29 0.0433869886
17.29 0.1473758780
18.29 -0.0941398370
19.29 0.1424268912
20.29 -0.0881325726
22.29 0.1077764787
23.29 0.0104872667
2.30 0.3417142646
3.30 0.0346593340
4.30 0.0637897466
5.30 0.0555392711
7.30 0.0969081931
8.30 0.5087087318
10.30 -0.0709161498
11.30 0.3752067949
13.30 0.1818276968
14.30 0.0318105110
15.30 -0.0306519710
16.30 0.2062958219
17.30 0.1343303136
18.30 -0.1456567504
19.30 -0.0088336425
20.30 -0.0950610004
22.30 -0.1597303761
23.30 0.3040330371
2.31 0.5626691731
3.31 0.2151697449
4.31 0.3098606664
5.31 0.0812267729
7.31 0.0117434317
8.31 0.5663340410
10.31 -0.1537717608
11.31 0.2500099985
13.31 0.3055601229
14.31 0.0647287406
15.31 -0.1858443330
16.31 0.3933839104
17.31 0.4640668419
18.31 0.1106026081
19.31 -0.0802695899
20.31 -0.0961792618
22.31 0.0243724203
23.31 0.1173455002
2.32 0.4214459313
3.32 0.3206807921
4.32 0.2781924370
5.32 0.0852240635
7.32 0.4044107572
8.32 0.5030796733
10.32 0.5385871309
11.32 2.4980560892
13.32 0.0732296258
14.32 -0.2559324727
15.32 0.2406417797
16.32 0.1744789828
17.32 0.2839094416
18.32 -0.0057261401
19.32 -0.0343643501
20.32 -0.1470672302
22.32 0.0299292423
23.32 0.2312333006
2.33 -0.1043500154
3.33 0.0506426786
4.33 -0.0691806613
5.33 0.0859985861
7.33 0.2723522891
8.33 0.1461270081
10.33 -0.1045250466
11.33 1.6140026139
13.33 0.1076859384
14.33 -0.1110816734
15.33 0.1253927657
16.33 0.6227810343
17.33 0.0856890071
18.33 -0.0718540576
19.33 -0.0187327288
20.33 0.0014129336
22.33 -0.1135958011
23.33 -0.0327723931
2.34 0.0682348718
3.34 0.2918522381
4.34 -0.1482165421
5.34 -0.0738946719
7.34 0.0205036897
8.34 0.2505164795
10.34 0.3228068124
11.34 0.8547778835
13.34 0.7596435928
14.34 -0.1733902811
15.34 0.1306253552
16.34 0.3105980594
17.34 0.1113683882
18.34 -0.1211975237
19.34 -0.0035538898
20.34 0.1006920472
22.34 0.0739214587
23.34 -0.3190995319
2.35 0.3418873485
3.35 -0.1334741258
4.35 -0.1350763183
5.35 -0.0904029037
7.35 0.0264103369
8.35 -0.1949431784
10.35 -0.1855162972
11.35 1.0318591366
13.35 0.3003152633
14.35 0.3715642627
15.35 0.4477975304
16.35 0.2139885446
17.35 0.2379387031
18.35 0.2251444162
19.35 0.0410654645
20.35 -0.0248168942
22.35 0.0423153420
23.35 0.1036944844
2.36 0.2345464216
3.36 0.1013345285
4.36 0.0455357995
5.36 -0.0412473694
7.36 0.3038906298
8.36 0.7390707951
10.36 -0.5913341711
11.36 0.0410405427
13.36 0.2294038348
14.36 0.2089174568
15.36 0.0762749553
16.36 0.3666811547
17.36 0.2326886187
18.36 -0.0278344989
19.36 0.1289289209
20.36 0.0284505439
22.36 0.1048210536
23.36 0.2178686756
2.37 0.3498897694
3.37 0.1293527797
4.37 0.1115277732
5.37 -0.0718396419
7.37 0.1212949456
8.37 -0.0590912107
10.37 -0.6765709107
11.37 -0.1782920333
13.37 0.0938693246
14.37 0.2362957490
15.37 -0.0581103251
16.37 0.0421701110
17.37 0.2531056094
18.37 0.5224653215
19.37 0.0036428566
20.37 0.0319192617
22.37 -0.0047492357
23.37 -0.1006370084
2.38 0.1498917895
3.38 -0.0617147425
4.38 -0.0754354793
5.38 -0.1568617042
7.38 0.0536732229
8.38 0.0430440859
10.38 -0.7881106345
11.38 -0.1903007773
13.38 0.0255144049
14.38 0.2418831704
15.38 0.2010475538
16.38 0.0858332865
17.38 0.0100317063
18.38 0.2366548718
19.38 0.0401669140
20.38 -0.2362054094
22.38 -0.0746680198
23.38 -0.1958428561
2.39 -0.0793728193
3.39 -0.2714268054
4.39 0.1406815521
5.39 -0.0790383586
7.39 -0.0521774630
8.39 -0.4011240432
10.39 -0.3475651825
11.39 -0.2347367108
13.39 -0.1146399687
14.39 0.3649832231
15.39 0.0540448734
16.39 -0.2302630996
17.39 0.1364814160
18.39 0.0265827718
19.39 0.0472021246
20.39 0.1074893076
22.39 0.2007477003
23.39 -0.6319175270
2.40 0.5678576186
3.40 -0.1420357187
4.40 0.0841951178
5.40 -0.0819116689
7.40 0.1865285429
8.40 0.1300002923
10.40 -0.1735003567
11.40 -0.5602583694
13.40 -0.3749146544
14.40 0.1555290919
15.40 -0.0481897494
16.40 0.1599466932
17.40 -0.0005244040
18.40 0.2317932490
19.40 -0.0548990969
20.40 0.1753484641
22.40 0.0230315207
23.40 -0.4843013158
2.41 0.0775345606
3.41 -0.0263722425
4.41 0.0330227888
5.41 -0.0273855139
7.41 -0.0582294042
8.41 -0.6138640128
10.41 -1.1599908455
11.41 -0.4163625582
13.41 -0.0752392404
14.41 -0.0741489802
15.41 -0.1109619105
16.41 0.0123611822
17.41 0.1596065033
18.41 0.0756128517
19.41 0.2621408298
20.41 -0.0604270099
22.41 0.2051919095
23.41 -0.4477558850
2.42 0.1381965591
3.42 0.0394652426
4.42 0.1868771760
5.42 0.1807227218
7.42 0.1463242429
8.42 -0.2593890587
10.42 -0.5248385078
11.42 -0.6166013929
13.42 -0.3909777663
14.42 0.0290575418
15.42 -0.2285423183
16.42 0.2872181383
17.42 -0.1602392279
18.42 0.3268480020
19.42 0.1764433456
20.42 -0.0267056643
22.42 0.1947357485
23.42 -0.1868578269
2.43 -0.0953254074
3.43 0.0425299359
4.43 -0.1362689233
5.43 0.0518769313
7.43 -0.0935050115
8.43 -0.8697646400
10.43 -0.6228571178
11.43 -0.1441461692
13.43 -0.3761847679
14.43 0.0666094792
15.43 -0.1929604348
16.43 -0.1923122046
17.43 -0.2394873222
18.43 -0.0195151857
19.43 -0.0198176205
20.43 0.0520995163
22.43 -0.1268048781
23.43 -0.4124376285
2.44 -0.6669598717
3.44 -0.1841126664
4.44 -0.0534531947
5.44 -0.1428007049
7.44 0.2667193719
8.44 -0.6593885036
10.44 -0.6719507303
11.44 -0.4506972008
13.44 -0.3390133430
14.44 0.0582724816
15.44 0.0192862189
16.44 -0.2078902750
17.44 -0.0659460316
18.44 0.0750853632
19.44 0.0540047034
20.44 0.0567561250
22.44 -0.1556325424
23.44 -0.4786718380
2.45 -0.5051183417
3.45 -0.3142923310
4.45 -0.1146971130
5.45 -0.1264272192
7.45 -0.3441753309
8.45 -0.3399491795
10.45 -0.9513584364
11.45 -0.5353512781
13.45 -0.1344754568
14.45 -0.3921403570
15.45 -0.0947532955
16.45 -0.2889738574
17.45 -0.1253209555
18.45 -0.1520474421
19.45 -0.0058345987
20.45 0.0249003156
22.45 -0.2293324962
23.45 -0.7279700905
2.46 -0.5818680458
3.46 -0.5151623263
4.46 0.0647929976
5.46 -0.1314973119
7.46 -0.2792936206
8.46 -0.2902012973
10.46 -0.6631275970
11.46 -0.3184590969
13.46 -0.4224829646
14.46 -0.4899821159
15.46 -0.0107394705
16.46 -0.4510616047
17.46 -0.4335956993
18.46 -0.5253833423
19.46 -0.1137530543
20.46 0.0460919965
22.46 -0.3181268747
23.46 -0.7427908702
2.47 -0.6457177603
3.47 -0.7628743793
4.47 -0.0340158402
5.47 -0.1898112495
7.47 -0.2098882367
8.47 -0.8390808006
10.47 -1.1632890883
11.47 -0.6719263611
13.47 -0.2779226663
14.47 -0.4290194763
15.47 -0.0793994466
16.47 -0.5497717960
17.47 -0.3348278282
18.47 -0.4212055913
19.47 -0.2360824923
20.47 -0.0803406267
22.47 -0.3461443872
2.48 -0.7722286167
$subject
(Intercept)
2 0.30529001
3 0.21122891
4 -0.24754892
5 -0.31297207
7 -0.14923126
8 0.36259191
10 0.61449218
11 0.31542831
13 -0.22295393
14 -0.02068731
15 -0.12330032
16 -0.01356412
17 -0.13571958
18 -0.01174790
19 -0.28696396
20 -0.24132776
22 -0.28319581
23 0.24018163
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.8866836 -0.7231567 -0.8338333 -0.8955007 -1.1491418 -1.0943523
=============================================================
--- RMS_Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 241.66 120.832 2 18878 272.113 < 2.2e-16 ***
Step 99.16 9.015 11 18547 20.301 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 2:
Step emmean SE df lower.CL upper.CL
1 1.61 0.141 17.4 1.316 1.91
2 1.64 0.141 17.6 1.340 1.93
3 1.64 0.141 17.8 1.341 1.94
4 1.60 0.141 17.4 1.306 1.90
5 1.60 0.141 17.6 1.306 1.90
6 1.56 0.141 17.8 1.267 1.86
7 1.55 0.141 17.6 1.251 1.84
8 1.53 0.141 17.6 1.234 1.83
9 1.48 0.141 17.6 1.187 1.78
10 1.46 0.141 17.6 1.165 1.76
11 1.47 0.141 17.6 1.176 1.77
12 1.41 0.141 17.6 1.118 1.71
Block = 4:
Step emmean SE df lower.CL upper.CL
1 1.63 0.141 17.4 1.339 1.93
2 1.66 0.141 17.5 1.363 1.96
3 1.66 0.141 17.8 1.364 1.96
4 1.63 0.141 17.4 1.329 1.92
5 1.62 0.141 17.5 1.328 1.92
6 1.59 0.141 17.8 1.289 1.88
7 1.57 0.141 17.5 1.274 1.87
8 1.55 0.141 17.5 1.257 1.85
9 1.51 0.141 17.5 1.210 1.80
10 1.48 0.141 17.5 1.188 1.78
11 1.50 0.141 17.5 1.199 1.79
12 1.44 0.141 17.5 1.141 1.73
Block = 5:
Step emmean SE df lower.CL upper.CL
1 1.37 0.141 17.4 1.077 1.67
2 1.40 0.141 17.5 1.101 1.69
3 1.40 0.141 17.8 1.102 1.70
4 1.36 0.141 17.4 1.068 1.66
5 1.36 0.141 17.5 1.067 1.66
6 1.33 0.141 17.8 1.028 1.62
7 1.31 0.141 17.5 1.012 1.60
8 1.29 0.141 17.5 0.995 1.59
9 1.24 0.141 17.5 0.948 1.54
10 1.22 0.141 17.5 0.926 1.52
11 1.23 0.141 17.5 0.937 1.53
12 1.18 0.141 17.5 0.879 1.47
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block2 - Block4 -0.0227 0.0127 18924 -1.786 0.1744
Block2 - Block5 0.2389 0.0127 18934 18.779 <.0001
Block4 - Block5 0.2616 0.0123 18811 21.202 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
1.612243340 0.022735903 -0.238897564 0.024289598 0.026144157 -0.009754036
Step5 Step6 Step7 Step8 Step9 Step10
-0.010088031 -0.048259656 -0.065012215 -0.081557277 -0.129023943 -0.150639855
Step11 Step12
-0.139641584 -0.197993013
Random Effects:
$trial_id
(Intercept)
3.1 -0.0364990487
4.1 -0.0160792165
5.1 0.1183656083
7.1 0.5079102664
8.1 -0.1411510843
10.1 -0.2884533172
11.1 -0.3898068074
13.1 -0.1234836746
14.1 0.5649476040
15.1 -0.1421084241
16.1 -0.2896532345
17.1 -0.2963058386
18.1 0.3112620210
19.1 0.0359059786
20.1 0.1524046719
22.1 0.1731609722
23.1 -0.2186061281
2.2 0.5271943642
3.2 -0.5557439621
4.2 0.0590779940
5.2 0.2211647860
7.2 0.1213149347
8.2 -0.4715660974
10.2 -0.2892120306
11.2 -0.8607177714
13.2 0.3141755860
14.2 0.0165772605
15.2 0.2658670986
16.2 -0.1547787627
17.2 -0.2535140357
19.2 -0.1330291130
20.2 0.1114514849
22.2 -0.0315943431
23.2 3.8885900033
2.3 0.1522607931
3.3 0.1483849256
4.3 0.2328912253
5.3 -0.1564725749
7.3 0.4078804388
10.3 -0.0577733558
11.3 -0.4641435099
13.3 0.1811648193
14.3 -0.0641573356
15.3 0.4143203584
16.3 1.2300761553
17.3 -0.0648763986
18.3 -0.3834810918
19.3 -0.0503977628
20.3 0.1379849975
22.3 0.0093527671
23.3 -0.3887081842
2.4 -0.6336391955
3.4 -0.2395926282
4.4 -0.1159688135
5.4 -0.0245628251
7.4 0.1161061383
8.4 -0.5023573238
10.4 0.4624956929
11.4 -0.6369740141
13.4 0.1586611796
14.4 0.2649853696
15.4 -0.1070384497
16.4 0.0517824225
17.4 -0.0854629979
18.4 0.1472502854
19.4 -0.0499468769
20.4 -0.1925405138
22.4 0.1408242375
23.4 -0.4069348532
2.5 -0.2161524007
3.5 -0.5145923329
4.5 0.0141465282
5.5 -0.3207136551
7.5 0.3502153647
8.5 -0.5129269632
10.5 1.0379012607
11.5 0.3205979287
13.5 0.7706822996
14.5 -0.1391503938
15.5 0.4686344776
16.5 0.2584097245
17.5 -0.0549940287
18.5 0.2466848516
19.5 -0.2851202363
20.5 -0.2339420362
22.5 0.1764584769
23.5 -0.4475492756
2.6 -0.4400028360
3.6 0.1773009814
4.6 0.0617562636
5.6 -0.0895868855
7.6 0.8355353738
8.6 0.3695039335
10.6 0.1697449829
11.6 0.1856909033
13.6 0.4037037755
14.6 0.0376707391
15.6 -0.0001478610
16.6 -0.3366057887
17.6 -0.1137647894
18.6 0.6454884090
19.6 -0.0783858782
20.6 -0.1597117531
22.6 -0.0113417039
23.6 0.1180141770
2.7 -0.2990252197
3.7 0.2648989643
4.7 0.1798219967
5.7 -0.1692753978
7.7 0.6226889596
8.7 -0.4766305734
10.7 0.6221751285
11.7 0.9214606289
13.7 0.5839722382
14.7 0.1919246154
15.7 -0.0452122629
16.7 -0.0618070304
17.7 -0.1123157573
18.7 -0.0667751138
19.7 -0.1319429703
20.7 -0.1385136997
22.7 -0.0922948526
23.7 -0.0827619786
2.8 -0.2796184502
3.8 -0.1774151872
4.8 -0.1384687274
5.8 -0.2717057458
7.8 0.4738270597
8.8 -0.6843311660
10.8 0.4769290404
11.8 0.3989938069
13.8 0.5788671265
14.8 -0.1961198499
15.8 -0.0156732404
16.8 -0.3267036482
17.8 -0.1086997276
18.8 0.2414518867
19.8 -0.0710754097
20.8 -0.0558839006
22.8 -0.1002301482
23.8 -0.4374915524
2.9 0.0450418892
3.9 0.1068131745
4.9 0.0544888877
5.9 -0.1025310158
7.9 0.3647005018
8.9 -0.2717068259
10.9 1.6051097570
11.9 -0.4693115961
13.9 -0.1916245982
14.9 -0.0338986105
15.9 -0.0141688699
16.9 -0.1710319926
17.9 0.1797177215
18.9 0.0511513671
19.9 -0.0662719724
20.9 -0.3084614538
22.9 0.1273880176
23.9 -0.0358901590
2.10 0.5439891408
3.10 0.3127097717
4.10 0.2894359874
5.10 -0.0604000124
7.10 0.1984388034
8.10 -0.4813767775
10.10 0.8884344096
11.10 0.2617898211
13.10 -0.0985281279
14.10 -0.2059549966
15.10 0.0698747336
16.10 0.0549089038
17.10 -0.0103371224
18.10 0.3561709782
19.10 -0.0867199611
20.10 0.0280823198
22.10 0.0994763391
23.10 -0.3770910493
2.11 -0.2702172468
3.11 -0.2028480705
4.11 0.0283468003
5.11 0.0116202354
7.11 0.0322929578
8.11 -0.3322808731
10.11 1.1746623363
11.11 -0.6319850835
13.11 -0.1054845533
14.11 -0.2907649088
15.11 -0.0529686420
16.11 -0.0223816696
17.11 -0.1111453929
18.11 -0.0556610191
19.11 -0.2650660524
20.11 0.3615037487
22.11 0.1282971540
23.11 -0.5286913306
2.12 -0.2971731688
3.12 0.2476193401
4.12 0.1359822476
5.12 -0.0614892046
7.12 0.3844142210
8.12 0.5575695172
10.12 1.1195309031
11.12 -0.4543685410
13.12 0.1863311005
14.12 0.0671494070
15.12 0.0788234550
16.12 -0.0021072420
17.12 -0.0104651694
18.12 0.7821880884
19.12 0.4971538924
20.12 -0.3233102759
22.12 0.0719951279
23.12 -0.2982911555
2.13 -0.3754480886
3.13 -0.2381038024
4.13 -0.2321808695
5.13 -0.1194587752
7.13 -0.0298217792
8.13 -0.3090773941
10.13 0.1298445879
11.13 0.3699253537
13.13 0.3302941631
14.13 0.1117532538
15.13 -0.2421270926
16.13 0.1600605418
17.13 -0.0804124581
18.13 0.0802960751
19.13 -0.0538674361
20.13 0.2699405110
22.13 0.1485597308
23.13 -0.3870892821
2.14 -0.0690512701
3.14 0.2669027820
4.14 -0.0820661330
5.14 -0.2166035154
7.14 0.2846171786
8.14 0.3244074171
10.14 1.0944097595
11.14 -0.3146887389
13.14 0.2826844322
14.14 0.3052169688
15.14 0.2834975346
16.14 0.1641806561
17.14 0.1033367315
18.14 0.1928503427
19.14 0.0486791514
20.14 -0.0045453833
22.14 0.0775149967
23.14 -0.2748171414
2.15 -0.2068504748
3.15 -0.1260356700
4.15 -0.1174114178
5.15 0.0314511743
7.15 0.1584918360
8.15 0.0515302423
10.15 0.9357634997
11.15 0.0008789060
13.15 0.3206977381
14.15 -0.0773816924
15.15 -0.0097808145
16.15 0.6768091882
17.15 0.1544241422
18.15 0.4051713062
19.15 -0.1623875799
20.15 -0.0318153606
22.15 0.1335478608
23.15 0.2190353723
2.16 0.1902767037
3.16 -0.1112334969
4.16 -0.1154171834
5.16 -0.0250285352
7.16 0.1132336679
8.16 0.6042024733
10.16 0.4133884741
11.16 -0.3925931559
13.16 -0.2296108626
14.16 -0.0202136987
15.16 0.6175593522
16.16 0.1726855924
17.16 -0.1432704060
18.16 0.2253430702
19.16 -0.1476616461
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22.16 0.0564365545
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2.17 -0.0057447929
3.17 0.4252424060
4.17 -0.0948030884
5.17 0.1461748913
7.17 -0.5181588252
8.17 0.5367534744
10.17 1.0255444823
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13.17 0.1827715802
14.17 -0.2910100517
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19.17 0.1104014755
20.17 -0.2157920353
22.17 0.2351532807
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2.18 0.0379882746
3.18 0.2248066715
4.18 -0.0473312342
5.18 -0.0791845682
7.18 0.2364630711
8.18 0.0279623921
10.18 1.3528163820
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15.18 0.5091306517
16.18 0.2799277401
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22.18 0.3239023342
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2.19 0.0528949917
3.19 -0.0363263681
4.19 -0.2643846890
5.19 0.1173386601
7.19 0.3712672428
8.19 0.0972449538
10.19 2.0479545925
11.19 0.9927863953
13.19 0.2092262948
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20.20 -0.0161584667
22.20 0.0927402705
23.20 0.5074411654
2.21 0.0008130066
3.21 0.2335821558
4.21 0.0011374609
5.21 -0.1417126697
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8.21 0.6002482704
10.21 1.7557137100
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15.21 -0.1269733611
16.21 -0.0851652481
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18.21 -0.2263059302
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20.21 0.0573285324
22.21 0.2162535637
23.21 0.6661813568
2.22 -0.0886989815
3.22 -0.0306066925
4.22 0.2847921847
5.22 0.0752276735
7.22 0.4676697628
8.22 0.3723134965
10.22 1.3554855388
11.22 -0.2106654982
13.22 0.4402108132
14.22 -0.0908074812
15.22 0.1797661831
16.22 -0.0551381699
17.22 0.0113844803
18.22 0.0303626952
19.22 -0.0704611399
20.22 0.0538253112
22.22 0.0050561921
23.22 -0.0163288407
2.23 0.5604687928
3.23 0.2035850474
4.23 -0.0239515519
5.23 0.0242161231
7.23 0.1032743042
8.23 1.4911214113
10.23 0.1968434104
11.23 1.7064269716
13.23 0.1516946212
14.23 -0.4238122853
15.23 -0.1591283997
16.23 0.0797916793
17.23 -0.0574384749
18.23 -0.0006934136
19.23 0.1712870159
20.23 0.0639405728
22.23 0.0652107110
23.23 0.0216106368
2.24 0.1451576445
3.24 0.2434201842
4.24 0.0470165426
5.24 0.4546008426
7.24 0.1606650382
8.24 0.2485554787
10.24 1.2506982914
11.24 0.1095204900
13.24 0.2520284918
14.24 -0.0281125084
15.24 -0.2955766392
16.24 0.3452773150
17.24 -0.0201426976
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19.24 0.0453760932
20.24 0.0359006159
22.24 0.0579829796
23.24 -0.1264619422
2.25 0.4027492674
3.25 0.2791150127
4.25 0.1009375323
5.25 0.1077980956
7.25 -0.0327713931
8.25 -0.1319624516
10.25 0.7263894047
11.25 -0.1274792187
13.25 0.8430855609
14.25 0.0981674820
15.25 0.1297692080
16.25 0.4987261058
17.25 0.3516370303
18.25 0.2142413964
19.25 0.0889436573
20.25 -0.0110257302
22.25 0.0684830541
23.25 0.3667138732
2.26 0.1120012373
3.26 0.0116160952
4.26 -0.2497917586
5.26 -0.1064832764
7.26 0.3959715071
8.26 1.1036531486
10.26 0.5009095870
11.26 2.4715283887
13.26 0.7128473249
14.26 -0.3532079274
15.26 0.3945022968
16.26 0.2690230131
17.26 0.0216816027
18.26 0.0903453226
19.26 0.0759005637
20.26 0.2554270295
22.26 0.1006421374
23.26 -0.3606735299
2.27 -0.0424136402
3.27 0.0152227479
4.27 -0.1286926968
5.27 0.0272638834
7.27 0.0952443849
8.27 0.4489546178
10.27 0.1119063439
11.27 1.7007372546
13.27 0.2689924281
14.27 0.0592397023
15.27 -0.3379502677
16.27 0.4265047981
17.27 0.0996523436
18.27 0.0634509337
19.27 0.0304612718
20.27 0.1231166430
22.27 0.0514376684
23.27 0.3599645266
2.28 0.6040783776
3.28 0.2818623408
4.28 -0.0840765321
5.28 0.1002023079
7.28 0.2746783047
8.28 0.7700266459
10.28 1.8871095440
11.28 -0.5428278940
13.28 0.4676802686
14.28 -0.0461753763
15.28 -0.1719573514
16.28 0.2505279064
17.28 0.0058070822
18.28 0.5119441488
19.28 -0.0431229895
20.28 -0.0778147657
22.28 -0.1638587357
23.28 0.1609177546
2.29 0.3788127705
3.29 1.1342504229
4.29 -0.2061837466
5.29 0.1465926082
7.29 0.5820076148
8.29 0.5750213572
10.29 -0.0037983722
11.29 0.1905118622
13.29 0.7321851233
14.29 -0.1121357808
15.29 0.3591734070
16.29 0.2354921940
17.29 0.4065017420
18.29 -0.3290522553
19.29 0.1305860653
20.29 -0.0642709192
22.29 0.0683175897
23.29 0.7998318333
2.30 0.0948505429
3.30 0.4832456488
4.30 0.0259151456
5.30 0.1191754718
7.30 0.2624830529
8.30 0.6724154676
10.30 0.8649909834
11.30 -0.1145390486
13.30 0.3236546587
14.30 0.3905596604
15.30 -0.3181655279
16.30 0.0573774934
17.30 0.3930359022
18.30 0.3597384900
19.30 -0.1035285483
20.30 -0.2349365765
22.30 -0.0830301617
23.30 0.8447320927
2.31 0.3076661979
3.31 0.2031366788
4.31 0.2136310984
5.31 0.1625263587
7.31 0.4371251558
8.31 0.9248735837
10.31 -0.4330174322
11.31 1.2396855726
13.31 -0.1353206734
14.31 -0.0221639906
15.31 -0.0057612249
16.31 0.2598597316
17.31 0.0915634602
18.31 0.1916707112
19.31 0.1209628126
20.31 -0.1642039253
22.31 -0.1380656846
23.31 1.2648929051
2.32 0.4065259695
3.32 0.1347645731
4.32 0.2172345438
5.32 0.3829047777
7.32 -0.0861055553
8.32 0.7090013006
10.32 0.1126085849
11.32 3.1320552567
13.32 -0.3033105876
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15.32 0.9334571778
16.32 0.1065102527
17.32 0.1600889120
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19.32 -0.2089486010
20.32 0.1868061766
22.32 0.0790915223
23.32 0.1936698776
2.33 -0.0533960817
3.33 0.9223877188
4.33 0.1732715802
5.33 0.3443885056
7.33 -0.2225761168
8.33 0.7684879781
10.33 -0.7417823398
11.33 0.7237769862
13.33 0.1045968592
14.33 -0.0847555708
15.33 0.5072499405
16.33 -0.1959590299
17.33 0.1460552827
18.33 0.4837210181
19.33 -0.0857239171
20.33 0.0479726985
22.33 0.1789856554
23.33 0.5453963853
2.34 0.2010020819
3.34 -0.2832667643
4.34 0.0387923324
5.34 0.0658562379
7.34 -0.3130376470
8.34 0.7263589436
10.34 -0.5233995909
11.34 0.9662340521
13.34 1.0025545742
14.34 0.1528471323
15.34 0.0372571992
16.34 0.2248174925
17.34 -0.1576410619
18.34 -0.2508394080
19.34 0.1601426034
20.34 -0.0001884779
22.34 0.0288401026
23.34 0.0662596836
2.35 0.7420299869
3.35 -0.4834286575
4.35 -0.3833115045
5.35 -0.0596059424
7.35 -0.3974421144
8.35 -0.1575740296
10.35 0.4330187630
11.35 0.7157398255
13.35 0.0645052475
14.35 0.5801476113
15.35 0.7323384036
16.35 0.2661171138
17.35 0.1036286516
18.35 0.2602421658
19.35 0.2179446291
20.35 0.2373273953
22.35 0.2287626670
23.35 0.4609330738
2.36 0.2931622383
3.36 0.1152619296
4.36 0.0575122257
5.36 -0.0725448998
7.36 0.0465428510
8.36 0.3392975273
10.36 -1.7049389617
11.36 -0.1262479162
13.36 0.2672539127
14.36 0.2083623379
15.36 0.0481100790
16.36 -0.0126618639
17.36 0.0252615726
18.36 0.1359669933
19.36 -0.2205937008
20.36 0.1910352237
22.36 0.0076819501
23.36 0.2191061461
2.37 0.0123452470
3.37 0.3870441608
4.37 0.2016327653
5.37 -0.1671383019
7.37 0.0156768268
8.37 -0.0029941930
10.37 -0.6226910599
11.37 -0.2725300346
13.37 -0.5097655326
14.37 0.2857408182
15.37 -0.0090806007
16.37 -0.0754257832
17.37 0.4286562483
18.37 0.3638344160
19.37 0.1932616599
20.37 0.0309374262
22.37 0.1030646347
23.37 0.2876687264
2.38 1.1841815640
3.38 0.3059220975
4.38 -0.1583251558
5.38 -0.2225718800
7.38 -0.6528871047
8.38 0.2601973508
10.38 -1.7938160851
11.38 -0.9420845241
13.38 -0.5596348310
14.38 0.7972108793
15.38 -0.0676839454
16.38 0.8531053092
17.38 -0.0052375937
18.38 0.3427304781
19.38 0.2212572803
20.38 0.0364750670
22.38 0.0224556937
23.38 -0.2913632167
2.39 0.2106298241
3.39 -0.6112326792
4.39 0.0789041903
5.39 -0.0009279352
7.39 -0.2547054813
8.39 -0.8654251112
10.39 -1.6897524004
11.39 -0.4698680949
13.39 -0.7048288551
14.39 0.2779101411
15.39 -0.0297260187
16.39 -0.1304033845
17.39 0.1373501547
18.39 -0.3332100838
19.39 -0.0251024122
20.39 0.2401935991
22.39 0.0579398840
23.39 -0.5442485410
2.40 0.2681694153
3.40 0.0099392170
4.40 -0.0171741267
5.40 0.0394290584
7.40 -0.5826013905
8.40 0.1986537171
10.40 -1.1053471961
11.40 -1.3484255199
13.40 -1.0559794403
14.40 0.0654838855
15.40 -0.0783533334
16.40 0.4002367749
17.40 0.3722747295
18.40 0.0302499764
19.40 0.0009085087
20.40 -0.0008602856
22.40 0.0169273986
23.40 -0.6444346578
2.41 0.4576853204
3.41 -0.0076025315
4.41 0.0264797876
5.41 0.1403269600
7.41 -0.4144402228
8.41 -0.9577546551
10.41 -2.6894629805
11.41 -0.5051689387
13.41 -0.6094405209
14.41 0.2145755244
15.41 -0.1751463200
16.41 -0.6778546566
17.41 0.0958580681
18.41 0.3787901622
19.41 0.0433651464
20.41 -0.2648173338
22.41 -0.0234799950
23.41 -0.3260565232
2.42 -0.1561829405
3.42 -0.5666338713
4.42 0.1764781629
5.42 0.1143405780
7.42 -0.5804257095
8.42 -0.1131132441
10.42 -2.0254386928
11.42 -1.3823004336
13.42 -1.1249629012
14.42 0.3705583647
15.42 -0.7062372349
16.42 0.2328778372
17.42 -0.2556545152
18.42 -0.4855656394
19.42 0.0374123782
20.42 -0.0978044732
22.42 -0.0931355421
23.42 -0.8567547781
2.43 -0.5184650068
3.43 0.0049888535
4.43 -0.2679758994
5.43 0.0283237853
7.43 -0.9984871696
8.43 -1.6519119654
10.43 -1.4210866745
11.43 -0.9285051792
13.43 -0.9735516905
14.43 0.1201191139
15.43 -0.3270468248
16.43 -0.2709144915
17.43 -0.3424787248
18.43 -0.3565483744
19.43 -0.0690179194
20.43 0.1530445576
22.43 -0.5407764485
23.43 -0.3161804723
2.44 -0.8426618719
3.44 -0.1733408823
4.44 -0.0441811198
5.44 -0.2441186491
7.44 -0.8359864687
8.44 -1.1750100391
10.44 -1.7690542319
11.44 -1.1355468265
13.44 -1.0076006536
14.44 -0.4524493773
15.44 -0.9792319619
16.44 -0.4329128427
17.44 -0.0898537745
18.44 -0.0326801643
19.44 -0.3034199500
20.44 -0.1796980486
22.44 -0.5888063448
23.44 -0.6324116965
2.45 -0.7533086193
3.45 -0.6672278056
4.45 -0.4181287913
5.45 -0.2506909993
7.45 -1.3425951697
8.45 -0.5457047493
10.45 -2.0620794708
11.45 -1.6521756722
13.45 -0.7860502857
14.45 -0.6714317472
15.45 -0.7238849653
16.45 -0.7733333554
17.45 -0.2155078032
18.45 -0.9361782962
19.45 0.4146785491
20.45 -0.1315240518
22.45 -0.6719419782
23.45 -1.0655867902
2.46 -0.4165002670
3.46 -0.7815518091
4.46 0.0900803991
5.46 -0.2999992646
7.46 -1.0307356478
8.46 -0.8692342795
10.46 -1.9516103042
11.46 0.4560783980
13.46 -1.1265828297
14.46 -0.8677012751
15.46 -0.3879404634
16.46 -1.4285503719
17.46 -0.5614485361
18.46 -1.6108600555
19.46 -0.3489852840
20.46 -0.3314589543
22.46 -0.6335444804
23.46 -1.3557366330
2.47 -1.0071802947
3.47 -1.2175455207
4.47 -0.0685953489
5.47 -0.4637982735
7.47 -0.4562224761
8.47 -1.4994932613
10.47 -2.6132778772
11.47 -1.3898278792
13.47 -0.7462416342
14.47 -0.6205245685
15.47 -0.9472825030
16.47 -1.3061590485
17.47 -0.5989794581
18.47 -1.3271650646
19.47 -0.4062426953
20.47 -0.4064776899
22.47 -0.7796318831
2.48 -0.8918559574
$subject
(Intercept)
2 -0.064081264
3 0.246499710
4 -0.582398079
5 -0.749117450
7 0.229120346
8 0.561255026
10 1.497688495
11 0.685144091
13 -0.197212682
14 -0.317931165
15 -0.002069997
16 0.277735282
17 -0.619016563
18 0.384928586
19 -0.650023632
20 -0.443747688
22 -0.502991107
23 0.246218092
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.24739797 0.04512910 -0.05279874 0.18625117 -0.23543967 -0.12975756
=============================================================# -------- Identify Stepwise EMM Outliers vs. Overall Mean (per Axis × Block) --------
# Bind all EMMs into one dataframe
all_emm_12step <- bind_rows(lapply(rms_lmm_results, function(res) res$EmmeansStepBlock), .id = "AxisLabel")
# Extract axis from label (e.g., "RMS_X" -> "X")
all_emm_12step <- all_emm_12step %>%
mutate(
Axis = gsub("RMS_", "", AxisLabel),
Step = as.numeric(as.character(Step)),
Block = as.factor(Block)
)
# Compute overall mean ± 1.96*SE per Block × Axis
overall_stats_12step <- all_emm_12step %>%
group_by(Block, Axis) %>%
summarise(
overall_mean = mean(emmean, na.rm = TRUE),
overall_se = sd(emmean, na.rm = TRUE) / sqrt(n()),
lower_bound = overall_mean - 1.96 * overall_se,
upper_bound = overall_mean + 1.96 * overall_se,
.groups = "drop"
)
# Join back to EMM table and flag outliers
emm_outliers_12step <- left_join(all_emm_12step, overall_stats_12step, by = c("Block", "Axis")) %>%
mutate(
is_outlier = emmean < lower_bound | emmean > upper_bound
) %>%
filter(is_outlier)
# View flagged outlier steps
print(emm_outliers_12step) AxisLabel Step Block emmean SE df lower.CL upper.CL Axis
1 RMS_X 2 2 0.7306302 0.06186410 17.79598 0.6005517 0.8607088 X
2 RMS_X 3 2 0.7515602 0.06212763 18.10114 0.6210871 0.8820332 X
3 RMS_X 4 2 0.7242782 0.06173599 17.64903 0.5943906 0.8541658 X
4 RMS_X 5 2 0.7306718 0.06186456 17.79650 0.6005926 0.8607510 X
5 RMS_X 9 2 0.6864966 0.06186410 17.79598 0.5564181 0.8165752 X
6 RMS_X 10 2 0.6752055 0.06186456 17.79650 0.5451263 0.8052848 X
7 RMS_X 11 2 0.6697185 0.06186740 17.79978 0.5396350 0.7998019 X
8 RMS_X 12 2 0.6613209 0.06186456 17.79650 0.5312417 0.7914001 X
9 RMS_X 2 4 0.7176225 0.06184599 17.77518 0.5875710 0.8476739 X
10 RMS_X 3 4 0.7385524 0.06219015 18.17415 0.6079854 0.8691194 X
11 RMS_X 4 4 0.7112704 0.06167128 17.57519 0.5814790 0.8410618 X
12 RMS_X 5 4 0.7176640 0.06184655 17.77583 0.5876117 0.8477164 X
13 RMS_X 9 4 0.6734889 0.06184599 17.77518 0.5434374 0.8035404 X
14 RMS_X 10 4 0.6621978 0.06184655 17.77583 0.5321454 0.7922501 X
15 RMS_X 11 4 0.6567107 0.06184170 17.77026 0.5266656 0.7867558 X
16 RMS_X 12 4 0.6483131 0.06184655 17.77583 0.5182608 0.7783654 X
17 RMS_X 2 5 0.6156153 0.06184459 17.77358 0.4855659 0.7456647 X
18 RMS_X 3 5 0.6365452 0.06219098 18.17512 0.5059770 0.7671134 X
19 RMS_X 4 5 0.6092633 0.06166669 17.56997 0.4794787 0.7390478 X
20 RMS_X 5 5 0.6156569 0.06184499 17.77404 0.4856069 0.7457069 X
21 RMS_X 9 5 0.5714817 0.06184459 17.77358 0.4414323 0.7015311 X
22 RMS_X 10 5 0.5601906 0.06184499 17.77404 0.4301406 0.6902406 X
23 RMS_X 11 5 0.5547035 0.06183773 17.76571 0.4246643 0.6847427 X
24 RMS_X 12 5 0.5463059 0.06184499 17.77404 0.4162559 0.6763560 X
25 RMS_Y 1 2 0.7939634 0.06983346 17.57900 0.6469965 0.9409304 Y
26 RMS_Y 2 2 0.8004527 0.06996402 17.71083 0.6532915 0.9476138 Y
27 RMS_Y 3 2 0.7948602 0.07022995 17.98163 0.6473017 0.9424186 Y
28 RMS_Y 4 2 0.7875625 0.06983346 17.57900 0.6405956 0.9345294 Y
29 RMS_Y 5 2 0.7815330 0.06996450 17.71132 0.6343711 0.9286949 Y
30 RMS_Y 9 2 0.7235997 0.06996402 17.71083 0.5764386 0.8707609 Y
31 RMS_Y 10 2 0.7098687 0.06996450 17.71132 0.5627068 0.8570306 Y
32 RMS_Y 11 2 0.7140291 0.06996621 17.71306 0.5668646 0.8611935 Y
33 RMS_Y 12 2 0.6805071 0.06996450 17.71132 0.5333452 0.8276690 Y
34 RMS_Y 1 4 0.8012199 0.06976528 17.51048 0.6543542 0.9480856 Y
35 RMS_Y 2 4 0.8077091 0.06994316 17.68973 0.6605790 0.9548392 Y
36 RMS_Y 3 4 0.8021166 0.07029041 18.04365 0.6544676 0.9497657 Y
37 RMS_Y 4 4 0.7948190 0.06976528 17.51048 0.6479533 0.9416846 Y
38 RMS_Y 5 4 0.7887895 0.06994373 17.69031 0.6416585 0.9359204 Y
39 RMS_Y 9 4 0.7308562 0.06994316 17.68973 0.5837261 0.8779863 Y
40 RMS_Y 10 4 0.7171251 0.06994373 17.69031 0.5699942 0.8642560 Y
41 RMS_Y 11 4 0.7212855 0.06993725 17.68377 0.5741642 0.8684068 Y
42 RMS_Y 12 4 0.6877636 0.06994373 17.69031 0.5406326 0.8348945 Y
43 RMS_Y 1 5 0.6677998 0.06976003 17.50520 0.5209419 0.8146577 Y
44 RMS_Y 2 5 0.6742890 0.06994097 17.68752 0.5271622 0.8214158 Y
45 RMS_Y 3 5 0.6686965 0.07029040 18.04365 0.5210475 0.8163456 Y
46 RMS_Y 4 5 0.6613989 0.06976003 17.50520 0.5145410 0.8082567 Y
47 RMS_Y 5 5 0.6553694 0.06994138 17.68794 0.5082419 0.8024968 Y
48 RMS_Y 9 5 0.5974361 0.06994097 17.68752 0.4503093 0.7445629 Y
49 RMS_Y 10 5 0.5837050 0.06994138 17.68794 0.4365776 0.7308324 Y
50 RMS_Y 11 5 0.5878654 0.06993262 17.67908 0.4407510 0.7349798 Y
51 RMS_Y 12 5 0.5543435 0.06994138 17.68794 0.4072160 0.7014709 Y
52 RMS_Z 1 2 1.6122433 0.14065362 17.44900 1.3160708 1.9084159 Z
53 RMS_Z 2 2 1.6365329 0.14085790 17.55058 1.3400573 1.9330085 Z
54 RMS_Z 3 2 1.6383875 0.14127667 17.76022 1.3412887 1.9354863 Z
55 RMS_Z 4 2 1.6024893 0.14065362 17.44900 1.3063167 1.8986619 Z
56 RMS_Z 5 2 1.6021553 0.14085864 17.55095 1.3056786 1.8986320 Z
57 RMS_Z 9 2 1.4832194 0.14085790 17.55058 1.1867438 1.7796950 Z
58 RMS_Z 10 2 1.4616035 0.14085864 17.55095 1.1651268 1.7580802 Z
59 RMS_Z 11 2 1.4726018 0.14086241 17.55284 1.1761195 1.7690840 Z
60 RMS_Z 12 2 1.4142503 0.14085864 17.55095 1.1177736 1.7107270 Z
61 RMS_Z 1 4 1.6349792 0.14054875 17.39703 1.3389620 1.9309965 Z
62 RMS_Z 2 4 1.6592688 0.14082721 17.53531 1.3628388 1.9556988 Z
63 RMS_Z 3 4 1.6611234 0.14137414 17.80930 1.3638792 1.9583676 Z
64 RMS_Z 4 4 1.6252252 0.14054875 17.39703 1.3292080 1.9212425 Z
65 RMS_Z 5 4 1.6248912 0.14082811 17.53576 1.3284599 1.9213225 Z
66 RMS_Z 9 4 1.5059553 0.14082721 17.53531 1.2095253 1.8023853 Z
67 RMS_Z 10 4 1.4843394 0.14082811 17.53576 1.1879081 1.7807707 Z
68 RMS_Z 11 4 1.4953377 0.14081931 17.53138 1.1989194 1.7917559 Z
69 RMS_Z 12 4 1.4369862 0.14082811 17.53576 1.1405549 1.7334176 Z
70 RMS_Z 1 5 1.3733458 0.14054102 17.39321 1.0773400 1.6693516 Z
71 RMS_Z 2 5 1.3976354 0.14082446 17.53394 1.1012095 1.6940613 Z
72 RMS_Z 3 5 1.3994899 0.14137487 17.80967 1.1022447 1.6967352 Z
73 RMS_Z 4 5 1.3635917 0.14054102 17.39321 1.0675859 1.6595976 Z
74 RMS_Z 5 5 1.3632577 0.14082510 17.53426 1.0668309 1.6596846 Z
75 RMS_Z 9 5 1.2443218 0.14082446 17.53394 0.9478959 1.5407477 Z
76 RMS_Z 10 5 1.2227059 0.14082510 17.53426 0.9262790 1.5191328 Z
77 RMS_Z 11 5 1.2337042 0.14081256 17.52802 0.9372959 1.5301124 Z
78 RMS_Z 12 5 1.1753528 0.14082510 17.53426 0.8789259 1.4717796 Z
overall_mean overall_se lower_bound upper_bound is_outlier
1 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
2 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
3 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
4 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
5 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
6 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
7 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
8 0.7058953 0.008100902 0.6900176 0.7217731 TRUE
9 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
10 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
11 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
12 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
13 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
14 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
15 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
16 0.6928876 0.008100902 0.6770098 0.7087653 TRUE
17 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
18 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
19 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
20 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
21 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
22 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
23 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
24 0.5908804 0.008100902 0.5750026 0.6067582 TRUE
25 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
26 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
27 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
28 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
29 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
30 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
31 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
32 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
33 0.7531765 0.011439205 0.7307556 0.7755973 TRUE
34 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
35 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
36 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
37 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
38 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
39 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
40 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
41 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
42 0.7604329 0.011439205 0.7380121 0.7828537 TRUE
43 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
44 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
45 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
46 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
47 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
48 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
49 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
50 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
51 0.6270128 0.011439205 0.6045920 0.6494336 TRUE
52 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
53 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
54 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
55 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
56 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
57 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
58 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
59 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
60 1.5471154 0.021640708 1.5046996 1.5895311 TRUE
61 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
62 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
63 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
64 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
65 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
66 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
67 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
68 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
69 1.5698513 0.021640708 1.5274355 1.6122670 TRUE
70 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
71 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
72 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
73 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
74 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
75 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
76 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
77 1.3082178 0.021640708 1.2658020 1.3506336 TRUE
78 1.3082178 0.021640708 1.2658020 1.3506336 TRUE#2.3 18 steps Block 3,4 & 5 - preparation for rms analysis, skip completely to part 3
# --- Step-Wise RMS: Blocks 3, 4, 5 — First 18 Steps ---
plot_stepwise_rms_blocks_345_18steps <- function(tagged_data2) {
step_markers <- c(14, 15, 16, 17)
buffer <- 3
step_data <- tagged_data2 %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_block() %>%
filter(Block %in% c(3, 4, 5)) %>%
mutate(Step = as.numeric(Step)) %>%
group_by(subject, Block, trial) %>%
mutate(step_count = max(Step, na.rm = TRUE)) %>%
ungroup() %>%
filter(step_count == 18) %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup() %>%
filter(Step <= 18)
step_indices <- step_data %>%
select(subject, Block, trial, row_id, Step)
window_data <- map_dfr(1:nrow(step_indices), function(i) {
step <- step_indices[i, ]
rows <- (step$row_id - buffer):(step$row_id + buffer)
step_data %>%
filter(subject == step$subject,
Block == step$Block,
trial == step$trial,
row_id %in% rows) %>%
mutate(Step = step$Step)
})
step_summary <- window_data %>%
group_by(subject, Block, trial, Step) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = toupper(gsub("rms_", "", Axis)),
Step = factor(Step),
Block = factor(Block),
subject = factor(subject),
trial_id = interaction(subject, trial, drop = TRUE)
)
plot_data <- step_summary %>%
group_by(Block, Step, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
se_rms = sd(RMS, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)
axis_labels <- unique(plot_data$Axis)
plots <- map(axis_labels, function(ax) {
axis_data <- filter(plot_data, Axis == ax)
ggplot(axis_data, aes(x = Step, y = mean_rms, fill = Block)) +
geom_col(position = position_dodge(width = 0.8), width = 0.7) +
geom_errorbar(
aes(ymin = mean_rms - se_rms, ymax = mean_rms + se_rms),
position = position_dodge(width = 0.8),
width = 0.3
) +
ylim(0, 3.25) +
labs(
title = paste("Step-wise CoM RMS — Axis", ax),
x = "Step Number",
y = "RMS Acceleration (m/s²)",
fill = "Block"
) +
theme_minimal() +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
text = element_text(size = 12),
plot.title = element_text(face = "bold"),
axis.text.x = element_text(angle = 0)
)
})
names(plots) <- axis_labels
return(list(
plots = plots,
step_summary = step_summary,
plot_data = plot_data,
window_data = window_data
))
}
# --- Run function and extract results ---
result <- plot_stepwise_rms_blocks_345_18steps(tagged_data2)
stepwise_block345_plots <- result$plots
step_summary <- result$step_summary
plot_data <- result$plot_data
window_data <- result$window_data
# --- Print plots ---
for (plot_name in names(stepwise_block345_plots)) {
cat("\n\n==== Axis:", plot_name, "====\n\n")
print(stepwise_block345_plots[[plot_name]])
}
==== Axis: X ====
==== Axis: Y ====
==== Axis: Z ====
# --- RMS LMMs: Blocks 3, 4, 5 --------
print_stepwise_lmm_diagnostics <- function(results_list, dataset_name = "Mixed") {
cat(glue::glue("\n=========== STEPWISE LMM DIAGNOSTICS: {dataset_name} ===========\n"))
for (key in names(results_list)) {
cat("\n---", key, "---\n")
cat("ANOVA:\n")
print(results_list[[key]]$ANOVA)
cat("\nEstimated Marginal Means (Step | Block):\n")
print(results_list[[key]]$EmmeansStepBlock)
cat("\nPairwise Comparisons:\n")
print(results_list[[key]]$Pairwise)
cat("\nFixed Effects:\n")
print(results_list[[key]]$FixedEffects)
cat("\nRandom Effects:\n")
print(results_list[[key]]$RandomEffects)
cat("\nSample Scaled Residuals:\n")
print(head(results_list[[key]]$ScaledResiduals))
cat("\n=============================================================\n")
}
}
rms_lmm_results_18step <- list()
axes <- c("X", "Y", "Z")
for (ax in axes) {
cat(glue("\n\n========== Running models for 18-step Axis: {ax} ==========\n\n"))
df_rms <- step_summary %>% filter(Axis == ax)
rms_model <- lmer(RMS ~ Block + Step + (1 | subject) + (1 | trial_id), data = df_rms)
emmeans_step_block <- emmeans(rms_model, ~ Step | Block)
rms_lmm_results_18step[[paste0("RMS_", ax)]] <- list(
Model = rms_model,
ANOVA = anova(rms_model, type = 3),
Pairwise = emmeans(rms_model, pairwise ~ Block)$contrasts,
EmmeansStepBlock = summary(emmeans_step_block),
FixedEffects = fixef(rms_model),
RandomEffects = ranef(rms_model),
ScaledResiduals = resid(rms_model, scaled = TRUE)
)
}
========== Running models for 18-step Axis: X ==========
========== Running models for 18-step Axis: Y ==========
========== Running models for 18-step Axis: Z ==========print_stepwise_lmm_diagnostics(rms_lmm_results_18step, dataset_name = "18-Step RMS Acceleration")=========== STEPWISE LMM DIAGNOSTICS: 18-Step RMS Acceleration ===========
--- RMS_X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 82.899 41.450 2 26973 362.497 < 2.2e-16 ***
Step 27.994 1.647 17 26303 14.401 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 3:
Step emmean SE df lower.CL upper.CL
1 0.535 0.0511 17.9 0.427 0.642
2 0.544 0.0513 18.2 0.436 0.652
3 0.567 0.0516 18.7 0.459 0.675
4 0.547 0.0511 17.9 0.439 0.654
5 0.548 0.0513 18.2 0.441 0.656
6 0.547 0.0516 18.7 0.439 0.655
7 0.541 0.0513 18.2 0.433 0.649
8 0.533 0.0513 18.2 0.425 0.641
9 0.529 0.0513 18.2 0.422 0.637
10 0.518 0.0513 18.2 0.410 0.626
11 0.517 0.0513 18.2 0.409 0.624
12 0.518 0.0513 18.2 0.411 0.626
13 0.505 0.0516 18.7 0.397 0.613
14 0.494 0.0513 18.2 0.386 0.602
15 0.486 0.0511 17.9 0.379 0.593
16 0.468 0.0516 18.7 0.360 0.576
17 0.463 0.0513 18.2 0.355 0.571
18 0.452 0.0511 17.9 0.345 0.560
Block = 4:
Step emmean SE df lower.CL upper.CL
1 0.685 0.0510 17.8 0.578 0.792
2 0.694 0.0512 18.1 0.587 0.802
3 0.717 0.0516 18.7 0.609 0.826
4 0.697 0.0510 17.8 0.589 0.804
5 0.699 0.0512 18.1 0.591 0.806
6 0.697 0.0516 18.7 0.589 0.805
7 0.691 0.0512 18.1 0.584 0.799
8 0.683 0.0512 18.1 0.576 0.791
9 0.679 0.0512 18.1 0.572 0.787
10 0.668 0.0512 18.1 0.561 0.776
11 0.667 0.0512 18.1 0.559 0.774
12 0.669 0.0512 18.1 0.561 0.776
13 0.655 0.0516 18.7 0.547 0.763
14 0.644 0.0512 18.1 0.537 0.752
15 0.636 0.0510 17.8 0.529 0.743
16 0.618 0.0516 18.7 0.510 0.726
17 0.613 0.0512 18.1 0.506 0.721
18 0.602 0.0510 17.8 0.495 0.709
Block = 5:
Step emmean SE df lower.CL upper.CL
1 0.596 0.0510 17.8 0.489 0.703
2 0.605 0.0512 18.1 0.498 0.713
3 0.629 0.0516 18.7 0.521 0.737
4 0.608 0.0510 17.8 0.501 0.715
5 0.610 0.0512 18.1 0.502 0.717
6 0.608 0.0516 18.7 0.500 0.717
7 0.602 0.0512 18.1 0.495 0.710
8 0.595 0.0512 18.1 0.487 0.702
9 0.591 0.0512 18.1 0.483 0.698
10 0.579 0.0512 18.1 0.472 0.687
11 0.578 0.0512 18.1 0.471 0.686
12 0.580 0.0512 18.1 0.472 0.687
13 0.566 0.0516 18.7 0.458 0.674
14 0.555 0.0512 18.1 0.448 0.663
15 0.547 0.0510 17.8 0.440 0.655
16 0.529 0.0516 18.7 0.421 0.637
17 0.524 0.0512 18.1 0.417 0.632
18 0.514 0.0510 17.8 0.406 0.621
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block3 - Block4 -0.1501 0.00574 27071 -26.160 <.0001
Block3 - Block5 -0.0614 0.00575 27082 -10.675 <.0001
Block4 - Block5 0.0887 0.00512 26855 17.306 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
0.534613138 0.150106169 0.061429607 0.009308136 0.032708550 0.011926236
Step5 Step6 Step7 Step8 Step9 Step10
0.013860913 0.012365908 0.006437524 -0.001510637 -0.005492789 -0.016692701
Step11 Step12 Step13 Step14 Step15 Step16
-0.017758291 -0.016200609 -0.029797690 -0.040592702 -0.048590058 -0.066748979
Step17 Step18
-0.071561944 -0.082432572
Random Effects:
$trial_id
(Intercept)
3.1 -0.1485566338
4.1 0.0723254788
5.1 -0.0570174329
7.1 0.0762323903
8.1 -0.0719646224
10.1 0.0248797104
11.1 -0.2744443412
13.1 0.0539508914
14.1 -0.0491619682
15.1 0.1164448823
16.1 0.0193356495
17.1 -0.1433769455
18.1 -0.0616414781
19.1 0.0207849440
20.1 0.0258654070
22.1 0.0424740525
23.1 0.0231260855
2.2 0.0772075436
3.2 -0.0861561279
4.2 0.0842229365
5.2 -0.0617640846
7.2 -0.0118966261
8.2 -0.1685331113
10.2 0.0193672079
11.2 0.0423717059
13.2 -0.0396149590
14.2 -0.0593437038
15.2 0.4008446459
16.2 -0.1053459910
17.2 0.0014453364
19.2 -0.0332924164
20.2 -0.0001032285
22.2 0.0681555601
23.2 0.9283930397
2.3 0.0375839611
3.3 0.0024656475
4.3 -0.0809143934
5.3 -0.0846000364
7.3 -0.0744836763
8.3 -0.0734182597
10.3 0.5399820114
11.3 0.0514352257
13.3 0.0319439754
14.3 -0.0422683471
15.3 0.0257996510
16.3 0.0382936533
17.3 -0.0223782376
18.3 -0.0701784584
19.3 -0.0365718372
20.3 0.0605363874
22.3 -0.0469577995
23.3 0.1407725655
2.4 -0.1880524340
3.4 -0.0394522592
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2.43 -0.2847270587
3.43 -0.2071479138
4.43 -0.1117575453
5.43 -0.0830800564
7.43 -0.0341330878
8.43 -0.5447601027
10.43 -0.2377225590
11.43 -0.1684710642
13.43 -0.3399458373
14.43 -0.0444654056
15.43 -0.0982239181
16.43 -0.1896313581
17.43 -0.3398532247
18.43 0.0170370888
19.43 -0.0554966803
20.43 -0.0537758301
22.43 -0.3418400864
23.43 -0.2171216497
2.44 -0.3764330106
3.44 -0.1594723900
4.44 0.0288382471
5.44 0.0136865816
7.44 -0.0547609887
8.44 -0.1661613685
10.44 -0.0215217724
11.44 -0.0025262623
13.44 -0.2195776863
14.44 -0.1173569154
15.44 0.0351452027
16.44 -0.1162540231
17.44 -0.0675643903
18.44 0.2608099989
19.44 0.0604091456
20.44 -0.0886312255
22.44 -0.3654401112
23.44 -0.1863957026
2.45 0.0409762917
3.45 0.1770228762
4.45 -0.2522791483
5.45 0.0234750544
7.45 -0.2751431087
8.45 0.4343539933
10.45 -0.7098366439
11.45 -0.4691885483
13.45 -0.1591207392
14.45 -0.1936821591
15.45 -0.0069298133
16.45 -0.2733561689
17.45 -0.0993149895
18.45 0.2956275067
19.45 0.0419511259
20.45 0.0180763995
22.45 -0.3877155233
23.45 -0.3242682791
2.46 -0.3905033342
3.46 -0.2509640598
4.46 0.0043597929
5.46 -0.0320579261
7.46 -0.3392250209
8.46 -0.5835871640
10.46 -0.8335056089
11.46 -0.0427333628
13.46 -0.2828708431
14.46 -0.2647457303
15.46 -0.1849578867
16.46 -0.3402214659
17.46 -0.1935879659
18.46 -0.3599376522
19.46 -0.0405866456
20.46 -0.1823797669
22.46 -0.0763015115
23.46 -0.3768656216
2.47 -0.1805938112
3.47 -0.2973687140
4.47 -0.0493834782
5.47 -0.1290130875
7.47 -0.1863961010
8.47 -0.3258602820
10.47 -0.7782023831
11.47 -0.4441289494
13.47 -0.2205225011
14.47 -0.3805842397
15.47 -0.1782922846
16.47 -0.4012269914
17.47 -0.0719212778
18.47 -0.2403244389
19.47 -0.1910120717
20.47 -0.1592447301
22.47 -0.2887199347
2.48 -0.3976628514
$subject
(Intercept)
2 0.069182352
3 -0.026390443
4 -0.165820844
5 -0.283550460
7 -0.102850472
8 0.246301798
10 0.643821985
11 0.227122951
13 -0.161636510
14 -0.019523555
15 0.018783237
16 0.004583795
17 -0.083039451
18 0.030074406
19 -0.175841242
20 -0.162848242
22 -0.064591129
23 0.006221823
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
1.0478162 0.7428822 0.6653752 0.5246917 0.3266944 0.3663530
=============================================================
--- RMS_Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 148.589 74.295 2 26916 467.851 < 2.2e-16 ***
Step 66.067 3.886 17 26321 24.473 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 3:
Step emmean SE df lower.CL upper.CL
1 0.565 0.0548 18.1 0.450 0.680
2 0.573 0.0551 18.4 0.458 0.689
3 0.572 0.0555 19.1 0.456 0.688
4 0.559 0.0548 18.1 0.444 0.675
5 0.563 0.0551 18.4 0.447 0.678
6 0.539 0.0555 19.1 0.423 0.655
7 0.542 0.0551 18.4 0.427 0.658
8 0.533 0.0551 18.4 0.417 0.648
9 0.523 0.0551 18.4 0.407 0.638
10 0.510 0.0551 18.4 0.394 0.625
11 0.516 0.0551 18.4 0.401 0.632
12 0.495 0.0551 18.4 0.380 0.611
13 0.493 0.0555 19.1 0.377 0.609
14 0.467 0.0551 18.4 0.352 0.583
15 0.464 0.0548 18.1 0.349 0.580
16 0.436 0.0555 19.1 0.320 0.552
17 0.426 0.0551 18.4 0.311 0.542
18 0.427 0.0548 18.1 0.312 0.543
Block = 4:
Step emmean SE df lower.CL upper.CL
1 0.770 0.0547 18.0 0.655 0.885
2 0.779 0.0550 18.3 0.664 0.894
3 0.778 0.0556 19.1 0.662 0.894
4 0.765 0.0547 18.0 0.650 0.880
5 0.769 0.0550 18.3 0.653 0.884
6 0.745 0.0555 19.1 0.628 0.861
7 0.748 0.0550 18.3 0.633 0.863
8 0.738 0.0550 18.3 0.623 0.854
9 0.728 0.0550 18.3 0.613 0.844
10 0.716 0.0550 18.3 0.600 0.831
11 0.722 0.0550 18.3 0.607 0.838
12 0.701 0.0550 18.3 0.585 0.816
13 0.698 0.0555 19.1 0.582 0.815
14 0.673 0.0550 18.3 0.558 0.788
15 0.670 0.0547 18.0 0.555 0.785
16 0.642 0.0556 19.1 0.525 0.758
17 0.632 0.0550 18.3 0.516 0.747
18 0.633 0.0547 18.0 0.518 0.748
Block = 5:
Step emmean SE df lower.CL upper.CL
1 0.669 0.0547 18.0 0.554 0.784
2 0.678 0.0550 18.3 0.562 0.793
3 0.677 0.0556 19.1 0.560 0.793
4 0.664 0.0547 18.0 0.549 0.779
5 0.667 0.0550 18.3 0.552 0.783
6 0.643 0.0556 19.1 0.527 0.760
7 0.647 0.0550 18.3 0.531 0.762
8 0.637 0.0550 18.3 0.522 0.752
9 0.627 0.0550 18.3 0.512 0.742
10 0.614 0.0550 18.3 0.499 0.730
11 0.621 0.0550 18.3 0.506 0.736
12 0.600 0.0550 18.3 0.484 0.715
13 0.597 0.0556 19.1 0.481 0.714
14 0.572 0.0550 18.3 0.456 0.687
15 0.569 0.0547 18.0 0.454 0.684
16 0.540 0.0556 19.1 0.424 0.657
17 0.531 0.0550 18.3 0.415 0.646
18 0.532 0.0547 18.0 0.417 0.647
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block3 - Block4 -0.206 0.00678 27005 -30.366 <.0001
Block3 - Block5 -0.105 0.00680 27019 -15.382 <.0001
Block4 - Block5 0.101 0.00605 26788 16.742 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
0.564698502 0.205740644 0.104527475 0.008600584 0.007507351 -0.005306805
Step5 Step6 Step7 Step8 Step9 Step10
-0.001828625 -0.025930414 -0.022401145 -0.032117734 -0.042148276 -0.054752408
Step11 Step12 Step13 Step14 Step15 Step16
-0.048302497 -0.069683969 -0.071950813 -0.097427331 -0.100261067 -0.128738678
Step17 Step18
-0.138648904 -0.137219795
Random Effects:
$trial_id
(Intercept)
3.1 -0.1249850239
4.1 -0.0507612361
5.1 -0.0743652753
7.1 0.0535520789
8.1 -0.0155482118
10.1 0.0356888472
11.1 -0.2067755309
13.1 -0.1065102611
14.1 -0.0679722960
15.1 -0.0667694286
16.1 -0.1710121509
17.1 -0.0880749348
18.1 0.0498897410
19.1 -0.0593279683
20.1 0.0628224262
22.1 -0.0513277619
23.1 -0.0873936871
2.2 -0.0520185392
3.2 -0.1736317456
4.2 -0.0565550992
5.2 -0.0367301271
7.2 -0.0339239647
8.2 0.0032443894
10.2 0.0770491813
11.2 -0.2074658634
13.2 0.0451123628
14.2 0.0081659916
15.2 0.0283667184
16.2 -0.0211579673
17.2 0.0049272856
19.2 0.0774209484
20.2 0.1193435736
22.2 0.1089094366
23.2 4.2554432960
2.3 -0.0939453904
3.3 -0.0874007835
4.3 -0.0222194001
5.3 -0.0006909712
7.3 -0.0442442311
8.3 0.2355886072
10.3 0.2805184376
11.3 0.2192081785
13.3 -0.1188600553
14.3 -0.0440594349
15.3 -0.2173023992
16.3 0.0793179206
17.3 0.0934769154
18.3 0.1319356267
19.3 -0.0779252066
20.3 0.1612296127
22.3 -0.0110808173
23.3 0.0364498737
2.4 0.0026456352
3.4 -0.0183255098
4.4 -0.0730641992
5.4 -0.0653325310
7.4 0.1487270928
8.4 0.0221258429
10.4 -0.3902158865
11.4 0.3084427814
13.4 0.0536271910
14.4 0.1123399933
15.4 -0.1049387805
16.4 -0.0433720075
17.4 -0.0735023543
18.4 -0.0659384170
19.4 -0.0564009654
20.4 0.0477451661
22.4 -0.0309993123
23.4 -0.0521092531
2.5 0.0715995856
3.5 0.0321257160
4.5 -0.0746859546
5.5 -0.1448126310
7.5 0.0087168201
8.5 0.0974080925
10.5 0.4493299951
11.5 0.0852095138
13.5 0.1371156990
14.5 0.2111198566
15.5 0.0565919215
16.5 0.0801718824
17.5 0.2959578713
18.5 -0.0294540078
19.5 -0.1302533343
20.5 -0.1003996158
22.5 -0.0432860518
23.5 -0.1263321925
2.6 0.1125182124
3.6 0.0220213523
4.6 0.0611815377
5.6 0.1081766266
7.6 0.2198953285
8.6 0.3118973882
10.6 0.4667503757
11.6 0.1775909449
13.6 0.2238376994
14.6 0.0593784778
15.6 -0.1675148033
16.6 -0.1877329896
17.6 0.0264522701
18.6 0.0268067411
19.6 -0.1285887692
20.6 0.0370161245
22.6 0.0515345136
23.6 -0.0946008337
2.7 -0.2165920701
3.7 0.2678615948
4.7 -0.0779945031
5.7 0.1043837778
7.7 0.0156796819
8.7 -0.0049178881
10.7 0.3323878968
11.7 0.0559680122
13.7 0.0516886576
14.7 0.1745044672
15.7 -0.1340693411
16.7 0.1666298403
17.7 0.0450750663
18.7 0.0368136702
19.7 0.0347198175
20.7 -0.0975262283
22.7 -0.0340496503
23.7 0.0675085410
2.8 0.1753137370
3.8 0.0839150555
4.8 -0.0464004044
5.8 -0.1557681037
7.8 -0.0513599060
8.8 0.2382704843
10.8 0.0717098154
11.8 -0.1479630446
13.8 0.1127875871
14.8 -0.0230054581
15.8 -0.0982746255
16.8 -0.0386125765
17.8 -0.0155207253
18.8 0.0024887996
19.8 -0.0053340139
20.8 -0.0994347272
22.8 -0.0143409639
23.8 0.0296373205
2.9 0.0521680010
3.9 0.0108337554
4.9 -0.0587989755
5.9 0.0370065980
7.9 0.0314152082
8.9 -0.2313001781
10.9 0.2576649755
11.9 0.0677721760
13.9 0.0051458938
14.9 -0.0375230496
15.9 -0.1050447054
16.9 0.0603729675
17.9 0.1203548931
18.9 -0.0886236843
19.9 -0.0829578500
20.9 0.0013990325
22.9 0.0246365155
23.9 -0.1056274852
2.10 -0.0624521933
3.10 0.1432915730
4.10 -0.0107847647
5.10 0.0050076763
7.10 0.0331576593
8.10 -0.1028210276
10.10 0.3684022335
11.10 -0.1409659342
13.10 -0.0469404736
14.10 0.1553778281
15.10 -0.1115684716
16.10 -0.0572443602
17.10 0.1099854087
18.10 0.0949159527
19.10 0.1021088172
20.10 0.2013803900
22.10 0.0155000618
23.10 -0.2877322793
2.11 0.0817316656
3.11 0.1720244549
4.11 -0.0653169249
5.11 -0.0459221313
7.11 0.0200875738
8.11 0.2548269352
10.11 0.2003903254
11.11 -0.1320898836
13.11 0.0380423731
14.11 -0.1106400734
15.11 -0.0869735609
16.11 -0.0168289734
17.11 -0.0521590440
18.11 0.0666125555
19.11 -0.0930012030
20.11 0.0935266515
22.11 0.0310761363
23.11 -0.0408460705
2.12 -0.0044033596
3.12 0.4927388238
4.12 0.1933658743
5.12 0.0649214323
7.12 -0.0566285587
8.12 0.0580566513
10.12 0.3885316353
11.12 -0.1620765247
13.12 0.0153586803
14.12 0.0810767239
15.12 -0.0224369365
16.12 0.0142839752
17.12 0.0290208505
18.12 -0.0516820589
19.12 0.0904001847
20.12 0.0008358097
22.12 -0.0527317362
23.12 -0.1692314669
2.13 0.0320505756
3.13 -0.0279115303
4.13 -0.0904533347
5.13 -0.0958309596
7.13 -0.0217755630
8.13 0.0377449867
10.13 0.4410434182
11.13 -0.1227630596
13.13 0.0439547145
14.13 0.1596401383
15.13 -0.1437172397
16.13 -0.0648925437
17.13 0.0664192455
18.13 0.0417208531
19.13 -0.0490649142
20.13 -0.0153892931
22.13 0.0477506037
23.13 -0.0952635011
2.14 0.0144997608
3.14 0.1665451343
4.14 -0.2130704048
5.14 0.0297493170
7.14 0.0863642480
8.14 0.5248586058
10.14 0.3021242886
11.14 0.0615389193
13.14 -0.0191112743
14.14 0.0293953676
15.14 0.2664294588
16.14 -0.0503582781
17.14 -0.0822124505
18.14 0.2567763418
19.14 0.0272673263
20.14 0.2889518074
22.14 -0.0557530219
23.14 -0.1458842605
2.15 0.0580950086
3.15 0.0867187382
4.15 0.0088420633
5.15 0.0322119329
7.15 -0.0809067503
8.15 -0.0374360430
10.15 0.2488324133
11.15 -0.2230990834
13.15 -0.0002534088
14.15 -0.0723394201
15.15 0.1329972320
16.15 0.0239122130
17.15 0.0035108003
18.15 -0.0668108751
19.15 -0.0285441368
20.15 -0.0563268930
22.15 -0.0857297713
23.15 -0.1142601903
2.16 -0.0747833354
3.16 0.1860884104
4.16 -0.0921018859
5.16 0.1034270664
7.16 -0.1764072212
8.16 0.2494409871
10.16 0.3285454717
11.16 -0.0286459970
13.16 -0.0451445611
14.16 -0.0514266743
15.16 0.1515682290
16.16 -0.0399459040
17.16 0.0613555694
18.16 0.1920246053
19.16 -0.0824611797
20.16 -0.1100742299
22.16 -0.0570961026
23.16 -0.2480442508
2.17 0.0596768626
3.17 0.2399416884
4.17 0.0945529791
5.17 0.2028044790
7.17 -0.2365312268
8.17 0.2140907453
10.17 0.5581012915
11.17 -0.0416698262
13.17 0.0268601200
14.17 0.0612916699
15.17 0.1865290245
16.17 -0.0301306865
17.17 -0.0239062145
18.17 0.1238237499
19.17 0.0017820814
20.17 0.0008693159
22.17 -0.0015199524
23.17 -0.0438855412
2.18 0.2671418680
3.18 0.0213311728
4.18 0.0235358160
5.18 0.0716429515
7.18 0.1717990452
8.18 0.0196534845
10.18 0.2120986505
11.18 -0.1761867351
13.18 -0.1001395071
14.18 -0.1874947067
15.18 0.2846187236
16.18 0.0116426846
17.18 0.0002529696
18.18 0.1097239729
19.18 -0.0924117878
20.18 -0.0213198213
22.18 0.0276433973
23.18 0.1522366465
2.19 0.1586510370
3.19 0.2246922976
4.19 -0.1027770807
5.19 -0.1269687484
7.19 0.0683169882
8.19 -0.0265636643
10.19 0.2769706679
11.19 0.1345010391
13.19 0.0151308691
14.19 -0.0831092250
15.19 0.0462220572
16.19 0.2136742394
17.19 -0.1307127679
18.19 -0.1100791895
19.19 0.0277764171
20.19 -0.0589281230
22.19 -0.0785309028
23.19 0.2042793190
2.20 0.2415674991
3.20 0.2886368276
4.20 0.0568367011
5.20 -0.0399005127
7.20 -0.0587844758
8.20 -0.1009373474
10.20 0.4970654343
11.20 -0.2449104943
13.20 0.1652895616
14.20 -0.0008315372
15.20 -0.1367397571
16.20 -0.0737028505
17.20 0.1817559366
18.20 0.0364577611
19.20 -0.0036438563
20.20 -0.0246327905
22.20 -0.0283294381
23.20 -0.2579343055
2.21 0.3539916041
3.21 0.0304571251
4.21 -0.0202151653
5.21 -0.0992328512
7.21 0.1264649865
8.21 0.0888827342
10.21 0.5975974576
11.21 -0.1183065133
13.21 0.2456590404
14.21 0.0203284623
15.21 0.0603820157
16.21 0.0165958812
17.21 0.0102680366
18.21 -0.0166169245
19.21 0.0013765331
20.21 -0.1128055895
22.21 -0.0634312116
23.21 -0.1107886375
2.22 0.3244458679
3.22 -0.0968086250
4.22 0.1476282660
5.22 0.0291604513
7.22 -0.0408374460
8.22 0.3828106232
10.22 0.3163048809
11.22 0.0608810486
13.22 0.0363627441
14.22 -0.0612848487
15.22 -0.0574171231
16.22 0.0764248654
17.22 0.0780763089
18.22 0.0120684934
19.22 0.0246538336
20.22 -0.0111643756
22.22 -0.0137288118
23.22 0.2218607354
2.23 -0.0909212666
3.23 0.1413902141
4.23 0.2065393769
5.23 0.0452051470
7.23 0.0187513758
8.23 0.3247168688
10.23 0.4758739235
11.23 -0.1086617607
13.23 -0.0354580593
14.23 -0.0135956002
15.23 0.1468609310
16.23 0.0921746466
17.23 0.0996909737
18.23 0.1554258673
19.23 -0.0216911225
20.23 -0.0341732561
22.23 0.0437412066
23.23 0.0408768273
2.24 0.0197330197
3.24 0.1082394295
4.24 -0.0039127474
5.24 0.0445391026
7.24 0.2104736048
8.24 0.2687071073
10.24 0.1215447592
11.24 -0.2148517233
13.24 0.1306882862
14.24 -0.0157354114
15.24 -0.0384008678
16.24 -0.0386677052
17.24 0.0849011726
18.24 0.1091221140
19.24 -0.0041405172
20.24 0.0516945117
22.24 -0.0097622727
23.24 0.0747996300
2.25 0.3771342963
3.25 -0.0488477781
4.25 -0.0744038374
5.25 -0.0828486581
7.25 0.0191862513
8.25 -0.0010374384
10.25 0.2400215585
11.25 0.5555810601
13.25 0.2300554589
14.25 -0.0749018613
15.25 0.0333340310
16.25 0.0739500686
17.25 0.0098992335
18.25 0.0384176178
19.25 -0.1211806585
20.25 -0.0789244015
22.25 -0.0479760948
23.25 0.2078609849
2.26 0.1913414934
3.26 0.0019219912
4.26 0.0739371844
5.26 0.1976030421
7.26 -0.1348411940
8.26 0.3893870761
10.26 0.6141414904
11.26 0.3935237847
13.26 0.1091116671
14.26 0.0439909110
15.26 -0.0654528861
16.26 0.0661338026
17.26 -0.0358747789
18.26 -0.0063596222
19.26 -0.0508079552
20.26 -0.0176989385
22.26 -0.0570269520
23.26 -0.0066163678
2.27 0.3431401410
3.27 0.1092189153
4.27 -0.1466679364
5.27 0.2338506269
7.27 0.0288124785
8.27 0.0764480807
10.27 0.2248864656
11.27 0.1890603345
13.27 0.1687302003
14.27 0.0369950017
15.27 -0.0718790740
16.27 0.1488707621
17.27 -0.0767151855
18.27 0.0967946303
19.27 0.0147565020
20.27 0.0222268488
22.27 0.0020218607
23.27 0.3187913669
2.28 0.0203117637
3.28 0.0047328743
4.28 -0.1604409434
5.28 0.0983313482
7.28 -0.0485502630
8.28 0.7264539321
10.28 -0.3325723602
11.28 -0.0810256738
13.28 0.3875295795
14.28 0.0100383896
15.28 0.0512143004
16.28 0.1503986540
17.28 0.2291630683
18.28 -0.2718808251
19.28 -0.0099372533
20.28 -0.0493994099
22.28 0.0301554246
23.28 -0.0664865007
2.29 0.2696799453
3.29 0.6525303337
4.29 0.1248665504
5.29 0.0294850513
7.29 0.0606702460
8.29 0.0908779017
10.29 0.1319553775
11.29 -0.3049006464
13.29 0.0607040112
14.29 0.3103422060
15.29 0.1213124491
16.29 0.1307913782
17.29 0.1344932908
18.29 -0.0796554578
19.29 0.2199584465
20.29 0.0655686776
22.29 0.1725346848
23.29 -0.1678371089
2.30 0.3638501072
3.30 -0.1549825211
4.30 0.1129065576
5.30 0.0445706788
7.30 -0.0082943798
8.30 0.1557952731
10.30 -0.4657210878
11.30 0.1761859102
13.30 0.0630996017
14.30 0.1517824915
15.30 -0.0320429105
16.30 0.1257847418
17.30 -0.0175286044
18.30 0.2460179885
19.30 0.0322356160
20.30 0.0094390644
22.30 0.0004541976
23.30 -0.3827670199
2.31 -0.0334701252
3.31 0.1951687604
4.31 0.2404129302
5.31 0.0157799726
7.31 -0.0981209137
8.31 -0.1400345417
10.31 0.1335015062
11.31 0.0243170609
13.31 0.1095786682
14.31 0.0238593939
15.31 0.1021623483
16.31 0.2472968702
17.31 0.0656362417
18.31 0.1722995752
19.31 -0.0457517754
20.31 -0.0811781434
22.31 -0.0275533198
23.31 -0.0131255321
2.32 -0.0222100838
3.32 -0.0642960692
4.32 0.2745761428
5.32 0.1074347953
7.32 0.1037456929
8.32 0.2166803153
10.32 -0.2269669128
11.32 0.9989938985
13.32 -0.1381189559
14.32 -0.2029845771
15.32 0.1256595159
16.32 0.0851167000
17.32 -0.0312070024
18.32 0.0532482027
19.32 -0.0487501338
20.32 -0.0478422931
22.32 0.0315591557
23.32 0.2281871256
2.33 0.0115932794
3.33 -0.1378499996
4.33 -0.1113740591
5.33 0.0703488379
7.33 0.1358480968
8.33 0.1153986601
10.33 -0.2546213207
11.33 0.4400189018
13.33 0.0667601826
14.33 -0.0131728411
15.33 -0.0851379938
16.33 -0.1875190850
17.33 -0.0860099898
18.33 0.1394010964
19.33 0.1243325840
20.33 0.0568981014
22.33 -0.0257564680
23.33 0.0316983316
2.34 0.0554741853
3.34 0.0944538853
4.34 -0.1823106985
5.34 -0.0847040951
7.34 0.2915144203
8.34 0.0491679483
10.34 0.2289964458
11.34 0.1740680150
13.34 0.3273208461
14.34 -0.0936233325
15.34 0.0795309868
16.34 0.1792610763
17.34 0.0372408898
18.34 -0.0882444277
19.34 0.0154623462
20.34 0.0470468400
22.34 0.0063297675
23.34 -0.2301229377
2.35 -0.0260431395
3.35 -0.3495914583
4.35 -0.0316098531
5.35 0.0091603084
7.35 -0.0608855858
8.35 -0.3762505515
10.35 -0.3699674708
11.35 0.8563854875
13.35 -0.0663588751
14.35 0.4006780585
15.35 0.3001223539
16.35 0.1640447123
17.35 0.0816657613
18.35 -0.1550006898
19.35 -0.0171700603
20.35 -0.1010177352
22.35 0.1719399139
23.35 0.1709546412
2.36 0.0450284193
3.36 0.1189279675
4.36 -0.0809722337
5.36 -0.1676568948
7.36 0.0670363726
8.36 -0.4065741080
10.36 -0.1858712941
11.36 0.1343802179
13.36 0.2273485805
14.36 0.1412542993
15.36 -0.0147839588
16.36 0.1481485023
17.36 0.0320217599
18.36 -0.1934872796
19.36 -0.0034194552
20.36 -0.0513515349
22.36 0.1854579914
23.36 -0.0005476344
2.37 -0.0418937243
3.37 0.1122156434
4.37 0.1076234327
5.37 -0.0970879868
7.37 0.0386351124
8.37 -0.0918562563
10.37 -0.5381297042
11.37 -0.1833681916
13.37 -0.1721084060
14.37 -0.0141072581
15.37 -0.1082684458
16.37 0.0686621219
17.37 0.0927961127
18.37 0.0408714227
19.37 0.0103900001
20.37 0.0756988944
22.37 0.1152915593
23.37 -0.2100572590
2.38 -0.1122335447
3.38 -0.3038522445
4.38 0.2131264925
5.38 -0.1565991024
7.38 -0.1032056667
8.38 -0.0561402553
10.38 -0.5566531859
11.38 -0.0308301834
13.38 -0.2434980173
14.38 -0.0703233436
15.38 0.0764988558
16.38 -0.0208237881
17.38 0.0184894615
18.38 -0.0607795644
19.38 -0.0063858726
20.38 -0.1199866634
22.38 0.0843691909
23.38 -0.2438350903
2.39 -0.0324030359
3.39 0.2736057691
4.39 -0.0562122036
5.39 -0.0888861127
7.39 -0.0619716062
8.39 -0.3955150882
10.39 -0.5255927369
11.39 0.0368413943
13.39 -0.1343450889
14.39 0.1195016405
15.39 0.0544903439
16.39 -0.0740269764
17.39 -0.1434619786
18.39 -0.0342415850
19.39 -0.0479732451
20.39 0.0273401660
22.39 0.1689969116
23.39 -0.3114128525
2.40 0.0371533059
3.40 -0.2363847788
4.40 -0.0279352637
5.40 -0.1272479756
7.40 0.1573856123
8.40 -0.2355314069
10.40 -0.4200678195
11.40 -0.3557265465
13.40 -0.1310922624
14.40 -0.1271791220
15.40 0.0151520326
16.40 0.1377009472
17.40 -0.1444236169
18.40 0.0685267176
19.40 0.0199647972
20.40 0.0827906064
22.40 -0.0839416047
23.40 -0.1898366663
2.41 -0.2656793311
3.41 -0.3503324090
4.41 0.0705667772
5.41 -0.0267981713
7.41 -0.1006352686
8.41 -0.3682060057
10.41 -0.9388897729
11.41 -0.2050693748
13.41 -0.3136526509
14.41 0.0169374272
15.41 -0.1692136011
16.41 0.2034128644
17.41 0.0199835372
18.41 -0.1146549719
19.41 0.1326690419
20.41 -0.1387395659
22.41 0.1124105221
23.41 -0.3551515640
2.42 -0.0836762810
3.42 -0.2061020718
4.42 0.0732653697
5.42 0.1108943760
7.42 -0.0272789196
8.42 -0.3974658800
10.42 0.0032216223
11.42 -0.2923814924
13.42 -0.3660535478
14.42 0.0576737168
15.42 -0.1737475751
16.42 0.0851555396
17.42 -0.1950518251
18.42 0.0111477034
19.42 0.1248030156
20.42 0.0081650306
22.42 0.0431385654
23.42 0.0911056411
2.43 0.0906488032
3.43 -0.0263688342
4.43 -0.1603000030
5.43 -0.0762300716
7.43 -0.0466217768
8.43 -0.6238581184
10.43 -0.4400309570
11.43 -0.1390727252
13.43 -0.3676821796
14.43 0.0157695898
15.43 -0.0863570830
16.43 -0.2760981203
17.43 -0.2540933018
18.43 0.0277921856
19.43 0.0058698409
20.43 0.0247636784
22.43 -0.1874149350
23.43 -0.3107931142
2.44 -0.5131265932
3.44 -0.3566035783
4.44 -0.0843803513
5.44 -0.1469636822
7.44 0.0938559299
8.44 -0.4274153888
10.44 -0.3706086799
11.44 -0.1485897498
13.44 -0.1902559931
14.44 -0.1173216309
15.44 0.0910637664
16.44 -0.2885242917
17.44 -0.1933249941
18.44 -0.1239149570
19.44 0.1367432474
20.44 0.0345573248
22.44 -0.1894618027
23.44 -0.3836843722
2.45 -0.2682180734
3.45 -0.1385298179
4.45 0.0273101929
5.45 -0.0093852545
7.45 -0.2443128751
8.45 -0.0921581880
10.45 -0.5071733110
11.45 -0.3337310560
13.45 -0.2265411036
14.45 -0.3546996401
15.45 -0.1871766600
16.45 -0.3055263049
17.45 0.0913238367
18.45 -0.1775778814
19.45 0.0053848966
20.45 -0.0454884193
22.45 -0.2548470115
23.45 -0.5489506880
2.46 -0.5003081568
3.46 -0.5435190587
4.46 -0.0687881975
5.46 -0.0682242547
7.46 -0.3582018246
8.46 -0.3895426493
10.46 -0.8563974192
11.46 -0.2723164800
13.46 -0.3146854138
14.46 -0.3554080555
15.46 -0.0583913333
16.46 -0.3993427160
17.46 -0.2730550987
18.46 -0.2306147735
19.46 -0.1141265435
20.46 -0.1461225609
22.46 -0.2061831416
23.46 -0.5797271236
2.47 -0.4053964349
3.47 -0.5843442484
4.47 -0.1116486993
5.47 -0.0820804275
7.47 -0.2572971165
8.47 -0.2666242507
10.47 -0.7903973358
11.47 -0.4258296960
13.47 -0.2048171967
14.47 -0.2499083100
15.47 0.0806081849
16.47 -0.4569111886
17.47 -0.2520815913
18.47 -0.3183309038
19.47 -0.1957707604
20.47 -0.1570753890
22.47 -0.0698820576
2.48 -0.5925574955
$subject
(Intercept)
2 0.265190990
3 0.196405543
4 -0.191804327
5 -0.238361803
7 -0.110759101
8 0.285496441
10 0.556729862
11 0.079196385
13 -0.191526422
14 -0.032248022
15 -0.040620783
16 0.005868336
17 -0.034999755
18 0.044746566
19 -0.271522903
20 -0.200106459
22 -0.239706031
23 0.118021482
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.6184802 0.3341352 0.1630040 0.1137539 0.1767147 0.1234074
=============================================================
--- RMS_Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 466.10 233.050 2 26803 520.298 < 2.2e-16 ***
Step 219.17 12.893 17 26304 28.784 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means (Step | Block):
Block = 3:
Step emmean SE df lower.CL upper.CL
1 1.220 0.131 17.6 0.945 1.50
2 1.238 0.131 17.7 0.963 1.51
3 1.243 0.132 18.0 0.967 1.52
4 1.214 0.131 17.6 0.939 1.49
5 1.228 0.131 17.7 0.953 1.50
6 1.179 0.132 18.0 0.903 1.46
7 1.188 0.131 17.7 0.912 1.46
8 1.148 0.131 17.7 0.872 1.42
9 1.139 0.131 17.7 0.863 1.41
10 1.129 0.131 17.7 0.853 1.40
11 1.128 0.131 17.7 0.852 1.40
12 1.108 0.131 17.7 0.832 1.38
13 1.110 0.132 18.0 0.833 1.39
14 1.058 0.131 17.7 0.783 1.33
15 1.044 0.131 17.6 0.769 1.32
16 1.017 0.132 18.0 0.740 1.29
17 0.971 0.131 17.7 0.696 1.25
18 0.956 0.131 17.6 0.681 1.23
Block = 4:
Step emmean SE df lower.CL upper.CL
1 1.577 0.131 17.5 1.302 1.85
2 1.595 0.131 17.6 1.320 1.87
3 1.601 0.132 18.0 1.324 1.88
4 1.571 0.131 17.5 1.296 1.85
5 1.585 0.131 17.6 1.310 1.86
6 1.537 0.132 18.0 1.260 1.81
7 1.545 0.131 17.6 1.270 1.82
8 1.505 0.131 17.6 1.230 1.78
9 1.496 0.131 17.6 1.221 1.77
10 1.486 0.131 17.6 1.211 1.76
11 1.485 0.131 17.6 1.210 1.76
12 1.465 0.131 17.6 1.190 1.74
13 1.467 0.132 18.0 1.191 1.74
14 1.416 0.131 17.6 1.140 1.69
15 1.401 0.131 17.5 1.126 1.68
16 1.374 0.132 18.0 1.098 1.65
17 1.329 0.131 17.6 1.053 1.60
18 1.314 0.131 17.5 1.039 1.59
Block = 5:
Step emmean SE df lower.CL upper.CL
1 1.366 0.131 17.5 1.091 1.64
2 1.384 0.131 17.6 1.109 1.66
3 1.390 0.132 18.0 1.113 1.67
4 1.360 0.131 17.5 1.085 1.63
5 1.374 0.131 17.6 1.099 1.65
6 1.325 0.132 18.0 1.049 1.60
7 1.334 0.131 17.6 1.059 1.61
8 1.294 0.131 17.6 1.019 1.57
9 1.285 0.131 17.6 1.010 1.56
10 1.275 0.131 17.6 1.000 1.55
11 1.274 0.131 17.6 0.999 1.55
12 1.254 0.131 17.6 0.979 1.53
13 1.256 0.132 18.0 0.980 1.53
14 1.205 0.131 17.6 0.929 1.48
15 1.190 0.131 17.5 0.915 1.46
16 1.163 0.132 18.0 0.887 1.44
17 1.118 0.131 17.6 0.842 1.39
18 1.103 0.131 17.5 0.828 1.38
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Block3 - Block4 -0.357 0.0114 26883 -31.327 <.0001
Block3 - Block5 -0.146 0.0114 26899 -12.789 <.0001
Block4 - Block5 0.211 0.0102 26691 20.752 <.0001
Results are averaged over the levels of: Step
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 3 estimates
Fixed Effects:
(Intercept) Block4 Block5 Step2 Step3 Step4
1.219946849 0.357346392 0.146330522 0.018126705 0.023501131 -0.006224500
Step5 Step6 Step7 Step8 Step9 Step10
0.008083846 -0.040783021 -0.032341414 -0.072231370 -0.081163647 -0.091234498
Step11 Step12 Step13 Step14 Step15 Step16
-0.092201882 -0.112003318 -0.110229408 -0.161747523 -0.176319988 -0.203231972
Step17 Step18
-0.248616922 -0.263532713
Random Effects:
$trial_id
(Intercept)
3.1 -0.1637178779
4.1 -0.0815662041
5.1 0.2391863946
7.1 0.2598170089
8.1 -0.2152435949
10.1 0.4562292565
11.1 0.1689330846
13.1 -0.0795209696
14.1 0.5145645747
15.1 0.2498049222
16.1 0.1711051474
17.1 0.0192939388
18.1 0.4299560337
19.1 -0.1458772750
20.1 0.0399780995
22.1 0.0363615976
23.1 -0.1359486736
2.2 0.2224135775
3.2 -0.5654540629
4.2 -0.0197866798
5.2 0.1004132728
7.2 0.1701185563
8.2 -0.2981609962
10.2 0.5407991277
11.2 -0.3366076098
13.2 0.1358128256
14.2 -0.1701041686
15.2 0.2020154400
16.2 0.4743358998
17.2 0.2944297986
19.2 -0.1273922007
20.2 0.1265951821
22.2 -0.0435701128
23.2 1.7435503316
2.3 0.1552059024
3.3 0.2324814253
4.3 0.0788976625
5.3 -0.2255448059
7.3 0.4854633714
8.3 -0.0768119979
10.3 1.2357686732
11.3 0.5821999045
13.3 0.2572857554
14.3 -0.2108455467
15.3 0.3796907330
16.3 0.9959209531
17.3 0.1073085228
18.3 0.1290808922
19.3 0.1413520090
20.3 0.2825539387
22.3 -0.0700556417
23.3 -0.0845893774
2.4 -0.0147743894
3.4 -0.2488706283
4.4 0.0176608872
5.4 -0.0977085570
7.4 0.2163521567
8.4 -0.4275654711
10.4 0.7868973645
11.4 0.5747253244
13.4 0.0553946199
14.4 0.8504836850
15.4 -0.1214663559
16.4 0.4885082264
17.4 0.1332053042
18.4 0.6379447153
19.4 -0.0872818366
20.4 -0.1042941587
22.4 0.1470857244
23.4 -0.2898928244
2.5 -0.0381215095
3.5 0.1278701704
4.5 0.0680617778
5.5 -0.2875557739
7.5 0.2761482383
8.5 -0.1671252468
10.5 1.5631080563
11.5 0.4712355776
13.5 0.6039834947
14.5 0.6515499229
15.5 0.1742934388
16.5 0.5569457335
17.5 0.1014030174
18.5 0.3461924085
19.5 -0.1429768547
20.5 -0.3774947592
22.5 0.1964174535
23.5 -0.0939458890
2.6 -0.3144859623
3.6 -0.2143040077
4.6 0.0557566384
5.6 0.1710145587
7.6 0.7895814712
8.6 0.9495943047
10.6 0.7962235624
11.6 0.3113687694
13.6 0.4721727706
14.6 0.3776076188
15.6 -0.1340526231
16.6 -0.1843390745
17.6 0.0378271798
18.6 0.8005337152
19.6 -0.0995310330
20.6 -0.1686797486
22.6 0.0194948147
23.6 0.2654415601
2.7 -0.3738104887
3.7 0.4764205467
4.7 0.1535700688
5.7 0.0992422840
7.7 0.5303953042
8.7 0.0680191929
10.7 1.6413802011
11.7 0.2135127977
13.7 0.7812175686
14.7 0.4476528734
15.7 -0.1527852456
16.7 0.5883261616
17.7 0.0047338041
18.7 0.2726670880
19.7 0.1490500587
20.7 -0.2359969726
22.7 -0.0771724945
23.7 0.3341903800
2.8 0.1540431548
3.8 0.3491080847
4.8 -0.0491686941
5.8 -0.2197140625
7.8 0.5457403416
8.8 -0.0145456833
10.8 0.5776683060
11.8 0.1936162181
13.8 0.5674406852
14.8 -0.1359924087
15.8 -0.3747785934
16.8 0.3680817459
17.8 0.0073295806
18.8 0.2863425626
19.8 0.1191442084
20.8 -0.0954641962
22.8 0.2059830664
23.8 0.0497662384
2.9 -0.3191230933
3.9 0.1816075946
4.9 -0.0596588043
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18.47 -0.9720001357
19.47 -0.3694330857
20.47 -0.3132193255
22.47 -0.5633458196
2.48 -0.9226659263
$subject
(Intercept)
2 -0.02898547
3 0.18026470
4 -0.51925966
5 -0.65750137
7 0.18599708
8 0.37715748
10 1.68351789
11 0.22509990
13 -0.18066826
14 -0.15034864
15 0.09038732
16 0.19134839
17 -0.39320912
18 0.33325712
19 -0.61380972
20 -0.39736447
22 -0.47922581
23 0.15334265
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.9727586 0.6818716 0.4764641 0.4835448 0.3609605 0.2563628
=============================================================#3.1 concatenation analysis rms training blocks 1,2,3
# Generate step summaries separately to avoid overwriting
result_6 <- plot_stepwise_rms_blocks_145_first6(tagged_data2)
result_12 <- plot_stepwise_rms_blocks_245_12steps(tagged_data2)
result_18 <- plot_stepwise_rms_blocks_345_18steps(tagged_data2)
# Extract clean step_summary objects
step_summary_6 <- result_6$step_summary
step_summary_12 <- result_12$step_summary
step_summary_18 <- result_18$step_summaryaxes <- c("X", "Y", "Z")
cat("\n\n================ Block 1 (6 Steps) ================\n")
================ Block 1 (6 Steps) ================for (ax in axes) {
cat(glue::glue("\n--- Axis: {ax} ---\n"))
df_b1 <- step_summary_6 %>%
filter(Block == "1", Axis == ax, Step %in% as.character(1:6)) %>%
mutate(Step = factor(Step))
if (nrow(df_b1) == 0) {
cat("No valid data for Block 1, Axis", ax, "\n")
next
}
model_b1 <- lmer(RMS ~ Step + (1 | subject) + (1 | trial_id), data = df_b1)
anova_b1 <- car::Anova(model_b1, type = 2, test.statistic = "Chisq")
emms_b1 <- emmeans(model_b1, ~ Step)
pairwise_b1 <- contrast(emms_b1, method = "pairwise", adjust = "tukey")
print(anova_b1)
cat("\nEstimated Marginal Means:\n")
print(summary(emms_b1))
cat("\nPairwise Comparisons:\n")
print(pairwise_b1)
}--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 11.351 5 0.04485 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.868 0.128 17 0.599 1.14
2 0.869 0.128 17 0.599 1.14
3 0.860 0.128 17 0.591 1.13
4 0.861 0.128 17 0.591 1.13
5 0.880 0.128 17 0.611 1.15
6 0.865 0.128 17 0.596 1.13
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.000397 0.00677 3151 -0.059 1.0000
Step1 - Step3 0.007712 0.00677 3151 1.139 0.8653
Step1 - Step4 0.007607 0.00678 3151 1.121 0.8726
Step1 - Step5 -0.011848 0.00677 3151 -1.749 0.4991
Step1 - Step6 0.003061 0.00677 3151 0.452 0.9976
Step2 - Step3 0.008109 0.00677 3151 1.197 0.8384
Step2 - Step4 0.008004 0.00678 3151 1.180 0.8465
Step2 - Step5 -0.011451 0.00677 3151 -1.691 0.5381
Step2 - Step6 0.003458 0.00677 3151 0.511 0.9958
Step3 - Step4 -0.000106 0.00679 3151 -0.016 1.0000
Step3 - Step5 -0.019561 0.00678 3151 -2.886 0.0453
Step3 - Step6 -0.004651 0.00677 3151 -0.687 0.9835
Step4 - Step5 -0.019455 0.00679 3151 -2.865 0.0481
Step4 - Step6 -0.004546 0.00678 3151 -0.670 0.9852
Step5 - Step6 0.014909 0.00677 3151 2.201 0.2374
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 1.8679 5 0.8671
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.862 0.151 17 0.544 1.18
2 0.867 0.151 17 0.550 1.18
3 0.866 0.151 17 0.548 1.18
4 0.865 0.151 17 0.548 1.18
5 0.862 0.151 17 0.545 1.18
6 0.857 0.151 17 0.540 1.17
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -5.48e-03 0.00858 3151 -0.639 0.9881
Step1 - Step3 -3.55e-03 0.00859 3151 -0.413 0.9985
Step1 - Step4 -3.50e-03 0.00860 3151 -0.407 0.9986
Step1 - Step5 -2.64e-04 0.00859 3151 -0.031 1.0000
Step1 - Step6 4.92e-03 0.00858 3151 0.573 0.9927
Step2 - Step3 1.93e-03 0.00859 3151 0.224 0.9999
Step2 - Step4 1.98e-03 0.00860 3151 0.230 0.9999
Step2 - Step5 5.21e-03 0.00859 3151 0.607 0.9906
Step2 - Step6 1.04e-02 0.00858 3151 1.212 0.8312
Step3 - Step4 5.01e-05 0.00861 3151 0.006 1.0000
Step3 - Step5 3.29e-03 0.00859 3151 0.383 0.9989
Step3 - Step6 8.47e-03 0.00859 3151 0.986 0.9224
Step4 - Step5 3.24e-03 0.00861 3151 0.376 0.9990
Step4 - Step6 8.42e-03 0.00860 3151 0.979 0.9247
Step5 - Step6 5.18e-03 0.00859 3151 0.604 0.9908
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 21.5 5 0.0006515 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.78 0.249 17.1 1.25 2.30
2 1.85 0.249 17.1 1.33 2.37
3 1.81 0.249 17.1 1.29 2.34
4 1.81 0.249 17.1 1.29 2.34
5 1.82 0.249 17.1 1.30 2.35
6 1.79 0.249 17.1 1.27 2.32
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.07159 0.0169 3151 -4.238 0.0003
Step1 - Step3 -0.03566 0.0169 3151 -2.109 0.2830
Step1 - Step4 -0.03589 0.0169 3151 -2.119 0.2775
Step1 - Step5 -0.04665 0.0169 3151 -2.759 0.0646
Step1 - Step6 -0.01574 0.0169 3151 -0.932 0.9384
Step2 - Step3 0.03594 0.0169 3151 2.125 0.2744
Step2 - Step4 0.03571 0.0169 3151 2.109 0.2830
Step2 - Step5 0.02494 0.0169 3151 1.475 0.6803
Step2 - Step6 0.05585 0.0169 3151 3.306 0.0123
Step3 - Step4 -0.00023 0.0170 3151 -0.014 1.0000
Step3 - Step5 -0.01099 0.0169 3151 -0.650 0.9871
Step3 - Step6 0.01992 0.0169 3151 1.178 0.8475
Step4 - Step5 -0.01076 0.0170 3151 -0.635 0.9884
Step4 - Step6 0.02015 0.0169 3151 1.190 0.8419
Step5 - Step6 0.03091 0.0169 3151 1.828 0.4477
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates cat("\n\n================ Block 2 (12 Steps) ================\n")
================ Block 2 (12 Steps) ================for (ax in axes) {
cat(glue::glue("\n--- Axis: {ax} ---\n"))
df_b2 <- step_summary_12 %>%
filter(Block == "2", Axis == ax, Step %in% as.character(1:12)) %>%
mutate(Step = factor(Step))
if (nrow(df_b2) == 0) {
cat("No valid data for Block 2, Axis", ax, "\n")
next
}
model_b2 <- lmer(RMS ~ Step + (1 | subject) + (1 | trial_id), data = df_b2)
anova_b2 <- car::Anova(model_b2, type = 2, test.statistic = "Chisq")
emms_b2 <- emmeans(model_b2, ~ Step)
pairwise_b2 <- contrast(emms_b2, method = "pairwise", adjust = "tukey")
print(anova_b2)
cat("\nEstimated Marginal Means:\n")
print(summary(emms_b2))
cat("\nPairwise Comparisons:\n")
print(pairwise_b2)
}--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 185.79 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.769 0.0781 17.9 0.605 0.933
2 0.773 0.0781 17.9 0.609 0.937
3 0.775 0.0781 17.9 0.611 0.939
4 0.764 0.0781 17.9 0.600 0.929
5 0.769 0.0781 17.9 0.605 0.933
6 0.737 0.0781 17.9 0.573 0.902
7 0.717 0.0781 17.9 0.553 0.881
8 0.704 0.0781 17.9 0.540 0.868
9 0.678 0.0781 17.9 0.514 0.842
10 0.663 0.0781 17.9 0.498 0.827
11 0.651 0.0781 17.9 0.487 0.815
12 0.638 0.0781 17.9 0.474 0.802
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.003946 0.0179 6049 -0.220 1.0000
Step1 - Step3 -0.005719 0.0179 6049 -0.320 1.0000
Step1 - Step4 0.004589 0.0179 6049 0.256 1.0000
Step1 - Step5 0.000053 0.0179 6049 0.003 1.0000
Step1 - Step6 0.031659 0.0179 6049 1.769 0.8349
Step1 - Step7 0.052129 0.0179 6049 2.911 0.1370
Step1 - Step8 0.065019 0.0179 6049 3.633 0.0149
Step1 - Step9 0.090900 0.0179 6049 5.079 <.0001
Step1 - Step10 0.106504 0.0179 6049 5.951 <.0001
Step1 - Step11 0.118291 0.0179 6049 6.610 <.0001
Step1 - Step12 0.131198 0.0179 6049 7.331 <.0001
Step2 - Step3 -0.001773 0.0179 6049 -0.099 1.0000
Step2 - Step4 0.008535 0.0179 6049 0.477 1.0000
Step2 - Step5 0.003999 0.0179 6049 0.223 1.0000
Step2 - Step6 0.035605 0.0179 6049 1.989 0.7008
Step2 - Step7 0.056074 0.0179 6049 3.132 0.0753
Step2 - Step8 0.068965 0.0179 6049 3.854 0.0066
Step2 - Step9 0.094846 0.0179 6049 5.300 <.0001
Step2 - Step10 0.110450 0.0179 6049 6.172 <.0001
Step2 - Step11 0.122237 0.0179 6049 6.830 <.0001
Step2 - Step12 0.135144 0.0179 6049 7.551 <.0001
Step3 - Step4 0.010308 0.0179 6049 0.576 1.0000
Step3 - Step5 0.005772 0.0179 6049 0.323 1.0000
Step3 - Step6 0.037378 0.0179 6049 2.089 0.6311
Step3 - Step7 0.057848 0.0179 6049 3.231 0.0562
Step3 - Step8 0.070738 0.0179 6049 3.953 0.0045
Step3 - Step9 0.096619 0.0179 6049 5.399 <.0001
Step3 - Step10 0.112223 0.0179 6049 6.271 <.0001
Step3 - Step11 0.124010 0.0179 6049 6.929 <.0001
Step3 - Step12 0.136918 0.0179 6049 7.651 <.0001
Step4 - Step5 -0.004536 0.0179 6049 -0.253 1.0000
Step4 - Step6 0.027070 0.0179 6049 1.513 0.9375
Step4 - Step7 0.047540 0.0179 6049 2.655 0.2494
Step4 - Step8 0.060430 0.0179 6049 3.377 0.0356
Step4 - Step9 0.086311 0.0179 6049 4.823 0.0001
Step4 - Step10 0.101915 0.0179 6049 5.695 <.0001
Step4 - Step11 0.113702 0.0179 6049 6.353 <.0001
Step4 - Step12 0.126610 0.0179 6049 7.075 <.0001
Step5 - Step6 0.031606 0.0179 6049 1.766 0.8365
Step5 - Step7 0.052076 0.0179 6049 2.908 0.1380
Step5 - Step8 0.064966 0.0179 6049 3.630 0.0151
Step5 - Step9 0.090847 0.0179 6049 5.076 <.0001
Step5 - Step10 0.106451 0.0179 6049 5.948 <.0001
Step5 - Step11 0.118238 0.0179 6049 6.607 <.0001
Step5 - Step12 0.131145 0.0179 6049 7.328 <.0001
Step6 - Step7 0.020469 0.0179 6049 1.143 0.9927
Step6 - Step8 0.033360 0.0179 6049 1.864 0.7816
Step6 - Step9 0.059241 0.0179 6049 3.310 0.0440
Step6 - Step10 0.074845 0.0179 6049 4.182 0.0017
Step6 - Step11 0.086632 0.0179 6049 4.841 0.0001
Step6 - Step12 0.099539 0.0179 6049 5.562 <.0001
Step7 - Step8 0.012890 0.0179 6049 0.720 0.9999
Step7 - Step9 0.038771 0.0179 6049 2.165 0.5751
Step7 - Step10 0.054375 0.0179 6049 3.037 0.0983
Step7 - Step11 0.066162 0.0179 6049 3.695 0.0119
Step7 - Step12 0.079070 0.0179 6049 4.416 0.0006
Step8 - Step9 0.025881 0.0179 6049 1.446 0.9543
Step8 - Step10 0.041485 0.0179 6049 2.318 0.4636
Step8 - Step11 0.053272 0.0179 6049 2.977 0.1156
Step8 - Step12 0.066179 0.0179 6049 3.698 0.0118
Step9 - Step10 0.015604 0.0179 6049 0.872 0.9994
Step9 - Step11 0.027391 0.0179 6049 1.531 0.9323
Step9 - Step12 0.040299 0.0179 6049 2.252 0.5117
Step10 - Step11 0.011787 0.0179 6049 0.659 1.0000
Step10 - Step12 0.024695 0.0179 6049 1.380 0.9675
Step11 - Step12 0.012908 0.0179 6049 0.721 0.9999
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 126.61 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.808 0.0937 17.7 0.610 1.005
2 0.815 0.0937 17.7 0.618 1.012
3 0.818 0.0937 17.7 0.620 1.015
4 0.824 0.0937 17.7 0.627 1.022
5 0.811 0.0937 17.7 0.613 1.008
6 0.793 0.0937 17.7 0.595 0.990
7 0.784 0.0937 17.7 0.587 0.982
8 0.771 0.0937 17.7 0.574 0.969
9 0.751 0.0937 17.7 0.553 0.948
10 0.730 0.0937 17.7 0.533 0.927
11 0.700 0.0937 17.7 0.503 0.898
12 0.683 0.0937 17.7 0.486 0.880
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.00746 0.02 6049 -0.373 1.0000
Step1 - Step3 -0.01002 0.02 6049 -0.501 1.0000
Step1 - Step4 -0.01676 0.02 6049 -0.839 0.9996
Step1 - Step5 -0.00293 0.02 6049 -0.147 1.0000
Step1 - Step6 0.01510 0.02 6049 0.756 0.9998
Step1 - Step7 0.02316 0.02 6049 1.158 0.9919
Step1 - Step8 0.03614 0.02 6049 1.808 0.8137
Step1 - Step9 0.05712 0.02 6049 2.858 0.1563
Step1 - Step10 0.07741 0.02 6049 3.874 0.0061
Step1 - Step11 0.10730 0.02 6049 5.369 <.0001
Step1 - Step12 0.12487 0.02 6049 6.249 <.0001
Step2 - Step3 -0.00256 0.02 6049 -0.128 1.0000
Step2 - Step4 -0.00930 0.02 6049 -0.466 1.0000
Step2 - Step5 0.00452 0.02 6049 0.226 1.0000
Step2 - Step6 0.02256 0.02 6049 1.129 0.9934
Step2 - Step7 0.03061 0.02 6049 1.531 0.9321
Step2 - Step8 0.04360 0.02 6049 2.182 0.5631
Step2 - Step9 0.06458 0.02 6049 3.232 0.0561
Step2 - Step10 0.08487 0.02 6049 4.247 0.0013
Step2 - Step11 0.11476 0.02 6049 5.743 <.0001
Step2 - Step12 0.13233 0.02 6049 6.622 <.0001
Step3 - Step4 -0.00675 0.02 6049 -0.338 1.0000
Step3 - Step5 0.00708 0.02 6049 0.354 1.0000
Step3 - Step6 0.02512 0.02 6049 1.257 0.9841
Step3 - Step7 0.03317 0.02 6049 1.659 0.8865
Step3 - Step8 0.04615 0.02 6049 2.310 0.4696
Step3 - Step9 0.06714 0.02 6049 3.360 0.0376
Step3 - Step10 0.08742 0.02 6049 4.375 0.0008
Step3 - Step11 0.11731 0.02 6049 5.871 <.0001
Step3 - Step12 0.13489 0.02 6049 6.750 <.0001
Step4 - Step5 0.01383 0.02 6049 0.692 0.9999
Step4 - Step6 0.03186 0.02 6049 1.595 0.9114
Step4 - Step7 0.03992 0.02 6049 1.997 0.6960
Step4 - Step8 0.05290 0.02 6049 2.647 0.2535
Step4 - Step9 0.07388 0.02 6049 3.697 0.0118
Step4 - Step10 0.09417 0.02 6049 4.713 0.0002
Step4 - Step11 0.12406 0.02 6049 6.208 <.0001
Step4 - Step12 0.14163 0.02 6049 7.088 <.0001
Step5 - Step6 0.01804 0.02 6049 0.903 0.9991
Step5 - Step7 0.02609 0.02 6049 1.305 0.9787
Step5 - Step8 0.03907 0.02 6049 1.955 0.7239
Step5 - Step9 0.06005 0.02 6049 3.005 0.1071
Step5 - Step10 0.08034 0.02 6049 4.021 0.0034
Step5 - Step11 0.11023 0.02 6049 5.516 <.0001
Step5 - Step12 0.12780 0.02 6049 6.396 <.0001
Step6 - Step7 0.00805 0.02 6049 0.403 1.0000
Step6 - Step8 0.02104 0.02 6049 1.053 0.9964
Step6 - Step9 0.04202 0.02 6049 2.103 0.6209
Step6 - Step10 0.06231 0.02 6049 3.118 0.0784
Step6 - Step11 0.09219 0.02 6049 4.614 0.0003
Step6 - Step12 0.10977 0.02 6049 5.493 <.0001
Step7 - Step8 0.01298 0.02 6049 0.649 1.0000
Step7 - Step9 0.03397 0.02 6049 1.699 0.8692
Step7 - Step10 0.05425 0.02 6049 2.714 0.2195
Step7 - Step11 0.08414 0.02 6049 4.209 0.0016
Step7 - Step12 0.10171 0.02 6049 5.088 <.0001
Step8 - Step9 0.02098 0.02 6049 1.050 0.9965
Step8 - Step10 0.04127 0.02 6049 2.065 0.6478
Step8 - Step11 0.07116 0.02 6049 3.561 0.0192
Step8 - Step12 0.08873 0.02 6049 4.440 0.0006
Step9 - Step10 0.02029 0.02 6049 1.015 0.9974
Step9 - Step11 0.05018 0.02 6049 2.511 0.3330
Step9 - Step12 0.06775 0.02 6049 3.390 0.0341
Step10 - Step11 0.02989 0.02 6049 1.496 0.9421
Step10 - Step12 0.04746 0.02 6049 2.375 0.4232
Step11 - Step12 0.01757 0.02 6049 0.879 0.9993
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 199.22 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.65 0.173 17.6 1.29 2.01
2 1.68 0.173 17.6 1.32 2.05
3 1.65 0.173 17.6 1.29 2.02
4 1.65 0.173 17.6 1.28 2.01
5 1.64 0.173 17.6 1.27 2.00
6 1.60 0.173 17.6 1.24 1.97
7 1.57 0.173 17.6 1.20 1.93
8 1.55 0.173 17.6 1.18 1.91
9 1.48 0.173 17.6 1.12 1.85
10 1.47 0.173 17.6 1.10 1.83
11 1.43 0.173 17.6 1.07 1.80
12 1.39 0.173 17.6 1.02 1.75
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.03221 0.033 6049 -0.977 0.9982
Step1 - Step3 -0.00130 0.033 6049 -0.039 1.0000
Step1 - Step4 0.00384 0.033 6049 0.117 1.0000
Step1 - Step5 0.01112 0.033 6049 0.338 1.0000
Step1 - Step6 0.04710 0.033 6049 1.429 0.9580
Step1 - Step7 0.08058 0.033 6049 2.444 0.3764
Step1 - Step8 0.10316 0.033 6049 3.130 0.0757
Step1 - Step9 0.16877 0.033 6049 5.121 <.0001
Step1 - Step10 0.18490 0.033 6049 5.610 <.0001
Step1 - Step11 0.21682 0.033 6049 6.579 <.0001
Step1 - Step12 0.26287 0.033 6049 7.976 <.0001
Step2 - Step3 0.03092 0.033 6049 0.938 0.9987
Step2 - Step4 0.03606 0.033 6049 1.094 0.9950
Step2 - Step5 0.04334 0.033 6049 1.315 0.9774
Step2 - Step6 0.07931 0.033 6049 2.406 0.4016
Step2 - Step7 0.11280 0.033 6049 3.421 0.0309
Step2 - Step8 0.13538 0.033 6049 4.108 0.0024
Step2 - Step9 0.20099 0.033 6049 6.098 <.0001
Step2 - Step10 0.21711 0.033 6049 6.587 <.0001
Step2 - Step11 0.24904 0.033 6049 7.556 <.0001
Step2 - Step12 0.29508 0.033 6049 8.953 <.0001
Step3 - Step4 0.00514 0.033 6049 0.156 1.0000
Step3 - Step5 0.01242 0.033 6049 0.377 1.0000
Step3 - Step6 0.04840 0.033 6049 1.468 0.9491
Step3 - Step7 0.08188 0.033 6049 2.483 0.3507
Step3 - Step8 0.10446 0.033 6049 3.169 0.0675
Step3 - Step9 0.17007 0.033 6049 5.160 <.0001
Step3 - Step10 0.18619 0.033 6049 5.649 <.0001
Step3 - Step11 0.21812 0.033 6049 6.618 <.0001
Step3 - Step12 0.26417 0.033 6049 8.015 <.0001
Step4 - Step5 0.00728 0.033 6049 0.221 1.0000
Step4 - Step6 0.04326 0.033 6049 1.312 0.9777
Step4 - Step7 0.07674 0.033 6049 2.327 0.4571
Step4 - Step8 0.09932 0.033 6049 3.013 0.1048
Step4 - Step9 0.16493 0.033 6049 5.004 <.0001
Step4 - Step10 0.18105 0.033 6049 5.493 <.0001
Step4 - Step11 0.21298 0.033 6049 6.462 <.0001
Step4 - Step12 0.25903 0.033 6049 7.859 <.0001
Step5 - Step6 0.03598 0.033 6049 1.092 0.9951
Step5 - Step7 0.06946 0.033 6049 2.106 0.6182
Step5 - Step8 0.09204 0.033 6049 2.793 0.1832
Step5 - Step9 0.15765 0.033 6049 4.783 0.0001
Step5 - Step10 0.17377 0.033 6049 5.273 <.0001
Step5 - Step11 0.20570 0.033 6049 6.241 <.0001
Step5 - Step12 0.25175 0.033 6049 7.638 <.0001
Step6 - Step7 0.03348 0.033 6049 1.015 0.9974
Step6 - Step8 0.05606 0.033 6049 1.701 0.8682
Step6 - Step9 0.12167 0.033 6049 3.692 0.0121
Step6 - Step10 0.13780 0.033 6049 4.181 0.0018
Step6 - Step11 0.16973 0.033 6049 5.150 <.0001
Step6 - Step12 0.21577 0.033 6049 6.547 <.0001
Step7 - Step8 0.02258 0.033 6049 0.685 0.9999
Step7 - Step9 0.08819 0.033 6049 2.674 0.2392
Step7 - Step10 0.10431 0.033 6049 3.163 0.0687
Step7 - Step11 0.13624 0.033 6049 4.132 0.0022
Step7 - Step12 0.18229 0.033 6049 5.528 <.0001
Step8 - Step9 0.06561 0.033 6049 1.991 0.7000
Step8 - Step10 0.08173 0.033 6049 2.480 0.3528
Step8 - Step11 0.11366 0.033 6049 3.449 0.0282
Step8 - Step12 0.15971 0.033 6049 4.846 0.0001
Step9 - Step10 0.01612 0.033 6049 0.489 1.0000
Step9 - Step11 0.04805 0.033 6049 1.458 0.9515
Step9 - Step12 0.09410 0.033 6049 2.855 0.1576
Step10 - Step11 0.03193 0.033 6049 0.969 0.9983
Step10 - Step12 0.07797 0.033 6049 2.366 0.4297
Step11 - Step12 0.04604 0.033 6049 1.397 0.9643
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates cat("\n\n================ Block 3 (18 Steps) ================\n")
================ Block 3 (18 Steps) ================for (ax in axes) {
cat(glue::glue("\n--- Axis: {ax} ---\n"))
df_b3 <- step_summary_18 %>%
filter(Block == "3", Axis == ax, Step %in% as.character(1:18)) %>%
mutate(Step = factor(Step))
if (nrow(df_b3) == 0) {
cat("No valid data for Block 3, Axis", ax, "\n")
next
}
model_b3 <- lmer(RMS ~ Step + (1 | subject) + (1 | trial_id), data = df_b3)
anova_b3 <- car::Anova(model_b3, type = 2, test.statistic = "Chisq")
emms_b3 <- emmeans(model_b3, ~ Step)
pairwise_b3 <- contrast(emms_b3, method = "pairwise", adjust = "tukey")
print(anova_b3)
cat("\nEstimated Marginal Means:\n")
print(summary(emms_b3))
cat("\nPairwise Comparisons:\n")
print(pairwise_b3)
}--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 113.97 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.574 0.0461 19.9 0.478 0.670
2 0.577 0.0461 19.9 0.481 0.673
3 0.591 0.0461 19.9 0.495 0.688
4 0.597 0.0461 19.9 0.501 0.693
5 0.588 0.0461 19.9 0.491 0.684
6 0.579 0.0461 19.9 0.482 0.675
7 0.586 0.0461 19.9 0.489 0.682
8 0.580 0.0461 19.9 0.484 0.676
9 0.576 0.0461 19.9 0.480 0.673
10 0.560 0.0461 19.9 0.464 0.656
11 0.552 0.0461 19.9 0.456 0.648
12 0.547 0.0461 19.9 0.451 0.643
13 0.538 0.0461 19.9 0.442 0.634
14 0.524 0.0461 19.9 0.428 0.620
15 0.518 0.0461 19.9 0.422 0.614
16 0.509 0.0461 19.9 0.413 0.605
17 0.505 0.0461 19.9 0.409 0.602
18 0.486 0.0461 19.9 0.389 0.582
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.003040 0.0186 7531 -0.164 1.0000
Step1 - Step3 -0.017560 0.0186 7531 -0.946 1.0000
Step1 - Step4 -0.022849 0.0186 7531 -1.231 0.9991
Step1 - Step5 -0.013692 0.0186 7531 -0.738 1.0000
Step1 - Step6 -0.004735 0.0186 7531 -0.255 1.0000
Step1 - Step7 -0.011701 0.0186 7531 -0.630 1.0000
Step1 - Step8 -0.005799 0.0186 7531 -0.312 1.0000
Step1 - Step9 -0.002450 0.0186 7531 -0.132 1.0000
Step1 - Step10 0.014070 0.0186 7531 0.758 1.0000
Step1 - Step11 0.022179 0.0186 7531 1.195 0.9994
Step1 - Step12 0.026747 0.0186 7531 1.441 0.9941
Step1 - Step13 0.035647 0.0186 7531 1.920 0.9044
Step1 - Step14 0.050133 0.0186 7531 2.701 0.3798
Step1 - Step15 0.055940 0.0186 7531 3.014 0.1936
Step1 - Step16 0.064677 0.0186 7531 3.484 0.0509
Step1 - Step17 0.068608 0.0186 7531 3.696 0.0249
Step1 - Step18 0.088260 0.0186 7531 4.755 0.0003
Step2 - Step3 -0.014521 0.0186 7531 -0.782 1.0000
Step2 - Step4 -0.019810 0.0186 7531 -1.067 0.9999
Step2 - Step5 -0.010653 0.0186 7531 -0.574 1.0000
Step2 - Step6 -0.001696 0.0186 7531 -0.091 1.0000
Step2 - Step7 -0.008661 0.0186 7531 -0.467 1.0000
Step2 - Step8 -0.002760 0.0186 7531 -0.149 1.0000
Step2 - Step9 0.000589 0.0186 7531 0.032 1.0000
Step2 - Step10 0.017109 0.0186 7531 0.922 1.0000
Step2 - Step11 0.025218 0.0186 7531 1.359 0.9970
Step2 - Step12 0.029787 0.0186 7531 1.605 0.9812
Step2 - Step13 0.038687 0.0186 7531 2.084 0.8257
Step2 - Step14 0.053173 0.0186 7531 2.865 0.2730
Step2 - Step15 0.058980 0.0186 7531 3.177 0.1268
Step2 - Step16 0.067716 0.0186 7531 3.648 0.0295
Step2 - Step17 0.071648 0.0186 7531 3.860 0.0137
Step2 - Step18 0.091300 0.0186 7531 4.919 0.0001
Step3 - Step4 -0.005289 0.0186 7531 -0.285 1.0000
Step3 - Step5 0.003868 0.0186 7531 0.208 1.0000
Step3 - Step6 0.012825 0.0186 7531 0.691 1.0000
Step3 - Step7 0.005860 0.0186 7531 0.316 1.0000
Step3 - Step8 0.011761 0.0186 7531 0.634 1.0000
Step3 - Step9 0.015110 0.0186 7531 0.814 1.0000
Step3 - Step10 0.031630 0.0186 7531 1.704 0.9662
Step3 - Step11 0.039739 0.0186 7531 2.141 0.7921
Step3 - Step12 0.044308 0.0186 7531 2.387 0.6180
Step3 - Step13 0.053207 0.0186 7531 2.866 0.2719
Step3 - Step14 0.067694 0.0186 7531 3.647 0.0296
Step3 - Step15 0.073501 0.0186 7531 3.960 0.0094
Step3 - Step16 0.082237 0.0186 7531 4.430 0.0013
Step3 - Step17 0.086169 0.0186 7531 4.642 0.0005
Step3 - Step18 0.105820 0.0186 7531 5.701 <.0001
Step4 - Step5 0.009157 0.0186 7531 0.493 1.0000
Step4 - Step6 0.018114 0.0186 7531 0.976 1.0000
Step4 - Step7 0.011148 0.0186 7531 0.601 1.0000
Step4 - Step8 0.017050 0.0186 7531 0.919 1.0000
Step4 - Step9 0.020399 0.0186 7531 1.099 0.9998
Step4 - Step10 0.036919 0.0186 7531 1.989 0.8750
Step4 - Step11 0.045028 0.0186 7531 2.426 0.5880
Step4 - Step12 0.049596 0.0186 7531 2.672 0.4004
Step4 - Step13 0.058496 0.0186 7531 3.151 0.1361
Step4 - Step14 0.072982 0.0186 7531 3.932 0.0105
Step4 - Step15 0.078790 0.0186 7531 4.245 0.0029
Step4 - Step16 0.087526 0.0186 7531 4.715 0.0004
Step4 - Step17 0.091458 0.0186 7531 4.927 0.0001
Step4 - Step18 0.111109 0.0186 7531 5.986 <.0001
Step5 - Step6 0.008957 0.0186 7531 0.483 1.0000
Step5 - Step7 0.001991 0.0186 7531 0.107 1.0000
Step5 - Step8 0.007893 0.0186 7531 0.425 1.0000
Step5 - Step9 0.011242 0.0186 7531 0.606 1.0000
Step5 - Step10 0.027762 0.0186 7531 1.496 0.9911
Step5 - Step11 0.035871 0.0186 7531 1.932 0.8996
Step5 - Step12 0.040439 0.0186 7531 2.179 0.7681
Step5 - Step13 0.049339 0.0186 7531 2.658 0.4105
Step5 - Step14 0.063825 0.0186 7531 3.438 0.0589
Step5 - Step15 0.069633 0.0186 7531 3.751 0.0205
Step5 - Step16 0.078369 0.0186 7531 4.222 0.0032
Step5 - Step17 0.082301 0.0186 7531 4.434 0.0013
Step5 - Step18 0.101952 0.0186 7531 5.492 <.0001
Step6 - Step7 -0.006966 0.0186 7531 -0.375 1.0000
Step6 - Step8 -0.001064 0.0186 7531 -0.057 1.0000
Step6 - Step9 0.002285 0.0186 7531 0.123 1.0000
Step6 - Step10 0.018805 0.0186 7531 1.013 0.9999
Step6 - Step11 0.026914 0.0186 7531 1.450 0.9937
Step6 - Step12 0.031482 0.0186 7531 1.696 0.9676
Step6 - Step13 0.040382 0.0186 7531 2.176 0.7701
Step6 - Step14 0.054869 0.0186 7531 2.956 0.2222
Step6 - Step15 0.060676 0.0186 7531 3.269 0.0982
Step6 - Step16 0.069412 0.0186 7531 3.739 0.0214
Step6 - Step17 0.073344 0.0186 7531 3.951 0.0097
Step6 - Step18 0.092995 0.0186 7531 5.010 0.0001
Step7 - Step8 0.005902 0.0186 7531 0.318 1.0000
Step7 - Step9 0.009251 0.0186 7531 0.498 1.0000
Step7 - Step10 0.025771 0.0186 7531 1.388 0.9961
Step7 - Step11 0.033880 0.0186 7531 1.825 0.9372
Step7 - Step12 0.038448 0.0186 7531 2.071 0.8329
Step7 - Step13 0.047348 0.0186 7531 2.551 0.4910
Step7 - Step14 0.061834 0.0186 7531 3.331 0.0818
Step7 - Step15 0.067641 0.0186 7531 3.644 0.0299
Step7 - Step16 0.076377 0.0186 7531 4.115 0.0051
Step7 - Step17 0.080309 0.0186 7531 4.326 0.0021
Step7 - Step18 0.099961 0.0186 7531 5.385 <.0001
Step8 - Step9 0.003349 0.0186 7531 0.180 1.0000
Step8 - Step10 0.019869 0.0186 7531 1.070 0.9999
Step8 - Step11 0.027978 0.0186 7531 1.507 0.9903
Step8 - Step12 0.032546 0.0186 7531 1.753 0.9559
Step8 - Step13 0.041446 0.0186 7531 2.233 0.7316
Step8 - Step14 0.055932 0.0186 7531 3.013 0.1938
Step8 - Step15 0.061740 0.0186 7531 3.326 0.0830
Step8 - Step16 0.070476 0.0186 7531 3.797 0.0174
Step8 - Step17 0.074408 0.0186 7531 4.009 0.0078
Step8 - Step18 0.094059 0.0186 7531 5.067 0.0001
Step9 - Step10 0.016520 0.0186 7531 0.890 1.0000
Step9 - Step11 0.024629 0.0186 7531 1.327 0.9977
Step9 - Step12 0.029197 0.0186 7531 1.573 0.9847
Step9 - Step13 0.038097 0.0186 7531 2.052 0.8432
Step9 - Step14 0.052583 0.0186 7531 2.833 0.2922
Step9 - Step15 0.058391 0.0186 7531 3.146 0.1381
Step9 - Step16 0.067127 0.0186 7531 3.616 0.0329
Step9 - Step17 0.071059 0.0186 7531 3.828 0.0155
Step9 - Step18 0.090710 0.0186 7531 4.887 0.0002
Step10 - Step11 0.008109 0.0186 7531 0.437 1.0000
Step10 - Step12 0.012677 0.0186 7531 0.683 1.0000
Step10 - Step13 0.021577 0.0186 7531 1.162 0.9996
Step10 - Step14 0.036063 0.0186 7531 1.943 0.8953
Step10 - Step15 0.041870 0.0186 7531 2.256 0.7155
Step10 - Step16 0.050607 0.0186 7531 2.726 0.3620
Step10 - Step17 0.054539 0.0186 7531 2.938 0.2316
Step10 - Step18 0.074190 0.0186 7531 3.997 0.0081
Step11 - Step12 0.004568 0.0186 7531 0.246 1.0000
Step11 - Step13 0.013468 0.0186 7531 0.726 1.0000
Step11 - Step14 0.027954 0.0186 7531 1.506 0.9904
Step11 - Step15 0.033762 0.0186 7531 1.819 0.9390
Step11 - Step16 0.042498 0.0186 7531 2.289 0.6912
Step11 - Step17 0.046430 0.0186 7531 2.501 0.5293
Step11 - Step18 0.066081 0.0186 7531 3.560 0.0397
Step12 - Step13 0.008900 0.0186 7531 0.479 1.0000
Step12 - Step14 0.023386 0.0186 7531 1.260 0.9988
Step12 - Step15 0.029193 0.0186 7531 1.573 0.9847
Step12 - Step16 0.037929 0.0186 7531 2.043 0.8480
Step12 - Step17 0.041861 0.0186 7531 2.255 0.7159
Step12 - Step18 0.061513 0.0186 7531 3.314 0.0861
Step13 - Step14 0.014486 0.0186 7531 0.780 1.0000
Step13 - Step15 0.020293 0.0186 7531 1.093 0.9998
Step13 - Step16 0.029029 0.0186 7531 1.564 0.9856
Step13 - Step17 0.032961 0.0186 7531 1.776 0.9506
Step13 - Step18 0.052613 0.0186 7531 2.834 0.2913
Step14 - Step15 0.005807 0.0186 7531 0.313 1.0000
Step14 - Step16 0.014543 0.0186 7531 0.783 1.0000
Step14 - Step17 0.018475 0.0186 7531 0.995 0.9999
Step14 - Step18 0.038127 0.0186 7531 2.054 0.8423
Step15 - Step16 0.008736 0.0186 7531 0.471 1.0000
Step15 - Step17 0.012668 0.0186 7531 0.682 1.0000
Step15 - Step18 0.032320 0.0186 7531 1.741 0.9587
Step16 - Step17 0.003932 0.0186 7531 0.212 1.0000
Step16 - Step18 0.023584 0.0186 7531 1.271 0.9987
Step17 - Step18 0.019652 0.0186 7531 1.059 0.9999
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 156.54 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.582 0.0463 20.2 0.485 0.678
2 0.586 0.0463 20.2 0.490 0.683
3 0.610 0.0463 20.2 0.514 0.706
4 0.614 0.0463 20.2 0.517 0.710
5 0.614 0.0463 20.2 0.517 0.710
6 0.604 0.0463 20.2 0.507 0.700
7 0.614 0.0463 20.2 0.518 0.711
8 0.622 0.0463 20.2 0.525 0.718
9 0.623 0.0463 20.2 0.527 0.720
10 0.597 0.0463 20.2 0.501 0.694
11 0.587 0.0463 20.2 0.491 0.684
12 0.581 0.0463 20.2 0.485 0.678
13 0.570 0.0463 20.2 0.473 0.666
14 0.550 0.0463 20.2 0.454 0.647
15 0.533 0.0463 20.2 0.436 0.629
16 0.512 0.0463 20.2 0.416 0.609
17 0.506 0.0463 20.2 0.409 0.602
18 0.493 0.0463 20.2 0.397 0.590
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.004258 0.0195 7531 -0.219 1.0000
Step1 - Step3 -0.028112 0.0195 7531 -1.444 0.9939
Step1 - Step4 -0.031987 0.0195 7531 -1.643 0.9762
Step1 - Step5 -0.031731 0.0195 7531 -1.630 0.9780
Step1 - Step6 -0.021659 0.0195 7531 -1.112 0.9998
Step1 - Step7 -0.032485 0.0195 7531 -1.669 0.9723
Step1 - Step8 -0.039907 0.0195 7531 -2.050 0.8446
Step1 - Step9 -0.041413 0.0195 7531 -2.127 0.8006
Step1 - Step10 -0.015332 0.0195 7531 -0.788 1.0000
Step1 - Step11 -0.005256 0.0195 7531 -0.270 1.0000
Step1 - Step12 0.000724 0.0195 7531 0.037 1.0000
Step1 - Step13 0.011942 0.0195 7531 0.613 1.0000
Step1 - Step14 0.031394 0.0195 7531 1.612 0.9803
Step1 - Step15 0.049294 0.0195 7531 2.532 0.5056
Step1 - Step16 0.069784 0.0195 7531 3.584 0.0366
Step1 - Step17 0.076068 0.0195 7531 3.907 0.0115
Step1 - Step18 0.088536 0.0195 7531 4.547 0.0008
Step2 - Step3 -0.023854 0.0195 7531 -1.225 0.9992
Step2 - Step4 -0.027729 0.0195 7531 -1.424 0.9948
Step2 - Step5 -0.027473 0.0195 7531 -1.411 0.9953
Step2 - Step6 -0.017401 0.0195 7531 -0.894 1.0000
Step2 - Step7 -0.028228 0.0195 7531 -1.450 0.9937
Step2 - Step8 -0.035649 0.0195 7531 -1.831 0.9354
Step2 - Step9 -0.037155 0.0195 7531 -1.908 0.9091
Step2 - Step10 -0.011075 0.0195 7531 -0.569 1.0000
Step2 - Step11 -0.000998 0.0195 7531 -0.051 1.0000
Step2 - Step12 0.004981 0.0195 7531 0.256 1.0000
Step2 - Step13 0.016200 0.0195 7531 0.832 1.0000
Step2 - Step14 0.035652 0.0195 7531 1.831 0.9354
Step2 - Step15 0.053552 0.0195 7531 2.751 0.3454
Step2 - Step16 0.074042 0.0195 7531 3.803 0.0170
Step2 - Step17 0.080326 0.0195 7531 4.126 0.0048
Step2 - Step18 0.092794 0.0195 7531 4.766 0.0003
Step3 - Step4 -0.003875 0.0195 7531 -0.199 1.0000
Step3 - Step5 -0.003619 0.0195 7531 -0.186 1.0000
Step3 - Step6 0.006453 0.0195 7531 0.331 1.0000
Step3 - Step7 -0.004373 0.0195 7531 -0.225 1.0000
Step3 - Step8 -0.011795 0.0195 7531 -0.606 1.0000
Step3 - Step9 -0.013301 0.0195 7531 -0.683 1.0000
Step3 - Step10 0.012780 0.0195 7531 0.656 1.0000
Step3 - Step11 0.022856 0.0195 7531 1.174 0.9995
Step3 - Step12 0.028836 0.0195 7531 1.481 0.9920
Step3 - Step13 0.040054 0.0195 7531 2.057 0.8406
Step3 - Step14 0.059506 0.0195 7531 3.056 0.1742
Step3 - Step15 0.077406 0.0195 7531 3.976 0.0088
Step3 - Step16 0.097896 0.0195 7531 5.028 0.0001
Step3 - Step17 0.104180 0.0195 7531 5.351 <.0001
Step3 - Step18 0.116648 0.0195 7531 5.991 <.0001
Step4 - Step5 0.000256 0.0195 7531 0.013 1.0000
Step4 - Step6 0.010328 0.0195 7531 0.530 1.0000
Step4 - Step7 -0.000499 0.0195 7531 -0.026 1.0000
Step4 - Step8 -0.007920 0.0195 7531 -0.407 1.0000
Step4 - Step9 -0.009426 0.0195 7531 -0.484 1.0000
Step4 - Step10 0.016655 0.0195 7531 0.855 1.0000
Step4 - Step11 0.026731 0.0195 7531 1.373 0.9966
Step4 - Step12 0.032710 0.0195 7531 1.680 0.9704
Step4 - Step13 0.043929 0.0195 7531 2.256 0.7151
Step4 - Step14 0.063381 0.0195 7531 3.255 0.1020
Step4 - Step15 0.081281 0.0195 7531 4.175 0.0040
Step4 - Step16 0.101771 0.0195 7531 5.227 <.0001
Step4 - Step17 0.108055 0.0195 7531 5.550 <.0001
Step4 - Step18 0.120523 0.0195 7531 6.190 <.0001
Step5 - Step6 0.010072 0.0195 7531 0.517 1.0000
Step5 - Step7 -0.000754 0.0195 7531 -0.039 1.0000
Step5 - Step8 -0.008176 0.0195 7531 -0.420 1.0000
Step5 - Step9 -0.009682 0.0195 7531 -0.497 1.0000
Step5 - Step10 0.016399 0.0195 7531 0.842 1.0000
Step5 - Step11 0.026475 0.0195 7531 1.360 0.9970
Step5 - Step12 0.032455 0.0195 7531 1.667 0.9726
Step5 - Step13 0.043674 0.0195 7531 2.243 0.7243
Step5 - Step14 0.063125 0.0195 7531 3.242 0.1059
Step5 - Step15 0.081026 0.0195 7531 4.162 0.0042
Step5 - Step16 0.101515 0.0195 7531 5.214 <.0001
Step5 - Step17 0.107799 0.0195 7531 5.537 <.0001
Step5 - Step18 0.120267 0.0195 7531 6.177 <.0001
Step6 - Step7 -0.010827 0.0195 7531 -0.556 1.0000
Step6 - Step8 -0.018248 0.0195 7531 -0.937 1.0000
Step6 - Step9 -0.019754 0.0195 7531 -1.015 0.9999
Step6 - Step10 0.006327 0.0195 7531 0.325 1.0000
Step6 - Step11 0.016403 0.0195 7531 0.843 1.0000
Step6 - Step12 0.022382 0.0195 7531 1.150 0.9996
Step6 - Step13 0.033601 0.0195 7531 1.726 0.9619
Step6 - Step14 0.053053 0.0195 7531 2.725 0.3629
Step6 - Step15 0.070953 0.0195 7531 3.644 0.0299
Step6 - Step16 0.091443 0.0195 7531 4.697 0.0004
Step6 - Step17 0.097727 0.0195 7531 5.020 0.0001
Step6 - Step18 0.110195 0.0195 7531 5.660 <.0001
Step7 - Step8 -0.007422 0.0195 7531 -0.381 1.0000
Step7 - Step9 -0.008928 0.0195 7531 -0.459 1.0000
Step7 - Step10 0.017153 0.0195 7531 0.881 1.0000
Step7 - Step11 0.027230 0.0195 7531 1.399 0.9958
Step7 - Step12 0.033209 0.0195 7531 1.706 0.9659
Step7 - Step13 0.044428 0.0195 7531 2.282 0.6967
Step7 - Step14 0.063879 0.0195 7531 3.281 0.0948
Step7 - Step15 0.081780 0.0195 7531 4.200 0.0036
Step7 - Step16 0.102269 0.0195 7531 5.253 <.0001
Step7 - Step17 0.108554 0.0195 7531 5.576 <.0001
Step7 - Step18 0.121021 0.0195 7531 6.216 <.0001
Step8 - Step9 -0.001506 0.0195 7531 -0.077 1.0000
Step8 - Step10 0.024575 0.0195 7531 1.262 0.9988
Step8 - Step11 0.034652 0.0195 7531 1.780 0.9496
Step8 - Step12 0.040631 0.0195 7531 2.087 0.8242
Step8 - Step13 0.051850 0.0195 7531 2.663 0.4068
Step8 - Step14 0.071301 0.0195 7531 3.662 0.0281
Step8 - Step15 0.089202 0.0195 7531 4.582 0.0007
Step8 - Step16 0.109691 0.0195 7531 5.634 <.0001
Step8 - Step17 0.115975 0.0195 7531 5.957 <.0001
Step8 - Step18 0.128443 0.0195 7531 6.597 <.0001
Step9 - Step10 0.026081 0.0195 7531 1.340 0.9975
Step9 - Step11 0.036157 0.0195 7531 1.857 0.9272
Step9 - Step12 0.042137 0.0195 7531 2.164 0.7774
Step9 - Step13 0.053355 0.0195 7531 2.740 0.3523
Step9 - Step14 0.072807 0.0195 7531 3.740 0.0214
Step9 - Step15 0.090707 0.0195 7531 4.659 0.0005
Step9 - Step16 0.111197 0.0195 7531 5.711 <.0001
Step9 - Step17 0.117481 0.0195 7531 6.034 <.0001
Step9 - Step18 0.129949 0.0195 7531 6.675 <.0001
Step10 - Step11 0.010077 0.0195 7531 0.518 1.0000
Step10 - Step12 0.016056 0.0195 7531 0.825 1.0000
Step10 - Step13 0.027275 0.0195 7531 1.401 0.9957
Step10 - Step14 0.046726 0.0195 7531 2.400 0.6080
Step10 - Step15 0.064627 0.0195 7531 3.319 0.0847
Step10 - Step16 0.085116 0.0195 7531 4.372 0.0017
Step10 - Step17 0.091401 0.0195 7531 4.695 0.0004
Step10 - Step18 0.103868 0.0195 7531 5.335 <.0001
Step11 - Step12 0.005979 0.0195 7531 0.307 1.0000
Step11 - Step13 0.017198 0.0195 7531 0.883 1.0000
Step11 - Step14 0.036650 0.0195 7531 1.882 0.9186
Step11 - Step15 0.054550 0.0195 7531 2.802 0.3117
Step11 - Step16 0.075040 0.0195 7531 3.854 0.0140
Step11 - Step17 0.081324 0.0195 7531 4.177 0.0039
Step11 - Step18 0.093792 0.0195 7531 4.817 0.0002
Step12 - Step13 0.011219 0.0195 7531 0.576 1.0000
Step12 - Step14 0.030670 0.0195 7531 1.575 0.9845
Step12 - Step15 0.048571 0.0195 7531 2.495 0.5344
Step12 - Step16 0.069060 0.0195 7531 3.547 0.0415
Step12 - Step17 0.075345 0.0195 7531 3.870 0.0132
Step12 - Step18 0.087812 0.0195 7531 4.510 0.0009
Step13 - Step14 0.019451 0.0195 7531 0.999 0.9999
Step13 - Step15 0.037352 0.0195 7531 1.918 0.9052
Step13 - Step16 0.057842 0.0195 7531 2.971 0.2146
Step13 - Step17 0.064126 0.0195 7531 3.294 0.0914
Step13 - Step18 0.076594 0.0195 7531 3.934 0.0104
Step14 - Step15 0.017900 0.0195 7531 0.919 1.0000
Step14 - Step16 0.038390 0.0195 7531 1.972 0.8828
Step14 - Step17 0.044674 0.0195 7531 2.295 0.6875
Step14 - Step18 0.057142 0.0195 7531 2.935 0.2333
Step15 - Step16 0.020490 0.0195 7531 1.052 0.9999
Step15 - Step17 0.026774 0.0195 7531 1.375 0.9965
Step15 - Step18 0.039242 0.0195 7531 2.016 0.8622
Step16 - Step17 0.006284 0.0195 7531 0.323 1.0000
Step16 - Step18 0.018752 0.0195 7531 0.963 1.0000
Step17 - Step18 0.012468 0.0195 7531 0.640 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 85.932 17 3.328e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.24 0.126 18.4 0.979 1.51
2 1.27 0.126 18.4 1.003 1.53
3 1.29 0.126 18.4 1.025 1.55
4 1.29 0.126 18.4 1.027 1.55
5 1.30 0.126 18.4 1.041 1.57
6 1.27 0.126 18.4 1.005 1.53
7 1.28 0.126 18.4 1.016 1.54
8 1.27 0.126 18.4 1.011 1.54
9 1.26 0.126 18.4 0.997 1.53
10 1.27 0.126 18.4 1.004 1.53
11 1.26 0.126 18.4 0.996 1.52
12 1.24 0.126 18.4 0.980 1.51
13 1.23 0.126 18.4 0.970 1.50
14 1.20 0.126 18.4 0.941 1.47
15 1.20 0.126 18.4 0.931 1.46
16 1.17 0.126 18.4 0.904 1.43
17 1.13 0.126 18.4 0.863 1.39
18 1.10 0.126 18.4 0.833 1.36
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.024279 0.0363 7531 -0.668 1.0000
Step1 - Step3 -0.045689 0.0363 7531 -1.257 0.9988
Step1 - Step4 -0.047983 0.0363 7531 -1.320 0.9979
Step1 - Step5 -0.061631 0.0363 7531 -1.696 0.9677
Step1 - Step6 -0.025692 0.0363 7531 -0.707 1.0000
Step1 - Step7 -0.037183 0.0363 7531 -1.023 0.9999
Step1 - Step8 -0.031626 0.0363 7531 -0.870 1.0000
Step1 - Step9 -0.018463 0.0363 7531 -0.508 1.0000
Step1 - Step10 -0.025220 0.0363 7531 -0.694 1.0000
Step1 - Step11 -0.016567 0.0363 7531 -0.456 1.0000
Step1 - Step12 -0.000650 0.0363 7531 -0.018 1.0000
Step1 - Step13 0.009126 0.0363 7531 0.251 1.0000
Step1 - Step14 0.037930 0.0363 7531 1.044 0.9999
Step1 - Step15 0.047521 0.0363 7531 1.308 0.9981
Step1 - Step16 0.074831 0.0363 7531 2.059 0.8397
Step1 - Step17 0.115652 0.0363 7531 3.182 0.1252
Step1 - Step18 0.146428 0.0363 7531 4.029 0.0072
Step2 - Step3 -0.021410 0.0363 7531 -0.589 1.0000
Step2 - Step4 -0.023704 0.0363 7531 -0.652 1.0000
Step2 - Step5 -0.037352 0.0363 7531 -1.028 0.9999
Step2 - Step6 -0.001414 0.0363 7531 -0.039 1.0000
Step2 - Step7 -0.012904 0.0363 7531 -0.355 1.0000
Step2 - Step8 -0.007348 0.0363 7531 -0.202 1.0000
Step2 - Step9 0.005816 0.0363 7531 0.160 1.0000
Step2 - Step10 -0.000941 0.0363 7531 -0.026 1.0000
Step2 - Step11 0.007711 0.0363 7531 0.212 1.0000
Step2 - Step12 0.023629 0.0363 7531 0.650 1.0000
Step2 - Step13 0.033405 0.0363 7531 0.919 1.0000
Step2 - Step14 0.062209 0.0363 7531 1.712 0.9647
Step2 - Step15 0.071800 0.0363 7531 1.976 0.8811
Step2 - Step16 0.099109 0.0363 7531 2.727 0.3615
Step2 - Step17 0.139931 0.0363 7531 3.850 0.0142
Step2 - Step18 0.170707 0.0363 7531 4.697 0.0004
Step3 - Step4 -0.002294 0.0363 7531 -0.063 1.0000
Step3 - Step5 -0.015942 0.0363 7531 -0.439 1.0000
Step3 - Step6 0.019997 0.0363 7531 0.550 1.0000
Step3 - Step7 0.008506 0.0363 7531 0.234 1.0000
Step3 - Step8 0.014062 0.0363 7531 0.387 1.0000
Step3 - Step9 0.027226 0.0363 7531 0.749 1.0000
Step3 - Step10 0.020469 0.0363 7531 0.563 1.0000
Step3 - Step11 0.029122 0.0363 7531 0.801 1.0000
Step3 - Step12 0.045039 0.0363 7531 1.239 0.9990
Step3 - Step13 0.054815 0.0363 7531 1.508 0.9902
Step3 - Step14 0.083619 0.0363 7531 2.301 0.6829
Step3 - Step15 0.093210 0.0363 7531 2.565 0.4804
Step3 - Step16 0.120519 0.0363 7531 3.316 0.0855
Step3 - Step17 0.161341 0.0363 7531 4.439 0.0013
Step3 - Step18 0.192117 0.0363 7531 5.286 <.0001
Step4 - Step5 -0.013648 0.0363 7531 -0.376 1.0000
Step4 - Step6 0.022290 0.0363 7531 0.613 1.0000
Step4 - Step7 0.010800 0.0363 7531 0.297 1.0000
Step4 - Step8 0.016356 0.0363 7531 0.450 1.0000
Step4 - Step9 0.029520 0.0363 7531 0.812 1.0000
Step4 - Step10 0.022763 0.0363 7531 0.626 1.0000
Step4 - Step11 0.031415 0.0363 7531 0.864 1.0000
Step4 - Step12 0.047333 0.0363 7531 1.302 0.9982
Step4 - Step13 0.057109 0.0363 7531 1.571 0.9849
Step4 - Step14 0.085913 0.0363 7531 2.364 0.6356
Step4 - Step15 0.095504 0.0363 7531 2.628 0.4327
Step4 - Step16 0.122813 0.0363 7531 3.379 0.0708
Step4 - Step17 0.163635 0.0363 7531 4.502 0.0009
Step4 - Step18 0.194411 0.0363 7531 5.349 <.0001
Step5 - Step6 0.035939 0.0363 7531 0.989 1.0000
Step5 - Step7 0.024448 0.0363 7531 0.673 1.0000
Step5 - Step8 0.030005 0.0363 7531 0.826 1.0000
Step5 - Step9 0.043168 0.0363 7531 1.188 0.9994
Step5 - Step10 0.036411 0.0363 7531 1.002 0.9999
Step5 - Step11 0.045064 0.0363 7531 1.240 0.9990
Step5 - Step12 0.060981 0.0363 7531 1.678 0.9708
Step5 - Step13 0.070757 0.0363 7531 1.947 0.8936
Step5 - Step14 0.099561 0.0363 7531 2.739 0.3530
Step5 - Step15 0.109152 0.0363 7531 3.003 0.1985
Step5 - Step16 0.136462 0.0363 7531 3.755 0.0202
Step5 - Step17 0.177283 0.0363 7531 4.878 0.0002
Step5 - Step18 0.208060 0.0363 7531 5.725 <.0001
Step6 - Step7 -0.011491 0.0363 7531 -0.316 1.0000
Step6 - Step8 -0.005934 0.0363 7531 -0.163 1.0000
Step6 - Step9 0.007229 0.0363 7531 0.199 1.0000
Step6 - Step10 0.000472 0.0363 7531 0.013 1.0000
Step6 - Step11 0.009125 0.0363 7531 0.251 1.0000
Step6 - Step12 0.025042 0.0363 7531 0.689 1.0000
Step6 - Step13 0.034818 0.0363 7531 0.958 1.0000
Step6 - Step14 0.063622 0.0363 7531 1.751 0.9566
Step6 - Step15 0.073214 0.0363 7531 2.014 0.8627
Step6 - Step16 0.100523 0.0363 7531 2.766 0.3351
Step6 - Step17 0.141344 0.0363 7531 3.889 0.0123
Step6 - Step18 0.172121 0.0363 7531 4.736 0.0003
Step7 - Step8 0.005557 0.0363 7531 0.153 1.0000
Step7 - Step9 0.018720 0.0363 7531 0.515 1.0000
Step7 - Step10 0.011963 0.0363 7531 0.329 1.0000
Step7 - Step11 0.020616 0.0363 7531 0.567 1.0000
Step7 - Step12 0.036533 0.0363 7531 1.005 0.9999
Step7 - Step13 0.046309 0.0363 7531 1.274 0.9986
Step7 - Step14 0.075113 0.0363 7531 2.067 0.8354
Step7 - Step15 0.084704 0.0363 7531 2.331 0.6608
Step7 - Step16 0.112014 0.0363 7531 3.082 0.1631
Step7 - Step17 0.152835 0.0363 7531 4.205 0.0035
Step7 - Step18 0.183611 0.0363 7531 5.052 0.0001
Step8 - Step9 0.013163 0.0363 7531 0.362 1.0000
Step8 - Step10 0.006406 0.0363 7531 0.176 1.0000
Step8 - Step11 0.015059 0.0363 7531 0.414 1.0000
Step8 - Step12 0.030976 0.0363 7531 0.852 1.0000
Step8 - Step13 0.040752 0.0363 7531 1.121 0.9997
Step8 - Step14 0.069556 0.0363 7531 1.914 0.9070
Step8 - Step15 0.079148 0.0363 7531 2.178 0.7686
Step8 - Step16 0.106457 0.0363 7531 2.929 0.2364
Step8 - Step17 0.147278 0.0363 7531 4.052 0.0065
Step8 - Step18 0.178055 0.0363 7531 4.899 0.0001
Step9 - Step10 -0.006757 0.0363 7531 -0.186 1.0000
Step9 - Step11 0.001896 0.0363 7531 0.052 1.0000
Step9 - Step12 0.017813 0.0363 7531 0.490 1.0000
Step9 - Step13 0.027589 0.0363 7531 0.759 1.0000
Step9 - Step14 0.056393 0.0363 7531 1.552 0.9867
Step9 - Step15 0.065985 0.0363 7531 1.816 0.9400
Step9 - Step16 0.093294 0.0363 7531 2.567 0.4786
Step9 - Step17 0.134115 0.0363 7531 3.690 0.0255
Step9 - Step18 0.164892 0.0363 7531 4.537 0.0008
Step10 - Step11 0.008653 0.0363 7531 0.238 1.0000
Step10 - Step12 0.024570 0.0363 7531 0.676 1.0000
Step10 - Step13 0.034346 0.0363 7531 0.945 1.0000
Step10 - Step14 0.063150 0.0363 7531 1.738 0.9594
Step10 - Step15 0.072741 0.0363 7531 2.002 0.8690
Step10 - Step16 0.100051 0.0363 7531 2.753 0.3438
Step10 - Step17 0.140872 0.0363 7531 3.876 0.0129
Step10 - Step18 0.171648 0.0363 7531 4.723 0.0003
Step11 - Step12 0.015917 0.0363 7531 0.438 1.0000
Step11 - Step13 0.025693 0.0363 7531 0.707 1.0000
Step11 - Step14 0.054497 0.0363 7531 1.500 0.9908
Step11 - Step15 0.064089 0.0363 7531 1.763 0.9536
Step11 - Step16 0.091398 0.0363 7531 2.515 0.5188
Step11 - Step17 0.132219 0.0363 7531 3.638 0.0305
Step11 - Step18 0.162996 0.0363 7531 4.485 0.0010
Step12 - Step13 0.009776 0.0363 7531 0.269 1.0000
Step12 - Step14 0.038580 0.0363 7531 1.062 0.9999
Step12 - Step15 0.048171 0.0363 7531 1.325 0.9978
Step12 - Step16 0.075481 0.0363 7531 2.077 0.8298
Step12 - Step17 0.116302 0.0363 7531 3.200 0.1192
Step12 - Step18 0.147078 0.0363 7531 4.047 0.0067
Step13 - Step14 0.028804 0.0363 7531 0.793 1.0000
Step13 - Step15 0.038395 0.0363 7531 1.056 0.9999
Step13 - Step16 0.065705 0.0363 7531 1.808 0.9421
Step13 - Step17 0.106526 0.0363 7531 2.931 0.2354
Step13 - Step18 0.137302 0.0363 7531 3.778 0.0186
Step14 - Step15 0.009591 0.0363 7531 0.264 1.0000
Step14 - Step16 0.036901 0.0363 7531 1.015 0.9999
Step14 - Step17 0.077722 0.0363 7531 2.139 0.7935
Step14 - Step18 0.108498 0.0363 7531 2.985 0.2073
Step15 - Step16 0.027309 0.0363 7531 0.751 1.0000
Step15 - Step17 0.068131 0.0363 7531 1.875 0.9213
Step15 - Step18 0.098907 0.0363 7531 2.721 0.3653
Step16 - Step17 0.040821 0.0363 7531 1.123 0.9997
Step16 - Step18 0.071598 0.0363 7531 1.970 0.8836
Step17 - Step18 0.030776 0.0363 7531 0.847 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates plot_stepwise_rms_per_block <- function(step_summary_block, block_number, step_range) {
df <- step_summary_block %>%
filter(Block == as.character(block_number),
Step %in% as.character(step_range)) %>%
group_by(Step, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
sd_rms = sd(RMS, na.rm = TRUE),
.groups = "drop"
)
step_levels <- as.character(step_range)
step_ticks <- step_levels[as.numeric(step_levels) %% 2 == 1 | step_levels == "1"]
ggplot(df, aes(x = Step, y = mean_rms)) +
geom_point(aes(color = Axis), size = 2) +
geom_errorbar(aes(ymin = mean_rms - sd_rms, ymax = mean_rms + sd_rms, color = Axis), width = 0.3) +
facet_wrap(~ Axis, ncol = 3, scales = "free_y") +
scale_x_discrete(breaks = step_ticks) +
ylim(0, 3.25) +
labs(
title = paste("Step-wise RMS Acceleration – Block", block_number),
x = "Step",
y = "Mean RMS Acceleration (m/s²)"
) +
theme_minimal() +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
text = element_text(size = 12),
plot.title = element_text(face = "bold"),
legend.position = "none"
)
}# Block 1: 6 steps
plot_block1 <- plot_stepwise_rms_per_block(step_summary_6, block_number = 1, step_range = 1:6)
print(plot_block1)
# Block 2: 12 steps
plot_block2 <- plot_stepwise_rms_per_block(step_summary_12, block_number = 2, step_range = 1:12)
print(plot_block2)
# Block 3: 18 steps
plot_block3 <- plot_stepwise_rms_per_block(step_summary_18, block_number = 3, step_range = 1:18)
print(plot_block3)
#3.2 concatenation analysis rms test blocks 4,5
run_mixed_length_lmms <- function(step_summary_block45, target_block, seq_length) {
axes <- c("X", "Y", "Z")
cat(glue::glue("\n\n=========== Block {target_block} | {seq_length}-Step Trials ===========\n"))
for (ax in axes) {
cat(glue::glue("\n--- Axis: {ax} ---\n"))
df <- step_summary_block45 %>%
filter(Block == as.character(target_block),
Axis == ax,
step_count == seq_length,
Step %in% as.character(1:seq_length)) %>%
mutate(Step = factor(Step))
if (nrow(df) == 0) {
cat("No valid data for Block", target_block, "Axis", ax, "Length", seq_length, "\n")
next
}
model <- lmer(RMS ~ Step + (1 | subject) + (1 | trial_id), data = df)
anova_res <- car::Anova(model, type = 2, test.statistic = "Chisq")
emms <- emmeans(model, ~ Step)
pairwise <- contrast(emms, method = "pairwise", adjust = "tukey")
print(anova_res)
cat("\nEstimated Marginal Means:\n")
print(summary(emms))
cat("\nPairwise Comparisons:\n")
print(pairwise)
}
}assign_steps_by_trial <- function(df) {
df %>%
group_by(subject, Block, trial) %>%
mutate(
step_count = n(), # Number of rows (data points) for this trial
Step = cut_number(row_number(), n = unique(step_count), labels = FALSE)
) %>%
ungroup()
}
# Parameters
step_markers <- c(14, 15, 16, 17)
buffer <- 3
# Extract and window data for Block 4 & 5 using correct step assignment
step_data_45 <- tagged_data2 %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_trial() %>% # ✅ Use correct assignment here
filter(Block %in% c(4, 5)) %>%
mutate(Step = as.numeric(Step)) %>%
group_by(subject, Block, trial) %>%
mutate(step_count = max(Step, na.rm = TRUE)) %>%
ungroup() %>%
filter(Step <= step_count) %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup()
# Create index of step events
step_indices_45 <- step_data_45 %>%
select(subject, Block, trial, row_id, Step, step_count)
# Apply buffer and extract windowed data
window_data_45 <- map_dfr(1:nrow(step_indices_45), function(i) {
step <- step_indices_45[i, ]
rows <- (step$row_id - buffer):(step$row_id + buffer)
step_data_45 %>%
filter(subject == step$subject,
Block == step$Block,
trial == step$trial,
row_id %in% rows) %>%
mutate(Step = step$Step, step_count = step$step_count)
})
# Compute stepwise RMS summary
step_summary_block45 <- window_data_45 %>%
group_by(subject, Block, trial, Step, step_count) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = toupper(gsub("rms_", "", Axis)),
Step = factor(Step),
Block = factor(Block),
subject = factor(subject),
trial_id = interaction(subject, trial, drop = TRUE)
)run_mixed_length_lmms <- function(step_summary_block45, target_block, seq_length) {
axes <- c("X", "Y", "Z")
cat(glue::glue("\n\n=========== Block {target_block} | {seq_length}-Step Trials ===========\n"))
for (ax in axes) {
cat(glue::glue("\n--- Axis: {ax} ---\n"))
df <- step_summary_block45 %>%
filter(Block == as.character(target_block),
Axis == ax,
step_count == seq_length,
Step %in% as.character(1:seq_length)) %>%
mutate(Step = factor(Step))
if (nrow(df) == 0) {
cat("No valid data for Block", target_block, "Axis", ax, "Length", seq_length, "\n")
next
}
model <- lmer(RMS ~ Step + (1 | subject) + (1 | trial_id), data = df)
anova_res <- car::Anova(model, type = 2, test.statistic = "Chisq")
emms <- emmeans(model, ~ Step)
pairwise <- contrast(emms, method = "pairwise", adjust = "tukey")
print(anova_res)
cat("\nEstimated Marginal Means:\n")
print(summary(emms))
cat("\nPairwise Comparisons:\n")
print(pairwise)
}
}# Block 4
run_mixed_length_lmms(step_summary_block45, target_block = 4, seq_length = 6)
=========== Block 4 | 6-Step Trials ===========--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 11.495 5 0.04241 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.688 0.0821 17.3 0.515 0.861
2 0.680 0.0821 17.3 0.507 0.853
3 0.675 0.0821 17.3 0.502 0.848
4 0.675 0.0821 17.3 0.502 0.848
5 0.683 0.0821 17.3 0.510 0.856
6 0.652 0.0821 17.3 0.479 0.825
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00820 0.0117 1275 0.698 0.9822
Step1 - Step3 0.01280 0.0117 1275 1.090 0.8856
Step1 - Step4 0.01280 0.0117 1275 1.090 0.8856
Step1 - Step5 0.00532 0.0117 1275 0.453 0.9976
Step1 - Step6 0.03630 0.0117 1275 3.091 0.0249
Step2 - Step3 0.00460 0.0117 1275 0.392 0.9988
Step2 - Step4 0.00460 0.0117 1275 0.392 0.9988
Step2 - Step5 -0.00288 0.0117 1275 -0.245 0.9999
Step2 - Step6 0.02810 0.0117 1275 2.393 0.1595
Step3 - Step4 0.00000 0.0117 1275 0.000 1.0000
Step3 - Step5 -0.00748 0.0117 1275 -0.637 0.9882
Step3 - Step6 0.02350 0.0117 1275 2.001 0.3423
Step4 - Step5 -0.00748 0.0117 1275 -0.637 0.9882
Step4 - Step6 0.02350 0.0117 1275 2.001 0.3423
Step5 - Step6 0.03098 0.0117 1275 2.638 0.0891
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 17.643 5 0.003429 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.748 0.0834 17.3 0.572 0.924
2 0.738 0.0834 17.3 0.563 0.914
3 0.748 0.0834 17.3 0.572 0.924
4 0.748 0.0834 17.3 0.572 0.924
5 0.755 0.0834 17.3 0.579 0.930
6 0.708 0.0834 17.3 0.532 0.883
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 9.48e-03 0.0128 1275 0.741 0.9767
Step1 - Step3 8.26e-05 0.0128 1275 0.006 1.0000
Step1 - Step4 8.26e-05 0.0128 1275 0.006 1.0000
Step1 - Step5 -6.76e-03 0.0128 1275 -0.529 0.9950
Step1 - Step6 4.02e-02 0.0128 1275 3.144 0.0211
Step2 - Step3 -9.39e-03 0.0128 1275 -0.735 0.9776
Step2 - Step4 -9.39e-03 0.0128 1275 -0.735 0.9776
Step2 - Step5 -1.62e-02 0.0128 1275 -1.270 0.8014
Step2 - Step6 3.07e-02 0.0128 1275 2.403 0.1560
Step3 - Step4 0.00e+00 0.0128 1275 0.000 1.0000
Step3 - Step5 -6.84e-03 0.0128 1275 -0.535 0.9947
Step3 - Step6 4.01e-02 0.0128 1275 3.138 0.0215
Step4 - Step5 -6.84e-03 0.0128 1275 -0.535 0.9947
Step4 - Step6 4.01e-02 0.0128 1275 3.138 0.0215
Step5 - Step6 4.69e-02 0.0128 1275 3.673 0.0034
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 45.445 5 1.178e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.60 0.145 17.4 1.29 1.90
2 1.57 0.145 17.4 1.26 1.87
3 1.53 0.145 17.4 1.23 1.84
4 1.53 0.145 17.4 1.23 1.84
5 1.52 0.145 17.4 1.21 1.82
6 1.45 0.145 17.4 1.15 1.76
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.0309 0.0227 1275 1.362 0.7497
Step1 - Step3 0.0616 0.0227 1275 2.717 0.0726
Step1 - Step4 0.0616 0.0227 1275 2.717 0.0726
Step1 - Step5 0.0789 0.0227 1275 3.482 0.0068
Step1 - Step6 0.1430 0.0227 1275 6.313 <.0001
Step2 - Step3 0.0307 0.0227 1275 1.355 0.7539
Step2 - Step4 0.0307 0.0227 1275 1.355 0.7539
Step2 - Step5 0.0480 0.0227 1275 2.120 0.2774
Step2 - Step6 0.1122 0.0227 1275 4.951 <.0001
Step3 - Step4 0.0000 0.0227 1275 0.000 1.0000
Step3 - Step5 0.0173 0.0227 1275 0.765 0.9732
Step3 - Step6 0.0815 0.0227 1275 3.596 0.0045
Step4 - Step5 0.0173 0.0227 1275 0.765 0.9732
Step4 - Step6 0.0815 0.0227 1275 3.596 0.0045
Step5 - Step6 0.0641 0.0227 1275 2.831 0.0533
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates run_mixed_length_lmms(step_summary_block45, target_block = 4, seq_length = 12)
=========== Block 4 | 12-Step Trials ===========--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 82.031 11 5.965e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.660 0.0741 18.5 0.505 0.816
2 0.680 0.0741 18.5 0.525 0.836
3 0.692 0.0741 18.5 0.537 0.847
4 0.695 0.0741 18.5 0.540 0.851
5 0.713 0.0741 18.5 0.557 0.868
6 0.698 0.0741 18.5 0.542 0.853
7 0.691 0.0741 18.5 0.535 0.846
8 0.682 0.0741 18.5 0.527 0.838
9 0.656 0.0741 18.5 0.501 0.811
10 0.638 0.0741 18.5 0.482 0.793
11 0.620 0.0741 18.5 0.464 0.775
12 0.562 0.0741 18.5 0.406 0.717
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.01971 0.022 2871 -0.897 0.9992
Step1 - Step3 -0.03163 0.022 2871 -1.439 0.9558
Step1 - Step4 -0.03484 0.022 2871 -1.585 0.9146
Step1 - Step5 -0.05257 0.022 2871 -2.392 0.4117
Step1 - Step6 -0.03745 0.022 2871 -1.704 0.8668
Step1 - Step7 -0.03037 0.022 2871 -1.382 0.9670
Step1 - Step8 -0.02208 0.022 2871 -1.005 0.9976
Step1 - Step9 0.00437 0.022 2871 0.199 1.0000
Step1 - Step10 0.02281 0.022 2871 1.038 0.9968
Step1 - Step11 0.04085 0.022 2871 1.858 0.7849
Step1 - Step12 0.09872 0.022 2871 4.492 0.0005
Step2 - Step3 -0.01191 0.022 2871 -0.542 1.0000
Step2 - Step4 -0.01513 0.022 2871 -0.688 0.9999
Step2 - Step5 -0.03286 0.022 2871 -1.495 0.9422
Step2 - Step6 -0.01774 0.022 2871 -0.807 0.9997
Step2 - Step7 -0.01066 0.022 2871 -0.485 1.0000
Step2 - Step8 -0.00237 0.022 2871 -0.108 1.0000
Step2 - Step9 0.02408 0.022 2871 1.096 0.9949
Step2 - Step10 0.04252 0.022 2871 1.935 0.7374
Step2 - Step11 0.06056 0.022 2871 2.755 0.2001
Step2 - Step12 0.11843 0.022 2871 5.389 <.0001
Step3 - Step4 -0.00322 0.022 2871 -0.146 1.0000
Step3 - Step5 -0.02094 0.022 2871 -0.953 0.9985
Step3 - Step6 -0.00582 0.022 2871 -0.265 1.0000
Step3 - Step7 0.00126 0.022 2871 0.057 1.0000
Step3 - Step8 0.00955 0.022 2871 0.434 1.0000
Step3 - Step9 0.03600 0.022 2871 1.638 0.8951
Step3 - Step10 0.05443 0.022 2871 2.477 0.3551
Step3 - Step11 0.07247 0.022 2871 3.297 0.0460
Step3 - Step12 0.13035 0.022 2871 5.931 <.0001
Step4 - Step5 -0.01773 0.022 2871 -0.807 0.9997
Step4 - Step6 -0.00261 0.022 2871 -0.119 1.0000
Step4 - Step7 0.00447 0.022 2871 0.203 1.0000
Step4 - Step8 0.01276 0.022 2871 0.581 1.0000
Step4 - Step9 0.03921 0.022 2871 1.784 0.8269
Step4 - Step10 0.05765 0.022 2871 2.623 0.2671
Step4 - Step11 0.07569 0.022 2871 3.444 0.0288
Step4 - Step12 0.13356 0.022 2871 6.077 <.0001
Step5 - Step6 0.01512 0.022 2871 0.688 0.9999
Step5 - Step7 0.02220 0.022 2871 1.010 0.9975
Step5 - Step8 0.03049 0.022 2871 1.387 0.9661
Step5 - Step9 0.05694 0.022 2871 2.591 0.2852
Step5 - Step10 0.07538 0.022 2871 3.430 0.0302
Step5 - Step11 0.09342 0.022 2871 4.250 0.0013
Step5 - Step12 0.15129 0.022 2871 6.884 <.0001
Step6 - Step7 0.00708 0.022 2871 0.322 1.0000
Step6 - Step8 0.01537 0.022 2871 0.699 0.9999
Step6 - Step9 0.04182 0.022 2871 1.903 0.7578
Step6 - Step10 0.06025 0.022 2871 2.742 0.2065
Step6 - Step11 0.07829 0.022 2871 3.562 0.0193
Step6 - Step12 0.13617 0.022 2871 6.196 <.0001
Step7 - Step8 0.00829 0.022 2871 0.377 1.0000
Step7 - Step9 0.03474 0.022 2871 1.581 0.9162
Step7 - Step10 0.05318 0.022 2871 2.420 0.3929
Step7 - Step11 0.07122 0.022 2871 3.240 0.0549
Step7 - Step12 0.12909 0.022 2871 5.873 <.0001
Step8 - Step9 0.02645 0.022 2871 1.203 0.9888
Step8 - Step10 0.04489 0.022 2871 2.042 0.6642
Step8 - Step11 0.06293 0.022 2871 2.863 0.1549
Step8 - Step12 0.12080 0.022 2871 5.496 <.0001
Step9 - Step10 0.01844 0.022 2871 0.839 0.9996
Step9 - Step11 0.03648 0.022 2871 1.660 0.8862
Step9 - Step12 0.09435 0.022 2871 4.293 0.0011
Step10 - Step11 0.01804 0.022 2871 0.821 0.9996
Step10 - Step12 0.07591 0.022 2871 3.454 0.0278
Step11 - Step12 0.05787 0.022 2871 2.633 0.2615
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 258.72 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.817 0.0859 18.7 0.637 0.997
2 0.813 0.0859 18.7 0.633 0.994
3 0.821 0.0859 18.7 0.641 1.001
4 0.802 0.0859 18.7 0.622 0.982
5 0.806 0.0859 18.7 0.626 0.986
6 0.741 0.0859 18.7 0.561 0.921
7 0.719 0.0859 18.7 0.539 0.899
8 0.687 0.0859 18.7 0.506 0.867
9 0.654 0.0859 18.7 0.474 0.834
10 0.615 0.0859 18.7 0.435 0.795
11 0.601 0.0859 18.7 0.421 0.781
12 0.563 0.0859 18.7 0.383 0.743
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00392 0.0275 2871 0.142 1.0000
Step1 - Step3 -0.00391 0.0275 2871 -0.142 1.0000
Step1 - Step4 0.01565 0.0275 2871 0.568 1.0000
Step1 - Step5 0.01185 0.0275 2871 0.430 1.0000
Step1 - Step6 0.07634 0.0275 2871 2.772 0.1924
Step1 - Step7 0.09804 0.0275 2871 3.561 0.0194
Step1 - Step8 0.13088 0.0275 2871 4.753 0.0001
Step1 - Step9 0.16336 0.0275 2871 5.933 <.0001
Step1 - Step10 0.20241 0.0275 2871 7.351 <.0001
Step1 - Step11 0.21613 0.0275 2871 7.849 <.0001
Step1 - Step12 0.25410 0.0275 2871 9.228 <.0001
Step2 - Step3 -0.00783 0.0275 2871 -0.284 1.0000
Step2 - Step4 0.01173 0.0275 2871 0.426 1.0000
Step2 - Step5 0.00793 0.0275 2871 0.288 1.0000
Step2 - Step6 0.07241 0.0275 2871 2.630 0.2633
Step2 - Step7 0.09412 0.0275 2871 3.418 0.0313
Step2 - Step8 0.12696 0.0275 2871 4.611 0.0003
Step2 - Step9 0.15944 0.0275 2871 5.790 <.0001
Step2 - Step10 0.19849 0.0275 2871 7.208 <.0001
Step2 - Step11 0.21221 0.0275 2871 7.707 <.0001
Step2 - Step12 0.25017 0.0275 2871 9.085 <.0001
Step3 - Step4 0.01956 0.0275 2871 0.710 0.9999
Step3 - Step5 0.01576 0.0275 2871 0.572 1.0000
Step3 - Step6 0.08025 0.0275 2871 2.914 0.1363
Step3 - Step7 0.10195 0.0275 2871 3.703 0.0117
Step3 - Step8 0.13479 0.0275 2871 4.895 0.0001
Step3 - Step9 0.16727 0.0275 2871 6.075 <.0001
Step3 - Step10 0.20632 0.0275 2871 7.493 <.0001
Step3 - Step11 0.22004 0.0275 2871 7.991 <.0001
Step3 - Step12 0.25800 0.0275 2871 9.370 <.0001
Step4 - Step5 -0.00380 0.0275 2871 -0.138 1.0000
Step4 - Step6 0.06069 0.0275 2871 2.204 0.5468
Step4 - Step7 0.08240 0.0275 2871 2.992 0.1112
Step4 - Step8 0.11524 0.0275 2871 4.185 0.0017
Step4 - Step9 0.14771 0.0275 2871 5.364 <.0001
Step4 - Step10 0.18677 0.0275 2871 6.783 <.0001
Step4 - Step11 0.20049 0.0275 2871 7.281 <.0001
Step4 - Step12 0.23845 0.0275 2871 8.660 <.0001
Step5 - Step6 0.06448 0.0275 2871 2.342 0.4468
Step5 - Step7 0.08619 0.0275 2871 3.130 0.0759
Step5 - Step8 0.11903 0.0275 2871 4.323 0.0010
Step5 - Step9 0.15151 0.0275 2871 5.502 <.0001
Step5 - Step10 0.19056 0.0275 2871 6.920 <.0001
Step5 - Step11 0.20428 0.0275 2871 7.419 <.0001
Step5 - Step12 0.24224 0.0275 2871 8.797 <.0001
Step6 - Step7 0.02171 0.0275 2871 0.788 0.9998
Step6 - Step8 0.05455 0.0275 2871 1.981 0.7066
Step6 - Step9 0.08702 0.0275 2871 3.160 0.0696
Step6 - Step10 0.12608 0.0275 2871 4.579 0.0003
Step6 - Step11 0.13980 0.0275 2871 5.077 <.0001
Step6 - Step12 0.17776 0.0275 2871 6.456 <.0001
Step7 - Step8 0.03284 0.0275 2871 1.193 0.9896
Step7 - Step9 0.06532 0.0275 2871 2.372 0.4255
Step7 - Step10 0.10437 0.0275 2871 3.790 0.0085
Step7 - Step11 0.11809 0.0275 2871 4.289 0.0011
Step7 - Step12 0.15605 0.0275 2871 5.667 <.0001
Step8 - Step9 0.03248 0.0275 2871 1.179 0.9905
Step8 - Step10 0.07153 0.0275 2871 2.598 0.2813
Step8 - Step11 0.08525 0.0275 2871 3.096 0.0837
Step8 - Step12 0.12321 0.0275 2871 4.475 0.0005
Step9 - Step10 0.03905 0.0275 2871 1.418 0.9602
Step9 - Step11 0.05277 0.0275 2871 1.917 0.7490
Step9 - Step12 0.09074 0.0275 2871 3.295 0.0464
Step10 - Step11 0.01372 0.0275 2871 0.498 1.0000
Step10 - Step12 0.05168 0.0275 2871 1.877 0.7738
Step11 - Step12 0.03796 0.0275 2871 1.379 0.9676
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 259.74 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.65 0.16 18.2 1.316 1.99
2 1.66 0.16 18.2 1.320 1.99
3 1.64 0.16 18.2 1.303 1.97
4 1.62 0.16 18.2 1.284 1.95
5 1.61 0.16 18.2 1.274 1.94
6 1.53 0.16 18.2 1.193 1.86
7 1.49 0.16 18.2 1.159 1.83
8 1.45 0.16 18.2 1.115 1.79
9 1.38 0.16 18.2 1.042 1.71
10 1.34 0.16 18.2 1.005 1.68
11 1.31 0.16 18.2 0.978 1.65
12 1.23 0.16 18.2 0.898 1.57
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.00448 0.0431 2871 -0.104 1.0000
Step1 - Step3 0.01291 0.0431 2871 0.300 1.0000
Step1 - Step4 0.03168 0.0431 2871 0.735 0.9999
Step1 - Step5 0.04161 0.0431 2871 0.966 0.9983
Step1 - Step6 0.12306 0.0431 2871 2.856 0.1577
Step1 - Step7 0.15719 0.0431 2871 3.648 0.0142
Step1 - Step8 0.20062 0.0431 2871 4.656 0.0002
Step1 - Step9 0.27331 0.0431 2871 6.343 <.0001
Step1 - Step10 0.31031 0.0431 2871 7.201 <.0001
Step1 - Step11 0.33804 0.0431 2871 7.845 <.0001
Step1 - Step12 0.41737 0.0431 2871 9.686 <.0001
Step2 - Step3 0.01739 0.0431 2871 0.404 1.0000
Step2 - Step4 0.03616 0.0431 2871 0.839 0.9996
Step2 - Step5 0.04610 0.0431 2871 1.070 0.9959
Step2 - Step6 0.12754 0.0431 2871 2.960 0.1211
Step2 - Step7 0.16167 0.0431 2871 3.752 0.0098
Step2 - Step8 0.20510 0.0431 2871 4.760 0.0001
Step2 - Step9 0.27779 0.0431 2871 6.447 <.0001
Step2 - Step10 0.31479 0.0431 2871 7.305 <.0001
Step2 - Step11 0.34252 0.0431 2871 7.949 <.0001
Step2 - Step12 0.42185 0.0431 2871 9.790 <.0001
Step3 - Step4 0.01877 0.0431 2871 0.436 1.0000
Step3 - Step5 0.02871 0.0431 2871 0.666 1.0000
Step3 - Step6 0.11015 0.0431 2871 2.556 0.3055
Step3 - Step7 0.14428 0.0431 2871 3.348 0.0392
Step3 - Step8 0.18771 0.0431 2871 4.356 0.0008
Step3 - Step9 0.26041 0.0431 2871 6.043 <.0001
Step3 - Step10 0.29740 0.0431 2871 6.902 <.0001
Step3 - Step11 0.32513 0.0431 2871 7.545 <.0001
Step3 - Step12 0.40447 0.0431 2871 9.386 <.0001
Step4 - Step5 0.00993 0.0431 2871 0.231 1.0000
Step4 - Step6 0.09138 0.0431 2871 2.121 0.6079
Step4 - Step7 0.12551 0.0431 2871 2.913 0.1368
Step4 - Step8 0.16894 0.0431 2871 3.921 0.0051
Step4 - Step9 0.24163 0.0431 2871 5.608 <.0001
Step4 - Step10 0.27863 0.0431 2871 6.466 <.0001
Step4 - Step11 0.30636 0.0431 2871 7.110 <.0001
Step4 - Step12 0.38569 0.0431 2871 8.951 <.0001
Step5 - Step6 0.08145 0.0431 2871 1.890 0.7656
Step5 - Step7 0.11558 0.0431 2871 2.682 0.2356
Step5 - Step8 0.15900 0.0431 2871 3.690 0.0122
Step5 - Step9 0.23170 0.0431 2871 5.377 <.0001
Step5 - Step10 0.26869 0.0431 2871 6.236 <.0001
Step5 - Step11 0.29642 0.0431 2871 6.879 <.0001
Step5 - Step12 0.37576 0.0431 2871 8.720 <.0001
Step6 - Step7 0.03413 0.0431 2871 0.792 0.9997
Step6 - Step8 0.07756 0.0431 2871 1.800 0.8184
Step6 - Step9 0.15025 0.0431 2871 3.487 0.0249
Step6 - Step10 0.18725 0.0431 2871 4.346 0.0009
Step6 - Step11 0.21498 0.0431 2871 4.989 <.0001
Step6 - Step12 0.29431 0.0431 2871 6.830 <.0001
Step7 - Step8 0.04343 0.0431 2871 1.008 0.9976
Step7 - Step9 0.11612 0.0431 2871 2.695 0.2291
Step7 - Step10 0.15312 0.0431 2871 3.553 0.0199
Step7 - Step11 0.18085 0.0431 2871 4.197 0.0017
Step7 - Step12 0.26018 0.0431 2871 6.038 <.0001
Step8 - Step9 0.07270 0.0431 2871 1.687 0.8744
Step8 - Step10 0.10969 0.0431 2871 2.546 0.3119
Step8 - Step11 0.13742 0.0431 2871 3.189 0.0639
Step8 - Step12 0.21676 0.0431 2871 5.030 <.0001
Step9 - Step10 0.03700 0.0431 2871 0.859 0.9994
Step9 - Step11 0.06473 0.0431 2871 1.502 0.9403
Step9 - Step12 0.14406 0.0431 2871 3.343 0.0399
Step10 - Step11 0.02773 0.0431 2871 0.644 1.0000
Step10 - Step12 0.10706 0.0431 2871 2.485 0.3499
Step11 - Step12 0.07933 0.0431 2871 1.841 0.7951
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates run_mixed_length_lmms(step_summary_block45, target_block = 4, seq_length = 18)
=========== Block 4 | 18-Step Trials ===========--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 168.51 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.712 0.0774 19 0.550 0.874
2 0.725 0.0774 19 0.563 0.887
3 0.739 0.0774 19 0.577 0.902
4 0.731 0.0774 19 0.569 0.893
5 0.736 0.0774 19 0.573 0.898
6 0.719 0.0774 19 0.556 0.881
7 0.700 0.0774 19 0.538 0.862
8 0.694 0.0774 19 0.532 0.856
9 0.690 0.0774 19 0.528 0.852
10 0.675 0.0774 19 0.513 0.837
11 0.674 0.0774 19 0.512 0.836
12 0.672 0.0774 19 0.510 0.834
13 0.649 0.0774 19 0.487 0.811
14 0.634 0.0774 19 0.472 0.796
15 0.613 0.0774 19 0.450 0.775
16 0.588 0.0774 19 0.426 0.750
17 0.568 0.0774 19 0.406 0.730
18 0.550 0.0774 19 0.388 0.712
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.012210 0.0263 4607 -0.464 1.0000
Step1 - Step3 -0.027059 0.0263 4607 -1.028 0.9999
Step1 - Step4 -0.018715 0.0263 4607 -0.711 1.0000
Step1 - Step5 -0.023106 0.0263 4607 -0.878 1.0000
Step1 - Step6 -0.006146 0.0263 4607 -0.234 1.0000
Step1 - Step7 0.012599 0.0263 4607 0.479 1.0000
Step1 - Step8 0.018323 0.0263 4607 0.696 1.0000
Step1 - Step9 0.022601 0.0263 4607 0.859 1.0000
Step1 - Step10 0.037658 0.0263 4607 1.431 0.9945
Step1 - Step11 0.038232 0.0263 4607 1.453 0.9935
Step1 - Step12 0.040537 0.0263 4607 1.541 0.9877
Step1 - Step13 0.063584 0.0263 4607 2.417 0.5952
Step1 - Step14 0.078633 0.0263 4607 2.989 0.2059
Step1 - Step15 0.099891 0.0263 4607 3.796 0.0175
Step1 - Step16 0.124087 0.0263 4607 4.716 0.0004
Step1 - Step17 0.144161 0.0263 4607 5.479 <.0001
Step1 - Step18 0.162179 0.0263 4607 6.164 <.0001
Step2 - Step3 -0.014849 0.0263 4607 -0.564 1.0000
Step2 - Step4 -0.006505 0.0263 4607 -0.247 1.0000
Step2 - Step5 -0.010896 0.0263 4607 -0.414 1.0000
Step2 - Step6 0.006064 0.0263 4607 0.230 1.0000
Step2 - Step7 0.024809 0.0263 4607 0.943 1.0000
Step2 - Step8 0.030533 0.0263 4607 1.160 0.9996
Step2 - Step9 0.034811 0.0263 4607 1.323 0.9978
Step2 - Step10 0.049868 0.0263 4607 1.895 0.9139
Step2 - Step11 0.050442 0.0263 4607 1.917 0.9057
Step2 - Step12 0.052747 0.0263 4607 2.005 0.8674
Step2 - Step13 0.075794 0.0263 4607 2.881 0.2638
Step2 - Step14 0.090843 0.0263 4607 3.453 0.0565
Step2 - Step15 0.112101 0.0263 4607 4.261 0.0028
Step2 - Step16 0.136297 0.0263 4607 5.180 <.0001
Step2 - Step17 0.156371 0.0263 4607 5.943 <.0001
Step2 - Step18 0.174389 0.0263 4607 6.628 <.0001
Step3 - Step4 0.008344 0.0263 4607 0.317 1.0000
Step3 - Step5 0.003953 0.0263 4607 0.150 1.0000
Step3 - Step6 0.020913 0.0263 4607 0.795 1.0000
Step3 - Step7 0.039659 0.0263 4607 1.507 0.9902
Step3 - Step8 0.045382 0.0263 4607 1.725 0.9621
Step3 - Step9 0.049660 0.0263 4607 1.887 0.9168
Step3 - Step10 0.064717 0.0263 4607 2.460 0.5617
Step3 - Step11 0.065291 0.0263 4607 2.481 0.5448
Step3 - Step12 0.067597 0.0263 4607 2.569 0.4771
Step3 - Step13 0.090643 0.0263 4607 3.445 0.0578
Step3 - Step14 0.105692 0.0263 4607 4.017 0.0075
Step3 - Step15 0.126950 0.0263 4607 4.825 0.0002
Step3 - Step16 0.151147 0.0263 4607 5.745 <.0001
Step3 - Step17 0.171220 0.0263 4607 6.507 <.0001
Step3 - Step18 0.189238 0.0263 4607 7.192 <.0001
Step4 - Step5 -0.004391 0.0263 4607 -0.167 1.0000
Step4 - Step6 0.012569 0.0263 4607 0.478 1.0000
Step4 - Step7 0.031314 0.0263 4607 1.190 0.9994
Step4 - Step8 0.037038 0.0263 4607 1.408 0.9955
Step4 - Step9 0.041316 0.0263 4607 1.570 0.9849
Step4 - Step10 0.056373 0.0263 4607 2.143 0.7910
Step4 - Step11 0.056947 0.0263 4607 2.164 0.7773
Step4 - Step12 0.059252 0.0263 4607 2.252 0.7181
Step4 - Step13 0.082299 0.0263 4607 3.128 0.1450
Step4 - Step14 0.097348 0.0263 4607 3.700 0.0247
Step4 - Step15 0.118606 0.0263 4607 4.508 0.0009
Step4 - Step16 0.142803 0.0263 4607 5.427 <.0001
Step4 - Step17 0.162876 0.0263 4607 6.190 <.0001
Step4 - Step18 0.180894 0.0263 4607 6.875 <.0001
Step5 - Step6 0.016960 0.0263 4607 0.645 1.0000
Step5 - Step7 0.035705 0.0263 4607 1.357 0.9970
Step5 - Step8 0.041429 0.0263 4607 1.575 0.9845
Step5 - Step9 0.045707 0.0263 4607 1.737 0.9595
Step5 - Step10 0.060763 0.0263 4607 2.309 0.6766
Step5 - Step11 0.061338 0.0263 4607 2.331 0.6603
Step5 - Step12 0.063643 0.0263 4607 2.419 0.5934
Step5 - Step13 0.086690 0.0263 4607 3.295 0.0912
Step5 - Step14 0.101739 0.0263 4607 3.867 0.0135
Step5 - Step15 0.122997 0.0263 4607 4.675 0.0004
Step5 - Step16 0.147193 0.0263 4607 5.594 <.0001
Step5 - Step17 0.167267 0.0263 4607 6.357 <.0001
Step5 - Step18 0.185284 0.0263 4607 7.042 <.0001
Step6 - Step7 0.018745 0.0263 4607 0.712 1.0000
Step6 - Step8 0.024469 0.0263 4607 0.930 1.0000
Step6 - Step9 0.028747 0.0263 4607 1.093 0.9998
Step6 - Step10 0.043804 0.0263 4607 1.665 0.9729
Step6 - Step11 0.044378 0.0263 4607 1.687 0.9693
Step6 - Step12 0.046683 0.0263 4607 1.774 0.9509
Step6 - Step13 0.069730 0.0263 4607 2.650 0.4163
Step6 - Step14 0.084779 0.0263 4607 3.222 0.1122
Step6 - Step15 0.106037 0.0263 4607 4.030 0.0072
Step6 - Step16 0.130233 0.0263 4607 4.950 0.0001
Step6 - Step17 0.150307 0.0263 4607 5.713 <.0001
Step6 - Step18 0.168325 0.0263 4607 6.397 <.0001
Step7 - Step8 0.005724 0.0263 4607 0.218 1.0000
Step7 - Step9 0.010002 0.0263 4607 0.380 1.0000
Step7 - Step10 0.025058 0.0263 4607 0.952 1.0000
Step7 - Step11 0.025633 0.0263 4607 0.974 1.0000
Step7 - Step12 0.027938 0.0263 4607 1.062 0.9999
Step7 - Step13 0.050985 0.0263 4607 1.938 0.8974
Step7 - Step14 0.066034 0.0263 4607 2.510 0.5228
Step7 - Step15 0.087292 0.0263 4607 3.318 0.0853
Step7 - Step16 0.111488 0.0263 4607 4.237 0.0031
Step7 - Step17 0.131562 0.0263 4607 5.000 0.0001
Step7 - Step18 0.149579 0.0263 4607 5.685 <.0001
Step8 - Step9 0.004278 0.0263 4607 0.163 1.0000
Step8 - Step10 0.019335 0.0263 4607 0.735 1.0000
Step8 - Step11 0.019909 0.0263 4607 0.757 1.0000
Step8 - Step12 0.022214 0.0263 4607 0.844 1.0000
Step8 - Step13 0.045261 0.0263 4607 1.720 0.9630
Step8 - Step14 0.060310 0.0263 4607 2.292 0.6892
Step8 - Step15 0.081568 0.0263 4607 3.100 0.1559
Step8 - Step16 0.105764 0.0263 4607 4.020 0.0075
Step8 - Step17 0.125838 0.0263 4607 4.783 0.0003
Step8 - Step18 0.143856 0.0263 4607 5.467 <.0001
Step9 - Step10 0.015057 0.0263 4607 0.572 1.0000
Step9 - Step11 0.015631 0.0263 4607 0.594 1.0000
Step9 - Step12 0.017936 0.0263 4607 0.682 1.0000
Step9 - Step13 0.040983 0.0263 4607 1.558 0.9862
Step9 - Step14 0.056032 0.0263 4607 2.130 0.7990
Step9 - Step15 0.077290 0.0263 4607 2.938 0.2321
Step9 - Step16 0.101487 0.0263 4607 3.857 0.0139
Step9 - Step17 0.121560 0.0263 4607 4.620 0.0006
Step9 - Step18 0.139578 0.0263 4607 5.305 <.0001
Step10 - Step11 0.000574 0.0263 4607 0.022 1.0000
Step10 - Step12 0.002880 0.0263 4607 0.109 1.0000
Step10 - Step13 0.025926 0.0263 4607 0.985 1.0000
Step10 - Step14 0.040975 0.0263 4607 1.557 0.9862
Step10 - Step15 0.062233 0.0263 4607 2.365 0.6346
Step10 - Step16 0.086430 0.0263 4607 3.285 0.0939
Step10 - Step17 0.106503 0.0263 4607 4.048 0.0067
Step10 - Step18 0.124521 0.0263 4607 4.733 0.0003
Step11 - Step12 0.002305 0.0263 4607 0.088 1.0000
Step11 - Step13 0.025352 0.0263 4607 0.964 1.0000
Step11 - Step14 0.040401 0.0263 4607 1.536 0.9881
Step11 - Step15 0.061659 0.0263 4607 2.343 0.6511
Step11 - Step16 0.085856 0.0263 4607 3.263 0.1000
Step11 - Step17 0.105929 0.0263 4607 4.026 0.0073
Step11 - Step18 0.123947 0.0263 4607 4.711 0.0004
Step12 - Step13 0.023047 0.0263 4607 0.876 1.0000
Step12 - Step14 0.038096 0.0263 4607 1.448 0.9937
Step12 - Step15 0.059354 0.0263 4607 2.256 0.7154
Step12 - Step16 0.083550 0.0263 4607 3.175 0.1277
Step12 - Step17 0.103624 0.0263 4607 3.938 0.0102
Step12 - Step18 0.121641 0.0263 4607 4.623 0.0005
Step13 - Step14 0.015049 0.0263 4607 0.572 1.0000
Step13 - Step15 0.036307 0.0263 4607 1.380 0.9964
Step13 - Step16 0.060503 0.0263 4607 2.300 0.6839
Step13 - Step17 0.080577 0.0263 4607 3.062 0.1717
Step13 - Step18 0.098595 0.0263 4607 3.747 0.0209
Step14 - Step15 0.021258 0.0263 4607 0.808 1.0000
Step14 - Step16 0.045454 0.0263 4607 1.728 0.9615
Step14 - Step17 0.065528 0.0263 4607 2.490 0.5378
Step14 - Step18 0.083545 0.0263 4607 3.175 0.1277
Step15 - Step16 0.024196 0.0263 4607 0.920 1.0000
Step15 - Step17 0.044270 0.0263 4607 1.683 0.9700
Step15 - Step18 0.062288 0.0263 4607 2.367 0.6330
Step16 - Step17 0.020073 0.0263 4607 0.763 1.0000
Step16 - Step18 0.038091 0.0263 4607 1.448 0.9938
Step17 - Step18 0.018018 0.0263 4607 0.685 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 368.68 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.834 0.0764 18.9 0.674 0.994
2 0.826 0.0764 18.9 0.666 0.986
3 0.814 0.0764 18.9 0.654 0.974
4 0.806 0.0764 18.9 0.646 0.966
5 0.796 0.0764 18.9 0.636 0.956
6 0.747 0.0764 18.9 0.587 0.907
7 0.727 0.0764 18.9 0.567 0.887
8 0.714 0.0764 18.9 0.554 0.874
9 0.700 0.0764 18.9 0.540 0.860
10 0.698 0.0764 18.9 0.538 0.858
11 0.687 0.0764 18.9 0.527 0.847
12 0.673 0.0764 18.9 0.513 0.833
13 0.664 0.0764 18.9 0.504 0.824
14 0.643 0.0764 18.9 0.483 0.803
15 0.629 0.0764 18.9 0.469 0.789
16 0.611 0.0764 18.9 0.451 0.771
17 0.588 0.0764 18.9 0.428 0.748
18 0.575 0.0764 18.9 0.415 0.734
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00755 0.0251 4607 0.301 1.0000
Step1 - Step3 0.01958 0.0251 4607 0.780 1.0000
Step1 - Step4 0.02739 0.0251 4607 1.092 0.9998
Step1 - Step5 0.03796 0.0251 4607 1.513 0.9899
Step1 - Step6 0.08659 0.0251 4607 3.451 0.0568
Step1 - Step7 0.10695 0.0251 4607 4.262 0.0028
Step1 - Step8 0.11966 0.0251 4607 4.769 0.0003
Step1 - Step9 0.13328 0.0251 4607 5.312 <.0001
Step1 - Step10 0.13565 0.0251 4607 5.406 <.0001
Step1 - Step11 0.14669 0.0251 4607 5.846 <.0001
Step1 - Step12 0.16101 0.0251 4607 6.416 <.0001
Step1 - Step13 0.17001 0.0251 4607 6.775 <.0001
Step1 - Step14 0.19040 0.0251 4607 7.588 <.0001
Step1 - Step15 0.20443 0.0251 4607 8.147 <.0001
Step1 - Step16 0.22292 0.0251 4607 8.884 <.0001
Step1 - Step17 0.24551 0.0251 4607 9.784 <.0001
Step1 - Step18 0.25903 0.0251 4607 10.323 <.0001
Step2 - Step3 0.01203 0.0251 4607 0.480 1.0000
Step2 - Step4 0.01984 0.0251 4607 0.791 1.0000
Step2 - Step5 0.03041 0.0251 4607 1.212 0.9993
Step2 - Step6 0.07905 0.0251 4607 3.150 0.1366
Step2 - Step7 0.09940 0.0251 4607 3.961 0.0094
Step2 - Step8 0.11211 0.0251 4607 4.468 0.0011
Step2 - Step9 0.12574 0.0251 4607 5.011 0.0001
Step2 - Step10 0.12810 0.0251 4607 5.105 0.0001
Step2 - Step11 0.13914 0.0251 4607 5.545 <.0001
Step2 - Step12 0.15346 0.0251 4607 6.116 <.0001
Step2 - Step13 0.16246 0.0251 4607 6.474 <.0001
Step2 - Step14 0.18285 0.0251 4607 7.287 <.0001
Step2 - Step15 0.19688 0.0251 4607 7.846 <.0001
Step2 - Step16 0.21537 0.0251 4607 8.583 <.0001
Step2 - Step17 0.23796 0.0251 4607 9.483 <.0001
Step2 - Step18 0.25149 0.0251 4607 10.022 <.0001
Step3 - Step4 0.00781 0.0251 4607 0.311 1.0000
Step3 - Step5 0.01838 0.0251 4607 0.732 1.0000
Step3 - Step6 0.06701 0.0251 4607 2.671 0.4015
Step3 - Step7 0.08737 0.0251 4607 3.482 0.0514
Step3 - Step8 0.10008 0.0251 4607 3.988 0.0084
Step3 - Step9 0.11370 0.0251 4607 4.531 0.0008
Step3 - Step10 0.11607 0.0251 4607 4.626 0.0005
Step3 - Step11 0.12711 0.0251 4607 5.065 0.0001
Step3 - Step12 0.14143 0.0251 4607 5.636 <.0001
Step3 - Step13 0.15043 0.0251 4607 5.995 <.0001
Step3 - Step14 0.17082 0.0251 4607 6.807 <.0001
Step3 - Step15 0.18485 0.0251 4607 7.367 <.0001
Step3 - Step16 0.20334 0.0251 4607 8.104 <.0001
Step3 - Step17 0.22593 0.0251 4607 9.004 <.0001
Step3 - Step18 0.23945 0.0251 4607 9.543 <.0001
Step4 - Step5 0.01057 0.0251 4607 0.421 1.0000
Step4 - Step6 0.05920 0.0251 4607 2.359 0.6391
Step4 - Step7 0.07956 0.0251 4607 3.171 0.1294
Step4 - Step8 0.09227 0.0251 4607 3.677 0.0268
Step4 - Step9 0.10589 0.0251 4607 4.220 0.0033
Step4 - Step10 0.10826 0.0251 4607 4.314 0.0022
Step4 - Step11 0.11930 0.0251 4607 4.754 0.0003
Step4 - Step12 0.13362 0.0251 4607 5.325 <.0001
Step4 - Step13 0.14262 0.0251 4607 5.684 <.0001
Step4 - Step14 0.16301 0.0251 4607 6.496 <.0001
Step4 - Step15 0.17704 0.0251 4607 7.055 <.0001
Step4 - Step16 0.19553 0.0251 4607 7.792 <.0001
Step4 - Step17 0.21812 0.0251 4607 8.692 <.0001
Step4 - Step18 0.23164 0.0251 4607 9.231 <.0001
Step5 - Step6 0.04864 0.0251 4607 1.938 0.8971
Step5 - Step7 0.06899 0.0251 4607 2.750 0.3463
Step5 - Step8 0.08170 0.0251 4607 3.256 0.1020
Step5 - Step9 0.09533 0.0251 4607 3.799 0.0173
Step5 - Step10 0.09769 0.0251 4607 3.893 0.0122
Step5 - Step11 0.10873 0.0251 4607 4.333 0.0020
Step5 - Step12 0.12305 0.0251 4607 4.904 0.0001
Step5 - Step13 0.13205 0.0251 4607 5.262 <.0001
Step5 - Step14 0.15244 0.0251 4607 6.075 <.0001
Step5 - Step15 0.16647 0.0251 4607 6.634 <.0001
Step5 - Step16 0.18496 0.0251 4607 7.371 <.0001
Step5 - Step17 0.20755 0.0251 4607 8.271 <.0001
Step5 - Step18 0.22107 0.0251 4607 8.810 <.0001
Step6 - Step7 0.02036 0.0251 4607 0.811 1.0000
Step6 - Step8 0.03306 0.0251 4607 1.318 0.9979
Step6 - Step9 0.04669 0.0251 4607 1.861 0.9260
Step6 - Step10 0.04905 0.0251 4607 1.955 0.8901
Step6 - Step11 0.06009 0.0251 4607 2.395 0.6120
Step6 - Step12 0.07441 0.0251 4607 2.965 0.2175
Step6 - Step13 0.08341 0.0251 4607 3.324 0.0837
Step6 - Step14 0.10380 0.0251 4607 4.137 0.0047
Step6 - Step15 0.11784 0.0251 4607 4.696 0.0004
Step6 - Step16 0.13633 0.0251 4607 5.433 <.0001
Step6 - Step17 0.15891 0.0251 4607 6.333 <.0001
Step6 - Step18 0.17244 0.0251 4607 6.872 <.0001
Step7 - Step8 0.01271 0.0251 4607 0.506 1.0000
Step7 - Step9 0.02633 0.0251 4607 1.049 0.9999
Step7 - Step10 0.02870 0.0251 4607 1.144 0.9997
Step7 - Step11 0.03974 0.0251 4607 1.584 0.9836
Step7 - Step12 0.05406 0.0251 4607 2.154 0.7837
Step7 - Step13 0.06306 0.0251 4607 2.513 0.5203
Step7 - Step14 0.08345 0.0251 4607 3.326 0.0833
Step7 - Step15 0.09748 0.0251 4607 3.885 0.0126
Step7 - Step16 0.11597 0.0251 4607 4.622 0.0006
Step7 - Step17 0.13856 0.0251 4607 5.522 <.0001
Step7 - Step18 0.15208 0.0251 4607 6.061 <.0001
Step8 - Step9 0.01363 0.0251 4607 0.543 1.0000
Step8 - Step10 0.01599 0.0251 4607 0.637 1.0000
Step8 - Step11 0.02703 0.0251 4607 1.077 0.9998
Step8 - Step12 0.04135 0.0251 4607 1.648 0.9755
Step8 - Step13 0.05035 0.0251 4607 2.007 0.8665
Step8 - Step14 0.07074 0.0251 4607 2.819 0.3009
Step8 - Step15 0.08477 0.0251 4607 3.378 0.0711
Step8 - Step16 0.10326 0.0251 4607 4.115 0.0051
Step8 - Step17 0.12585 0.0251 4607 5.015 0.0001
Step8 - Step18 0.13938 0.0251 4607 5.554 <.0001
Step9 - Step10 0.00237 0.0251 4607 0.094 1.0000
Step9 - Step11 0.01340 0.0251 4607 0.534 1.0000
Step9 - Step12 0.02772 0.0251 4607 1.105 0.9998
Step9 - Step13 0.03672 0.0251 4607 1.464 0.9929
Step9 - Step14 0.05711 0.0251 4607 2.276 0.7009
Step9 - Step15 0.07115 0.0251 4607 2.835 0.2908
Step9 - Step16 0.08964 0.0251 4607 3.572 0.0383
Step9 - Step17 0.11223 0.0251 4607 4.472 0.0011
Step9 - Step18 0.12575 0.0251 4607 5.011 0.0001
Step10 - Step11 0.01104 0.0251 4607 0.440 1.0000
Step10 - Step12 0.02536 0.0251 4607 1.011 0.9999
Step10 - Step13 0.03436 0.0251 4607 1.369 0.9967
Step10 - Step14 0.05475 0.0251 4607 2.182 0.7659
Step10 - Step15 0.06878 0.0251 4607 2.741 0.3520
Step10 - Step16 0.08727 0.0251 4607 3.478 0.0521
Step10 - Step17 0.10986 0.0251 4607 4.378 0.0017
Step10 - Step18 0.12338 0.0251 4607 4.917 0.0001
Step11 - Step12 0.01432 0.0251 4607 0.571 1.0000
Step11 - Step13 0.02332 0.0251 4607 0.929 1.0000
Step11 - Step14 0.04371 0.0251 4607 1.742 0.9584
Step11 - Step15 0.05774 0.0251 4607 2.301 0.6826
Step11 - Step16 0.07623 0.0251 4607 3.038 0.1825
Step11 - Step17 0.09882 0.0251 4607 3.938 0.0102
Step11 - Step18 0.11234 0.0251 4607 4.477 0.0011
Step12 - Step13 0.00900 0.0251 4607 0.359 1.0000
Step12 - Step14 0.02939 0.0251 4607 1.171 0.9995
Step12 - Step15 0.04342 0.0251 4607 1.731 0.9609
Step12 - Step16 0.06192 0.0251 4607 2.467 0.5557
Step12 - Step17 0.08450 0.0251 4607 3.368 0.0735
Step12 - Step18 0.09803 0.0251 4607 3.907 0.0116
Step13 - Step14 0.02039 0.0251 4607 0.813 1.0000
Step13 - Step15 0.03442 0.0251 4607 1.372 0.9966
Step13 - Step16 0.05291 0.0251 4607 2.109 0.8115
Step13 - Step17 0.07550 0.0251 4607 3.009 0.1960
Step13 - Step18 0.08903 0.0251 4607 3.548 0.0415
Step14 - Step15 0.01403 0.0251 4607 0.559 1.0000
Step14 - Step16 0.03253 0.0251 4607 1.296 0.9983
Step14 - Step17 0.05511 0.0251 4607 2.196 0.7563
Step14 - Step18 0.06864 0.0251 4607 2.735 0.3560
Step15 - Step16 0.01849 0.0251 4607 0.737 1.0000
Step15 - Step17 0.04108 0.0251 4607 1.637 0.9770
Step15 - Step18 0.05460 0.0251 4607 2.176 0.7697
Step16 - Step17 0.02259 0.0251 4607 0.900 1.0000
Step16 - Step18 0.03611 0.0251 4607 1.439 0.9942
Step17 - Step18 0.01352 0.0251 4607 0.539 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 459.7 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.67 0.155 18.5 1.339 1.99
2 1.66 0.155 18.5 1.332 1.98
3 1.67 0.155 18.5 1.347 2.00
4 1.65 0.155 18.5 1.320 1.97
5 1.62 0.155 18.5 1.297 1.95
6 1.56 0.155 18.5 1.230 1.88
7 1.55 0.155 18.5 1.220 1.87
8 1.53 0.155 18.5 1.204 1.86
9 1.50 0.155 18.5 1.172 1.82
10 1.49 0.155 18.5 1.159 1.81
11 1.48 0.155 18.5 1.153 1.80
12 1.46 0.155 18.5 1.137 1.79
13 1.42 0.155 18.5 1.094 1.75
14 1.37 0.155 18.5 1.042 1.69
15 1.28 0.155 18.5 0.950 1.60
16 1.24 0.155 18.5 0.911 1.56
17 1.17 0.155 18.5 0.844 1.50
18 1.13 0.155 18.5 0.806 1.46
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00719 0.0464 4607 0.155 1.0000
Step1 - Step3 -0.00751 0.0464 4607 -0.162 1.0000
Step1 - Step4 0.01942 0.0464 4607 0.418 1.0000
Step1 - Step5 0.04192 0.0464 4607 0.903 1.0000
Step1 - Step6 0.10942 0.0464 4607 2.357 0.6405
Step1 - Step7 0.11865 0.0464 4607 2.556 0.4869
Step1 - Step8 0.13517 0.0464 4607 2.912 0.2459
Step1 - Step9 0.16665 0.0464 4607 3.590 0.0360
Step1 - Step10 0.17966 0.0464 4607 3.871 0.0133
Step1 - Step11 0.18638 0.0464 4607 4.016 0.0076
Step1 - Step12 0.20219 0.0464 4607 4.356 0.0018
Step1 - Step13 0.24532 0.0464 4607 5.285 <.0001
Step1 - Step14 0.29679 0.0464 4607 6.394 <.0001
Step1 - Step15 0.38876 0.0464 4607 8.375 <.0001
Step1 - Step16 0.42815 0.0464 4607 9.224 <.0001
Step1 - Step17 0.49494 0.0464 4607 10.663 <.0001
Step1 - Step18 0.53270 0.0464 4607 11.477 <.0001
Step2 - Step3 -0.01470 0.0464 4607 -0.317 1.0000
Step2 - Step4 0.01223 0.0464 4607 0.264 1.0000
Step2 - Step5 0.03473 0.0464 4607 0.748 1.0000
Step2 - Step6 0.10224 0.0464 4607 2.203 0.7522
Step2 - Step7 0.11146 0.0464 4607 2.401 0.6069
Step2 - Step8 0.12799 0.0464 4607 2.757 0.3410
Step2 - Step9 0.15946 0.0464 4607 3.436 0.0596
Step2 - Step10 0.17247 0.0464 4607 3.716 0.0233
Step2 - Step11 0.17919 0.0464 4607 3.861 0.0138
Step2 - Step12 0.19500 0.0464 4607 4.201 0.0036
Step2 - Step13 0.23813 0.0464 4607 5.130 <.0001
Step2 - Step14 0.28960 0.0464 4607 6.239 <.0001
Step2 - Step15 0.38157 0.0464 4607 8.221 <.0001
Step2 - Step16 0.42096 0.0464 4607 9.069 <.0001
Step2 - Step17 0.48775 0.0464 4607 10.508 <.0001
Step2 - Step18 0.52551 0.0464 4607 11.322 <.0001
Step3 - Step4 0.02693 0.0464 4607 0.580 1.0000
Step3 - Step5 0.04943 0.0464 4607 1.065 0.9999
Step3 - Step6 0.11693 0.0464 4607 2.519 0.5154
Step3 - Step7 0.12616 0.0464 4607 2.718 0.3679
Step3 - Step8 0.14268 0.0464 4607 3.074 0.1667
Step3 - Step9 0.17416 0.0464 4607 3.752 0.0205
Step3 - Step10 0.18717 0.0464 4607 4.032 0.0071
Step3 - Step11 0.19389 0.0464 4607 4.177 0.0039
Step3 - Step12 0.20970 0.0464 4607 4.518 0.0009
Step3 - Step13 0.25283 0.0464 4607 5.447 <.0001
Step3 - Step14 0.30430 0.0464 4607 6.556 <.0001
Step3 - Step15 0.39627 0.0464 4607 8.537 <.0001
Step3 - Step16 0.43566 0.0464 4607 9.386 <.0001
Step3 - Step17 0.50245 0.0464 4607 10.825 <.0001
Step3 - Step18 0.54021 0.0464 4607 11.639 <.0001
Step4 - Step5 0.02250 0.0464 4607 0.485 1.0000
Step4 - Step6 0.09000 0.0464 4607 1.939 0.8968
Step4 - Step7 0.09923 0.0464 4607 2.138 0.7939
Step4 - Step8 0.11575 0.0464 4607 2.494 0.5352
Step4 - Step9 0.14723 0.0464 4607 3.172 0.1289
Step4 - Step10 0.16024 0.0464 4607 3.452 0.0565
Step4 - Step11 0.16696 0.0464 4607 3.597 0.0352
Step4 - Step12 0.18277 0.0464 4607 3.938 0.0103
Step4 - Step13 0.22590 0.0464 4607 4.867 0.0002
Step4 - Step14 0.27737 0.0464 4607 5.976 <.0001
Step4 - Step15 0.36933 0.0464 4607 7.957 <.0001
Step4 - Step16 0.40873 0.0464 4607 8.806 <.0001
Step4 - Step17 0.47551 0.0464 4607 10.245 <.0001
Step4 - Step18 0.51328 0.0464 4607 11.058 <.0001
Step5 - Step6 0.06750 0.0464 4607 1.454 0.9934
Step5 - Step7 0.07673 0.0464 4607 1.653 0.9747
Step5 - Step8 0.09325 0.0464 4607 2.009 0.8653
Step5 - Step9 0.12473 0.0464 4607 2.687 0.3895
Step5 - Step10 0.13774 0.0464 4607 2.968 0.2164
Step5 - Step11 0.14446 0.0464 4607 3.112 0.1510
Step5 - Step12 0.16027 0.0464 4607 3.453 0.0564
Step5 - Step13 0.20340 0.0464 4607 4.382 0.0016
Step5 - Step14 0.25487 0.0464 4607 5.491 <.0001
Step5 - Step15 0.34683 0.0464 4607 7.472 <.0001
Step5 - Step16 0.38623 0.0464 4607 8.321 <.0001
Step5 - Step17 0.45301 0.0464 4607 9.760 <.0001
Step5 - Step18 0.49078 0.0464 4607 10.574 <.0001
Step6 - Step7 0.00923 0.0464 4607 0.199 1.0000
Step6 - Step8 0.02575 0.0464 4607 0.555 1.0000
Step6 - Step9 0.05723 0.0464 4607 1.233 0.9991
Step6 - Step10 0.07024 0.0464 4607 1.513 0.9898
Step6 - Step11 0.07696 0.0464 4607 1.658 0.9740
Step6 - Step12 0.09276 0.0464 4607 1.999 0.8703
Step6 - Step13 0.13590 0.0464 4607 2.928 0.2373
Step6 - Step14 0.18737 0.0464 4607 4.037 0.0070
Step6 - Step15 0.27933 0.0464 4607 6.018 <.0001
Step6 - Step16 0.31873 0.0464 4607 6.867 <.0001
Step6 - Step17 0.38551 0.0464 4607 8.306 <.0001
Step6 - Step18 0.42328 0.0464 4607 9.119 <.0001
Step7 - Step8 0.01652 0.0464 4607 0.356 1.0000
Step7 - Step9 0.04800 0.0464 4607 1.034 0.9999
Step7 - Step10 0.06101 0.0464 4607 1.314 0.9980
Step7 - Step11 0.06773 0.0464 4607 1.459 0.9932
Step7 - Step12 0.08354 0.0464 4607 1.800 0.9443
Step7 - Step13 0.12667 0.0464 4607 2.729 0.3602
Step7 - Step14 0.17814 0.0464 4607 3.838 0.0150
Step7 - Step15 0.27011 0.0464 4607 5.819 <.0001
Step7 - Step16 0.30950 0.0464 4607 6.668 <.0001
Step7 - Step17 0.37629 0.0464 4607 8.107 <.0001
Step7 - Step18 0.41405 0.0464 4607 8.921 <.0001
Step8 - Step9 0.03148 0.0464 4607 0.678 1.0000
Step8 - Step10 0.04449 0.0464 4607 0.958 1.0000
Step8 - Step11 0.05121 0.0464 4607 1.103 0.9998
Step8 - Step12 0.06701 0.0464 4607 1.444 0.9939
Step8 - Step13 0.11015 0.0464 4607 2.373 0.6286
Step8 - Step14 0.16162 0.0464 4607 3.482 0.0514
Step8 - Step15 0.25358 0.0464 4607 5.463 <.0001
Step8 - Step16 0.29298 0.0464 4607 6.312 <.0001
Step8 - Step17 0.35976 0.0464 4607 7.751 <.0001
Step8 - Step18 0.39753 0.0464 4607 8.565 <.0001
Step9 - Step10 0.01301 0.0464 4607 0.280 1.0000
Step9 - Step11 0.01973 0.0464 4607 0.425 1.0000
Step9 - Step12 0.03554 0.0464 4607 0.766 1.0000
Step9 - Step13 0.07867 0.0464 4607 1.695 0.9678
Step9 - Step14 0.13014 0.0464 4607 2.804 0.3106
Step9 - Step15 0.22210 0.0464 4607 4.785 0.0003
Step9 - Step16 0.26150 0.0464 4607 5.634 <.0001
Step9 - Step17 0.32828 0.0464 4607 7.073 <.0001
Step9 - Step18 0.36605 0.0464 4607 7.886 <.0001
Step10 - Step11 0.00672 0.0464 4607 0.145 1.0000
Step10 - Step12 0.02253 0.0464 4607 0.485 1.0000
Step10 - Step13 0.06566 0.0464 4607 1.415 0.9952
Step10 - Step14 0.11713 0.0464 4607 2.523 0.5121
Step10 - Step15 0.20909 0.0464 4607 4.505 0.0009
Step10 - Step16 0.24849 0.0464 4607 5.354 <.0001
Step10 - Step17 0.31527 0.0464 4607 6.792 <.0001
Step10 - Step18 0.35304 0.0464 4607 7.606 <.0001
Step11 - Step12 0.01580 0.0464 4607 0.340 1.0000
Step11 - Step13 0.05894 0.0464 4607 1.270 0.9987
Step11 - Step14 0.11041 0.0464 4607 2.379 0.6244
Step11 - Step15 0.20237 0.0464 4607 4.360 0.0018
Step11 - Step16 0.24177 0.0464 4607 5.209 <.0001
Step11 - Step17 0.30855 0.0464 4607 6.648 <.0001
Step11 - Step18 0.34632 0.0464 4607 7.461 <.0001
Step12 - Step13 0.04314 0.0464 4607 0.929 1.0000
Step12 - Step14 0.09460 0.0464 4607 2.038 0.8506
Step12 - Step15 0.18657 0.0464 4607 4.019 0.0075
Step12 - Step16 0.22597 0.0464 4607 4.868 0.0002
Step12 - Step17 0.29275 0.0464 4607 6.307 <.0001
Step12 - Step18 0.33052 0.0464 4607 7.121 <.0001
Step13 - Step14 0.05147 0.0464 4607 1.109 0.9998
Step13 - Step15 0.14343 0.0464 4607 3.090 0.1600
Step13 - Step16 0.18283 0.0464 4607 3.939 0.0102
Step13 - Step17 0.24961 0.0464 4607 5.378 <.0001
Step13 - Step18 0.28738 0.0464 4607 6.191 <.0001
Step14 - Step15 0.09196 0.0464 4607 1.981 0.8784
Step14 - Step16 0.13136 0.0464 4607 2.830 0.2941
Step14 - Step17 0.19814 0.0464 4607 4.269 0.0027
Step14 - Step18 0.23591 0.0464 4607 5.083 0.0001
Step15 - Step16 0.03940 0.0464 4607 0.849 1.0000
Step15 - Step17 0.10618 0.0464 4607 2.288 0.6926
Step15 - Step18 0.14395 0.0464 4607 3.101 0.1555
Step16 - Step17 0.06678 0.0464 4607 1.439 0.9942
Step16 - Step18 0.10455 0.0464 4607 2.252 0.7178
Step17 - Step18 0.03777 0.0464 4607 0.814 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates # Block 5
run_mixed_length_lmms(step_summary_block45, target_block = 5, seq_length = 6)
=========== Block 5 | 6-Step Trials ===========--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 29.785 5 1.626e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.576 0.0483 17.6 0.474 0.677
2 0.575 0.0483 17.6 0.473 0.677
3 0.573 0.0483 17.6 0.471 0.675
4 0.573 0.0483 17.6 0.471 0.675
5 0.539 0.0483 17.6 0.438 0.641
6 0.543 0.0483 17.6 0.442 0.645
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000868 0.00993 1370 0.087 1.0000
Step1 - Step3 0.002848 0.00993 1370 0.287 0.9997
Step1 - Step4 0.002848 0.00993 1370 0.287 0.9997
Step1 - Step5 0.036714 0.00993 1370 3.696 0.0031
Step1 - Step6 0.032638 0.00993 1370 3.286 0.0133
Step2 - Step3 0.001980 0.00993 1370 0.199 1.0000
Step2 - Step4 0.001980 0.00993 1370 0.199 1.0000
Step2 - Step5 0.035847 0.00993 1370 3.609 0.0043
Step2 - Step6 0.031770 0.00993 1370 3.198 0.0177
Step3 - Step4 0.000000 0.00993 1370 0.000 1.0000
Step3 - Step5 0.033867 0.00993 1370 3.409 0.0088
Step3 - Step6 0.029790 0.00993 1370 2.999 0.0329
Step4 - Step5 0.033867 0.00993 1370 3.409 0.0088
Step4 - Step6 0.029790 0.00993 1370 2.999 0.0329
Step5 - Step6 -0.004077 0.00993 1370 -0.410 0.9985
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 29.255 5 2.067e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.623 0.0578 17.6 0.502 0.745
2 0.625 0.0578 17.6 0.503 0.746
3 0.624 0.0578 17.6 0.502 0.745
4 0.624 0.0578 17.6 0.502 0.745
5 0.604 0.0578 17.6 0.483 0.726
6 0.575 0.0578 17.6 0.453 0.697
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.001374 0.0116 1370 -0.118 1.0000
Step1 - Step3 -0.000388 0.0116 1370 -0.033 1.0000
Step1 - Step4 -0.000388 0.0116 1370 -0.033 1.0000
Step1 - Step5 0.018927 0.0116 1370 1.629 0.5792
Step1 - Step6 0.048118 0.0116 1370 4.142 0.0005
Step2 - Step3 0.000986 0.0116 1370 0.085 1.0000
Step2 - Step4 0.000986 0.0116 1370 0.085 1.0000
Step2 - Step5 0.020301 0.0116 1370 1.748 0.5004
Step2 - Step6 0.049493 0.0116 1370 4.260 0.0003
Step3 - Step4 0.000000 0.0116 1370 0.000 1.0000
Step3 - Step5 0.019315 0.0116 1370 1.663 0.5568
Step3 - Step6 0.048507 0.0116 1370 4.176 0.0005
Step4 - Step5 0.019315 0.0116 1370 1.663 0.5568
Step4 - Step6 0.048507 0.0116 1370 4.176 0.0005
Step5 - Step6 0.029191 0.0116 1370 2.513 0.1210
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 57.448 5 4.088e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.31 0.135 17.3 1.029 1.60
2 1.29 0.135 17.3 1.002 1.57
3 1.27 0.135 17.3 0.984 1.55
4 1.27 0.135 17.3 0.984 1.55
5 1.23 0.135 17.3 0.951 1.52
6 1.18 0.135 17.3 0.901 1.47
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.0265 0.0185 1370 1.432 0.7073
Step1 - Step3 0.0450 0.0185 1370 2.437 0.1444
Step1 - Step4 0.0450 0.0185 1370 2.437 0.1444
Step1 - Step5 0.0778 0.0185 1370 4.216 0.0004
Step1 - Step6 0.1274 0.0185 1370 6.900 <.0001
Step2 - Step3 0.0185 0.0185 1370 1.004 0.9166
Step2 - Step4 0.0185 0.0185 1370 1.004 0.9166
Step2 - Step5 0.0514 0.0185 1370 2.783 0.0607
Step2 - Step6 0.1010 0.0185 1370 5.468 <.0001
Step3 - Step4 0.0000 0.0185 1370 0.000 1.0000
Step3 - Step5 0.0329 0.0185 1370 1.779 0.4798
Step3 - Step6 0.0824 0.0185 1370 4.463 0.0001
Step4 - Step5 0.0329 0.0185 1370 1.779 0.4798
Step4 - Step6 0.0824 0.0185 1370 4.463 0.0001
Step5 - Step6 0.0496 0.0185 1370 2.684 0.0790
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates run_mixed_length_lmms(step_summary_block45, target_block = 5, seq_length = 12)
=========== Block 5 | 12-Step Trials ===========--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 33.393 11 0.0004542 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.585 0.0485 19.2 0.484 0.687
2 0.592 0.0485 19.2 0.491 0.694
3 0.598 0.0485 19.2 0.497 0.700
4 0.594 0.0485 19.2 0.493 0.696
5 0.587 0.0485 19.2 0.486 0.689
6 0.572 0.0485 19.2 0.470 0.673
7 0.567 0.0485 19.2 0.466 0.669
8 0.579 0.0485 19.2 0.477 0.680
9 0.566 0.0485 19.2 0.465 0.667
10 0.551 0.0485 19.2 0.449 0.652
11 0.548 0.0485 19.2 0.446 0.649
12 0.528 0.0485 19.2 0.426 0.629
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.00707 0.0176 2970 -0.402 1.0000
Step1 - Step3 -0.01308 0.0176 2970 -0.745 0.9999
Step1 - Step4 -0.00903 0.0176 2970 -0.514 1.0000
Step1 - Step5 -0.00199 0.0176 2970 -0.113 1.0000
Step1 - Step6 0.01390 0.0176 2970 0.791 0.9997
Step1 - Step7 0.01808 0.0176 2970 1.029 0.9971
Step1 - Step8 0.00671 0.0176 2970 0.382 1.0000
Step1 - Step9 0.01937 0.0176 2970 1.103 0.9946
Step1 - Step10 0.03473 0.0176 2970 1.977 0.7094
Step1 - Step11 0.03783 0.0176 2970 2.153 0.5841
Step1 - Step12 0.05768 0.0176 2970 3.283 0.0481
Step2 - Step3 -0.00601 0.0176 2970 -0.342 1.0000
Step2 - Step4 -0.00195 0.0176 2970 -0.111 1.0000
Step2 - Step5 0.00508 0.0176 2970 0.289 1.0000
Step2 - Step6 0.02097 0.0176 2970 1.193 0.9895
Step2 - Step7 0.02515 0.0176 2970 1.431 0.9574
Step2 - Step8 0.01378 0.0176 2970 0.784 0.9998
Step2 - Step9 0.02645 0.0176 2970 1.505 0.9395
Step2 - Step10 0.04180 0.0176 2970 2.379 0.4205
Step2 - Step11 0.04490 0.0176 2970 2.556 0.3059
Step2 - Step12 0.06476 0.0176 2970 3.686 0.0124
Step3 - Step4 0.00406 0.0176 2970 0.231 1.0000
Step3 - Step5 0.01109 0.0176 2970 0.631 1.0000
Step3 - Step6 0.02698 0.0176 2970 1.535 0.9308
Step3 - Step7 0.03116 0.0176 2970 1.773 0.8325
Step3 - Step8 0.01979 0.0176 2970 1.126 0.9935
Step3 - Step9 0.03246 0.0176 2970 1.847 0.7915
Step3 - Step10 0.04781 0.0176 2970 2.721 0.2160
Step3 - Step11 0.05091 0.0176 2970 2.898 0.1421
Step3 - Step12 0.07077 0.0176 2970 4.028 0.0033
Step4 - Step5 0.00704 0.0176 2970 0.401 1.0000
Step4 - Step6 0.02292 0.0176 2970 1.305 0.9787
Step4 - Step7 0.02710 0.0176 2970 1.543 0.9286
Step4 - Step8 0.01574 0.0176 2970 0.896 0.9992
Step4 - Step9 0.02840 0.0176 2970 1.616 0.9034
Step4 - Step10 0.04376 0.0176 2970 2.491 0.3461
Step4 - Step11 0.04686 0.0176 2970 2.667 0.2434
Step4 - Step12 0.06671 0.0176 2970 3.797 0.0082
Step5 - Step6 0.01589 0.0176 2970 0.904 0.9991
Step5 - Step7 0.02007 0.0176 2970 1.142 0.9927
Step5 - Step8 0.00870 0.0176 2970 0.495 1.0000
Step5 - Step9 0.02136 0.0176 2970 1.216 0.9878
Step5 - Step10 0.03672 0.0176 2970 2.090 0.6300
Step5 - Step11 0.03982 0.0176 2970 2.266 0.5011
Step5 - Step12 0.05967 0.0176 2970 3.396 0.0336
Step6 - Step7 0.00418 0.0176 2970 0.238 1.0000
Step6 - Step8 -0.00719 0.0176 2970 -0.409 1.0000
Step6 - Step9 0.00548 0.0176 2970 0.312 1.0000
Step6 - Step10 0.02084 0.0176 2970 1.186 0.9901
Step6 - Step11 0.02393 0.0176 2970 1.362 0.9704
Step6 - Step12 0.04379 0.0176 2970 2.492 0.3450
Step7 - Step8 -0.01137 0.0176 2970 -0.647 1.0000
Step7 - Step9 0.00130 0.0176 2970 0.074 1.0000
Step7 - Step10 0.01665 0.0176 2970 0.948 0.9986
Step7 - Step11 0.01975 0.0176 2970 1.124 0.9936
Step7 - Step12 0.03961 0.0176 2970 2.254 0.5099
Step8 - Step9 0.01266 0.0176 2970 0.721 0.9999
Step8 - Step10 0.02802 0.0176 2970 1.595 0.9112
Step8 - Step11 0.03112 0.0176 2970 1.771 0.8337
Step8 - Step12 0.05097 0.0176 2970 2.901 0.1408
Step9 - Step10 0.01536 0.0176 2970 0.874 0.9993
Step9 - Step11 0.01846 0.0176 2970 1.050 0.9965
Step9 - Step12 0.03831 0.0176 2970 2.181 0.5640
Step10 - Step11 0.00310 0.0176 2970 0.176 1.0000
Step10 - Step12 0.02295 0.0176 2970 1.306 0.9785
Step11 - Step12 0.01985 0.0176 2970 1.130 0.9934
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 131.58 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.658 0.0587 18.5 0.535 0.781
2 0.658 0.0587 18.5 0.535 0.781
3 0.641 0.0587 18.5 0.518 0.764
4 0.630 0.0587 18.5 0.507 0.753
5 0.621 0.0587 18.5 0.498 0.744
6 0.581 0.0587 18.5 0.458 0.704
7 0.582 0.0587 18.5 0.459 0.705
8 0.568 0.0587 18.5 0.445 0.691
9 0.558 0.0587 18.5 0.435 0.681
10 0.557 0.0587 18.5 0.434 0.680
11 0.556 0.0587 18.5 0.433 0.679
12 0.543 0.0587 18.5 0.420 0.666
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 3.77e-05 0.0174 2970 0.002 1.0000
Step1 - Step3 1.67e-02 0.0174 2970 0.960 0.9984
Step1 - Step4 2.73e-02 0.0174 2970 1.565 0.9215
Step1 - Step5 3.67e-02 0.0174 2970 2.103 0.6206
Step1 - Step6 7.63e-02 0.0174 2970 4.377 0.0008
Step1 - Step7 7.58e-02 0.0174 2970 4.345 0.0009
Step1 - Step8 8.92e-02 0.0174 2970 5.117 <.0001
Step1 - Step9 9.97e-02 0.0174 2970 5.716 <.0001
Step1 - Step10 1.01e-01 0.0174 2970 5.780 <.0001
Step1 - Step11 1.02e-01 0.0174 2970 5.849 <.0001
Step1 - Step12 1.15e-01 0.0174 2970 6.574 <.0001
Step2 - Step3 1.67e-02 0.0174 2970 0.958 0.9985
Step2 - Step4 2.73e-02 0.0174 2970 1.563 0.9222
Step2 - Step5 3.66e-02 0.0174 2970 2.101 0.6222
Step2 - Step6 7.63e-02 0.0174 2970 4.375 0.0008
Step2 - Step7 7.57e-02 0.0174 2970 4.343 0.0009
Step2 - Step8 8.92e-02 0.0174 2970 5.115 <.0001
Step2 - Step9 9.96e-02 0.0174 2970 5.714 <.0001
Step2 - Step10 1.01e-01 0.0174 2970 5.778 <.0001
Step2 - Step11 1.02e-01 0.0174 2970 5.847 <.0001
Step2 - Step12 1.15e-01 0.0174 2970 6.572 <.0001
Step3 - Step4 1.05e-02 0.0174 2970 0.605 1.0000
Step3 - Step5 1.99e-02 0.0174 2970 1.143 0.9927
Step3 - Step6 5.96e-02 0.0174 2970 3.417 0.0315
Step3 - Step7 5.90e-02 0.0174 2970 3.385 0.0349
Step3 - Step8 7.25e-02 0.0174 2970 4.156 0.0020
Step3 - Step9 8.29e-02 0.0174 2970 4.755 0.0001
Step3 - Step10 8.41e-02 0.0174 2970 4.819 0.0001
Step3 - Step11 8.53e-02 0.0174 2970 4.889 0.0001
Step3 - Step12 9.79e-02 0.0174 2970 5.614 <.0001
Step4 - Step5 9.39e-03 0.0174 2970 0.538 1.0000
Step4 - Step6 4.90e-02 0.0174 2970 2.812 0.1752
Step4 - Step7 4.85e-02 0.0174 2970 2.780 0.1889
Step4 - Step8 6.19e-02 0.0174 2970 3.552 0.0200
Step4 - Step9 7.24e-02 0.0174 2970 4.151 0.0020
Step4 - Step10 7.35e-02 0.0174 2970 4.215 0.0015
Step4 - Step11 7.47e-02 0.0174 2970 4.284 0.0011
Step4 - Step12 8.74e-02 0.0174 2970 5.009 <.0001
Step5 - Step6 3.97e-02 0.0174 2970 2.274 0.4956
Step5 - Step7 3.91e-02 0.0174 2970 2.242 0.5189
Step5 - Step8 5.26e-02 0.0174 2970 3.014 0.1050
Step5 - Step9 6.30e-02 0.0174 2970 3.613 0.0161
Step5 - Step10 6.41e-02 0.0174 2970 3.677 0.0128
Step5 - Step11 6.53e-02 0.0174 2970 3.746 0.0100
Step5 - Step12 7.80e-02 0.0174 2970 4.471 0.0005
Step6 - Step7 -5.56e-04 0.0174 2970 -0.032 1.0000
Step6 - Step8 1.29e-02 0.0174 2970 0.740 0.9999
Step6 - Step9 2.33e-02 0.0174 2970 1.339 0.9740
Step6 - Step10 2.45e-02 0.0174 2970 1.403 0.9632
Step6 - Step11 2.57e-02 0.0174 2970 1.472 0.9480
Step6 - Step12 3.83e-02 0.0174 2970 2.197 0.5517
Step7 - Step8 1.35e-02 0.0174 2970 0.772 0.9998
Step7 - Step9 2.39e-02 0.0174 2970 1.371 0.9690
Step7 - Step10 2.50e-02 0.0174 2970 1.435 0.9567
Step7 - Step11 2.62e-02 0.0174 2970 1.504 0.9398
Step7 - Step12 3.89e-02 0.0174 2970 2.229 0.5283
Step8 - Step9 1.04e-02 0.0174 2970 0.599 1.0000
Step8 - Step10 1.16e-02 0.0174 2970 0.663 1.0000
Step8 - Step11 1.28e-02 0.0174 2970 0.733 0.9999
Step8 - Step12 2.54e-02 0.0174 2970 1.458 0.9516
Step9 - Step10 1.12e-03 0.0174 2970 0.064 1.0000
Step9 - Step11 2.33e-03 0.0174 2970 0.134 1.0000
Step9 - Step12 1.50e-02 0.0174 2970 0.859 0.9994
Step10 - Step11 1.21e-03 0.0174 2970 0.070 1.0000
Step10 - Step12 1.39e-02 0.0174 2970 0.795 0.9997
Step11 - Step12 1.26e-02 0.0174 2970 0.725 0.9999
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 198.35 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.33 0.14 17.8 1.031 1.62
2 1.32 0.14 17.8 1.029 1.62
3 1.32 0.14 17.8 1.027 1.62
4 1.31 0.14 17.8 1.019 1.61
5 1.29 0.14 17.8 0.996 1.58
6 1.23 0.14 17.8 0.935 1.52
7 1.20 0.14 17.8 0.908 1.50
8 1.19 0.14 17.8 0.893 1.48
9 1.16 0.14 17.8 0.866 1.45
10 1.13 0.14 17.8 0.838 1.43
11 1.11 0.14 17.8 0.812 1.40
12 1.06 0.14 17.8 0.768 1.36
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00254 0.0311 2970 0.082 1.0000
Step1 - Step3 0.00479 0.0311 2970 0.154 1.0000
Step1 - Step4 0.01232 0.0311 2970 0.396 1.0000
Step1 - Step5 0.03570 0.0311 2970 1.147 0.9925
Step1 - Step6 0.09657 0.0311 2970 3.103 0.0819
Step1 - Step7 0.12326 0.0311 2970 3.961 0.0044
Step1 - Step8 0.13843 0.0311 2970 4.448 0.0006
Step1 - Step9 0.16506 0.0311 2970 5.304 <.0001
Step1 - Step10 0.19356 0.0311 2970 6.220 <.0001
Step1 - Step11 0.21914 0.0311 2970 7.042 <.0001
Step1 - Step12 0.26338 0.0311 2970 8.464 <.0001
Step2 - Step3 0.00224 0.0311 2970 0.072 1.0000
Step2 - Step4 0.00978 0.0311 2970 0.314 1.0000
Step2 - Step5 0.03316 0.0311 2970 1.066 0.9960
Step2 - Step6 0.09403 0.0311 2970 3.022 0.1028
Step2 - Step7 0.12072 0.0311 2970 3.879 0.0060
Step2 - Step8 0.13588 0.0311 2970 4.367 0.0008
Step2 - Step9 0.16251 0.0311 2970 5.222 <.0001
Step2 - Step10 0.19101 0.0311 2970 6.138 <.0001
Step2 - Step11 0.21660 0.0311 2970 6.960 <.0001
Step2 - Step12 0.26083 0.0311 2970 8.382 <.0001
Step3 - Step4 0.00753 0.0311 2970 0.242 1.0000
Step3 - Step5 0.03092 0.0311 2970 0.993 0.9979
Step3 - Step6 0.09178 0.0311 2970 2.949 0.1244
Step3 - Step7 0.11847 0.0311 2970 3.807 0.0079
Step3 - Step8 0.13364 0.0311 2970 4.294 0.0011
Step3 - Step9 0.16027 0.0311 2970 5.150 <.0001
Step3 - Step10 0.18877 0.0311 2970 6.066 <.0001
Step3 - Step11 0.21435 0.0311 2970 6.888 <.0001
Step3 - Step12 0.25859 0.0311 2970 8.310 <.0001
Step4 - Step5 0.02338 0.0311 2970 0.751 0.9998
Step4 - Step6 0.08425 0.0311 2970 2.707 0.2229
Step4 - Step7 0.11094 0.0311 2970 3.565 0.0191
Step4 - Step8 0.12610 0.0311 2970 4.052 0.0030
Step4 - Step9 0.15273 0.0311 2970 4.908 0.0001
Step4 - Step10 0.18123 0.0311 2970 5.824 <.0001
Step4 - Step11 0.20682 0.0311 2970 6.646 <.0001
Step4 - Step12 0.25105 0.0311 2970 8.068 <.0001
Step5 - Step6 0.06087 0.0311 2970 1.956 0.7233
Step5 - Step7 0.08756 0.0311 2970 2.814 0.1746
Step5 - Step8 0.10272 0.0311 2970 3.301 0.0455
Step5 - Step9 0.12935 0.0311 2970 4.157 0.0020
Step5 - Step10 0.15785 0.0311 2970 5.073 <.0001
Step5 - Step11 0.18344 0.0311 2970 5.895 <.0001
Step5 - Step12 0.22767 0.0311 2970 7.316 <.0001
Step6 - Step7 0.02669 0.0311 2970 0.858 0.9994
Step6 - Step8 0.04185 0.0311 2970 1.345 0.9731
Step6 - Step9 0.06848 0.0311 2970 2.201 0.5492
Step6 - Step10 0.09698 0.0311 2970 3.117 0.0789
Step6 - Step11 0.12257 0.0311 2970 3.939 0.0048
Step6 - Step12 0.16680 0.0311 2970 5.360 <.0001
Step7 - Step8 0.01517 0.0311 2970 0.487 1.0000
Step7 - Step9 0.04179 0.0311 2970 1.343 0.9734
Step7 - Step10 0.07030 0.0311 2970 2.259 0.5065
Step7 - Step11 0.09588 0.0311 2970 3.081 0.0872
Step7 - Step12 0.14012 0.0311 2970 4.503 0.0004
Step8 - Step9 0.02663 0.0311 2970 0.856 0.9995
Step8 - Step10 0.05513 0.0311 2970 1.772 0.8335
Step8 - Step11 0.08071 0.0311 2970 2.594 0.2835
Step8 - Step12 0.12495 0.0311 2970 4.015 0.0035
Step9 - Step10 0.02850 0.0311 2970 0.916 0.9990
Step9 - Step11 0.05409 0.0311 2970 1.738 0.8505
Step9 - Step12 0.09832 0.0311 2970 3.160 0.0697
Step10 - Step11 0.02559 0.0311 2970 0.822 0.9996
Step10 - Step12 0.06982 0.0311 2970 2.244 0.5176
Step11 - Step12 0.04424 0.0311 2970 1.422 0.9595
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates run_mixed_length_lmms(step_summary_block45, target_block = 5, seq_length = 18)
=========== Block 5 | 18-Step Trials ===========--- Axis: X ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 62.91 17 3.451e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.632 0.0563 19.7 0.514 0.749
2 0.630 0.0563 19.7 0.512 0.747
3 0.634 0.0563 19.7 0.517 0.752
4 0.630 0.0563 19.7 0.513 0.748
5 0.607 0.0563 19.7 0.489 0.725
6 0.604 0.0563 19.7 0.486 0.722
7 0.594 0.0563 19.7 0.476 0.712
8 0.599 0.0563 19.7 0.481 0.717
9 0.585 0.0563 19.7 0.468 0.703
10 0.573 0.0563 19.7 0.456 0.691
11 0.574 0.0563 19.7 0.456 0.691
12 0.597 0.0563 19.7 0.480 0.715
13 0.588 0.0563 19.7 0.470 0.705
14 0.575 0.0563 19.7 0.458 0.693
15 0.554 0.0563 19.7 0.436 0.672
16 0.559 0.0563 19.7 0.442 0.677
17 0.554 0.0563 19.7 0.436 0.672
18 0.535 0.0563 19.7 0.418 0.653
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.002072 0.0217 4403 0.095 1.0000
Step1 - Step3 -0.002645 0.0217 4403 -0.122 1.0000
Step1 - Step4 0.001392 0.0217 4403 0.064 1.0000
Step1 - Step5 0.024627 0.0217 4403 1.134 0.9997
Step1 - Step6 0.027744 0.0217 4403 1.278 0.9986
Step1 - Step7 0.037488 0.0217 4403 1.727 0.9616
Step1 - Step8 0.032507 0.0217 4403 1.497 0.9909
Step1 - Step9 0.046461 0.0217 4403 2.140 0.7925
Step1 - Step10 0.058221 0.0217 4403 2.682 0.3934
Step1 - Step11 0.057970 0.0217 4403 2.670 0.4017
Step1 - Step12 0.034198 0.0217 4403 1.575 0.9844
Step1 - Step13 0.043992 0.0217 4403 2.026 0.8566
Step1 - Step14 0.056123 0.0217 4403 2.585 0.4648
Step1 - Step15 0.077723 0.0217 4403 3.580 0.0373
Step1 - Step16 0.072145 0.0217 4403 3.323 0.0839
Step1 - Step17 0.077617 0.0217 4403 3.575 0.0379
Step1 - Step18 0.096413 0.0217 4403 4.441 0.0013
Step2 - Step3 -0.004717 0.0217 4403 -0.217 1.0000
Step2 - Step4 -0.000679 0.0217 4403 -0.031 1.0000
Step2 - Step5 0.022555 0.0217 4403 1.039 0.9999
Step2 - Step6 0.025672 0.0217 4403 1.183 0.9995
Step2 - Step7 0.035417 0.0217 4403 1.631 0.9778
Step2 - Step8 0.030435 0.0217 4403 1.402 0.9957
Step2 - Step9 0.044389 0.0217 4403 2.045 0.8472
Step2 - Step10 0.056150 0.0217 4403 2.586 0.4639
Step2 - Step11 0.055898 0.0217 4403 2.575 0.4727
Step2 - Step12 0.032126 0.0217 4403 1.480 0.9920
Step2 - Step13 0.041920 0.0217 4403 1.931 0.9001
Step2 - Step14 0.054051 0.0217 4403 2.490 0.5383
Step2 - Step15 0.075651 0.0217 4403 3.485 0.0510
Step2 - Step16 0.070073 0.0217 4403 3.228 0.1105
Step2 - Step17 0.075546 0.0217 4403 3.480 0.0518
Step2 - Step18 0.094342 0.0217 4403 4.346 0.0019
Step3 - Step4 0.004038 0.0217 4403 0.186 1.0000
Step3 - Step5 0.027273 0.0217 4403 1.256 0.9988
Step3 - Step6 0.030389 0.0217 4403 1.400 0.9957
Step3 - Step7 0.040134 0.0217 4403 1.849 0.9299
Step3 - Step8 0.035152 0.0217 4403 1.619 0.9794
Step3 - Step9 0.049106 0.0217 4403 2.262 0.7110
Step3 - Step10 0.060867 0.0217 4403 2.804 0.3107
Step3 - Step11 0.060616 0.0217 4403 2.792 0.3181
Step3 - Step12 0.036843 0.0217 4403 1.697 0.9674
Step3 - Step13 0.046637 0.0217 4403 2.148 0.7874
Step3 - Step14 0.058769 0.0217 4403 2.707 0.3755
Step3 - Step15 0.080368 0.0217 4403 3.702 0.0245
Step3 - Step16 0.074790 0.0217 4403 3.445 0.0578
Step3 - Step17 0.080263 0.0217 4403 3.697 0.0249
Step3 - Step18 0.099059 0.0217 4403 4.563 0.0007
Step4 - Step5 0.023235 0.0217 4403 1.070 0.9999
Step4 - Step6 0.026351 0.0217 4403 1.214 0.9993
Step4 - Step7 0.036096 0.0217 4403 1.663 0.9732
Step4 - Step8 0.031114 0.0217 4403 1.433 0.9944
Step4 - Step9 0.045068 0.0217 4403 2.076 0.8303
Step4 - Step10 0.056829 0.0217 4403 2.618 0.4404
Step4 - Step11 0.056578 0.0217 4403 2.606 0.4490
Step4 - Step12 0.032805 0.0217 4403 1.511 0.9900
Step4 - Step13 0.042599 0.0217 4403 1.962 0.8870
Step4 - Step14 0.054731 0.0217 4403 2.521 0.5140
Step4 - Step15 0.076330 0.0217 4403 3.516 0.0461
Step4 - Step16 0.070752 0.0217 4403 3.259 0.1011
Step4 - Step17 0.076225 0.0217 4403 3.511 0.0468
Step4 - Step18 0.095021 0.0217 4403 4.377 0.0017
Step5 - Step6 0.003116 0.0217 4403 0.144 1.0000
Step5 - Step7 0.012861 0.0217 4403 0.592 1.0000
Step5 - Step8 0.007880 0.0217 4403 0.363 1.0000
Step5 - Step9 0.021834 0.0217 4403 1.006 0.9999
Step5 - Step10 0.033594 0.0217 4403 1.547 0.9871
Step5 - Step11 0.033343 0.0217 4403 1.536 0.9881
Step5 - Step12 0.009571 0.0217 4403 0.441 1.0000
Step5 - Step13 0.019365 0.0217 4403 0.892 1.0000
Step5 - Step14 0.031496 0.0217 4403 1.451 0.9936
Step5 - Step15 0.053096 0.0217 4403 2.446 0.5726
Step5 - Step16 0.047518 0.0217 4403 2.189 0.7613
Step5 - Step17 0.052990 0.0217 4403 2.441 0.5763
Step5 - Step18 0.071786 0.0217 4403 3.307 0.0881
Step6 - Step7 0.009745 0.0217 4403 0.449 1.0000
Step6 - Step8 0.004763 0.0217 4403 0.219 1.0000
Step6 - Step9 0.018717 0.0217 4403 0.862 1.0000
Step6 - Step10 0.030478 0.0217 4403 1.404 0.9956
Step6 - Step11 0.030226 0.0217 4403 1.392 0.9960
Step6 - Step12 0.006454 0.0217 4403 0.297 1.0000
Step6 - Step13 0.016248 0.0217 4403 0.748 1.0000
Step6 - Step14 0.028379 0.0217 4403 1.307 0.9981
Step6 - Step15 0.049979 0.0217 4403 2.302 0.6819
Step6 - Step16 0.044401 0.0217 4403 2.045 0.8469
Step6 - Step17 0.049874 0.0217 4403 2.297 0.6854
Step6 - Step18 0.068670 0.0217 4403 3.163 0.1320
Step7 - Step8 -0.004982 0.0217 4403 -0.229 1.0000
Step7 - Step9 0.008972 0.0217 4403 0.413 1.0000
Step7 - Step10 0.020733 0.0217 4403 0.955 1.0000
Step7 - Step11 0.020482 0.0217 4403 0.943 1.0000
Step7 - Step12 -0.003291 0.0217 4403 -0.152 1.0000
Step7 - Step13 0.006503 0.0217 4403 0.300 1.0000
Step7 - Step14 0.018635 0.0217 4403 0.858 1.0000
Step7 - Step15 0.040234 0.0217 4403 1.853 0.9284
Step7 - Step16 0.034656 0.0217 4403 1.596 0.9822
Step7 - Step17 0.040129 0.0217 4403 1.848 0.9300
Step7 - Step18 0.058925 0.0217 4403 2.714 0.3705
Step8 - Step9 0.013954 0.0217 4403 0.643 1.0000
Step8 - Step10 0.025714 0.0217 4403 1.184 0.9995
Step8 - Step11 0.025463 0.0217 4403 1.173 0.9995
Step8 - Step12 0.001691 0.0217 4403 0.078 1.0000
Step8 - Step13 0.011485 0.0217 4403 0.529 1.0000
Step8 - Step14 0.023616 0.0217 4403 1.088 0.9998
Step8 - Step15 0.045216 0.0217 4403 2.083 0.8264
Step8 - Step16 0.039638 0.0217 4403 1.826 0.9369
Step8 - Step17 0.045110 0.0217 4403 2.078 0.8292
Step8 - Step18 0.063906 0.0217 4403 2.944 0.2288
Step9 - Step10 0.011760 0.0217 4403 0.542 1.0000
Step9 - Step11 0.011509 0.0217 4403 0.530 1.0000
Step9 - Step12 -0.012263 0.0217 4403 -0.565 1.0000
Step9 - Step13 -0.002469 0.0217 4403 -0.114 1.0000
Step9 - Step14 0.009662 0.0217 4403 0.445 1.0000
Step9 - Step15 0.031262 0.0217 4403 1.440 0.9941
Step9 - Step16 0.025684 0.0217 4403 1.183 0.9995
Step9 - Step17 0.031156 0.0217 4403 1.435 0.9943
Step9 - Step18 0.049952 0.0217 4403 2.301 0.6828
Step10 - Step11 -0.000251 0.0217 4403 -0.012 1.0000
Step10 - Step12 -0.024024 0.0217 4403 -1.107 0.9998
Step10 - Step13 -0.014230 0.0217 4403 -0.655 1.0000
Step10 - Step14 -0.002098 0.0217 4403 -0.097 1.0000
Step10 - Step15 0.019501 0.0217 4403 0.898 1.0000
Step10 - Step16 0.013923 0.0217 4403 0.641 1.0000
Step10 - Step17 0.019396 0.0217 4403 0.893 1.0000
Step10 - Step18 0.038192 0.0217 4403 1.759 0.9545
Step11 - Step12 -0.023772 0.0217 4403 -1.095 0.9998
Step11 - Step13 -0.013978 0.0217 4403 -0.644 1.0000
Step11 - Step14 -0.001847 0.0217 4403 -0.085 1.0000
Step11 - Step15 0.019753 0.0217 4403 0.910 1.0000
Step11 - Step16 0.014175 0.0217 4403 0.653 1.0000
Step11 - Step17 0.019647 0.0217 4403 0.905 1.0000
Step11 - Step18 0.038443 0.0217 4403 1.771 0.9518
Step12 - Step13 0.009794 0.0217 4403 0.451 1.0000
Step12 - Step14 0.021925 0.0217 4403 1.010 0.9999
Step12 - Step15 0.043525 0.0217 4403 2.005 0.8673
Step12 - Step16 0.037947 0.0217 4403 1.748 0.9571
Step12 - Step17 0.043420 0.0217 4403 2.000 0.8696
Step12 - Step18 0.062216 0.0217 4403 2.866 0.2725
Step13 - Step14 0.012131 0.0217 4403 0.559 1.0000
Step13 - Step15 0.033731 0.0217 4403 1.554 0.9865
Step13 - Step16 0.028153 0.0217 4403 1.297 0.9983
Step13 - Step17 0.033626 0.0217 4403 1.549 0.9870
Step13 - Step18 0.052422 0.0217 4403 2.415 0.5966
Step14 - Step15 0.021600 0.0217 4403 0.995 0.9999
Step14 - Step16 0.016022 0.0217 4403 0.738 1.0000
Step14 - Step17 0.021494 0.0217 4403 0.990 1.0000
Step14 - Step18 0.040290 0.0217 4403 1.856 0.9276
Step15 - Step16 -0.005578 0.0217 4403 -0.257 1.0000
Step15 - Step17 -0.000105 0.0217 4403 -0.005 1.0000
Step15 - Step18 0.018691 0.0217 4403 0.861 1.0000
Step16 - Step17 0.005473 0.0217 4403 0.252 1.0000
Step16 - Step18 0.024269 0.0217 4403 1.118 0.9997
Step17 - Step18 0.018796 0.0217 4403 0.866 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
--- Axis: Y ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 105.94 17 6.96e-15 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 0.727 0.0646 21 0.593 0.861
2 0.706 0.0646 21 0.572 0.840
3 0.691 0.0646 21 0.557 0.826
4 0.681 0.0646 21 0.547 0.815
5 0.668 0.0646 21 0.534 0.803
6 0.649 0.0646 21 0.515 0.784
7 0.626 0.0646 21 0.491 0.760
8 0.639 0.0646 21 0.505 0.773
9 0.632 0.0646 21 0.498 0.767
10 0.625 0.0646 21 0.491 0.759
11 0.633 0.0646 21 0.499 0.767
12 0.639 0.0646 21 0.505 0.774
13 0.621 0.0646 21 0.487 0.756
14 0.605 0.0646 21 0.471 0.739
15 0.561 0.0646 21 0.427 0.695
16 0.560 0.0646 21 0.426 0.694
17 0.558 0.0646 21 0.423 0.692
18 0.538 0.0646 21 0.404 0.673
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.020729 0.03 4403 0.691 1.0000
Step1 - Step3 0.035553 0.03 4403 1.186 0.9994
Step1 - Step4 0.046150 0.03 4403 1.539 0.9878
Step1 - Step5 0.058654 0.03 4403 1.956 0.8897
Step1 - Step6 0.077498 0.03 4403 2.584 0.4656
Step1 - Step7 0.101206 0.03 4403 3.375 0.0719
Step1 - Step8 0.087762 0.03 4403 2.926 0.2381
Step1 - Step9 0.094627 0.03 4403 3.155 0.1348
Step1 - Step10 0.102042 0.03 4403 3.403 0.0660
Step1 - Step11 0.094054 0.03 4403 3.136 0.1418
Step1 - Step12 0.087635 0.03 4403 2.922 0.2404
Step1 - Step13 0.105500 0.03 4403 3.518 0.0458
Step1 - Step14 0.121916 0.03 4403 4.065 0.0062
Step1 - Step15 0.166197 0.03 4403 5.542 <.0001
Step1 - Step16 0.167098 0.03 4403 5.572 <.0001
Step1 - Step17 0.169263 0.03 4403 5.644 <.0001
Step1 - Step18 0.188541 0.03 4403 6.287 <.0001
Step2 - Step3 0.014824 0.03 4403 0.494 1.0000
Step2 - Step4 0.025421 0.03 4403 0.848 1.0000
Step2 - Step5 0.037925 0.03 4403 1.265 0.9987
Step2 - Step6 0.056768 0.03 4403 1.893 0.9147
Step2 - Step7 0.080477 0.03 4403 2.684 0.3922
Step2 - Step8 0.067032 0.03 4403 2.235 0.7299
Step2 - Step9 0.073898 0.03 4403 2.464 0.5582
Step2 - Step10 0.081313 0.03 4403 2.711 0.3725
Step2 - Step11 0.073324 0.03 4403 2.445 0.5731
Step2 - Step12 0.066906 0.03 4403 2.231 0.7328
Step2 - Step13 0.084771 0.03 4403 2.827 0.2962
Step2 - Step14 0.101186 0.03 4403 3.374 0.0720
Step2 - Step15 0.145468 0.03 4403 4.851 0.0002
Step2 - Step16 0.146369 0.03 4403 4.881 0.0002
Step2 - Step17 0.148534 0.03 4403 4.953 0.0001
Step2 - Step18 0.167812 0.03 4403 5.596 <.0001
Step3 - Step4 0.010597 0.03 4403 0.353 1.0000
Step3 - Step5 0.023101 0.03 4403 0.770 1.0000
Step3 - Step6 0.041944 0.03 4403 1.399 0.9958
Step3 - Step7 0.065653 0.03 4403 2.189 0.7611
Step3 - Step8 0.052208 0.03 4403 1.741 0.9587
Step3 - Step9 0.059074 0.03 4403 1.970 0.8836
Step3 - Step10 0.066489 0.03 4403 2.217 0.7423
Step3 - Step11 0.058500 0.03 4403 1.951 0.8919
Step3 - Step12 0.052082 0.03 4403 1.737 0.9596
Step3 - Step13 0.069947 0.03 4403 2.332 0.6594
Step3 - Step14 0.086362 0.03 4403 2.880 0.2643
Step3 - Step15 0.130644 0.03 4403 4.356 0.0018
Step3 - Step16 0.131545 0.03 4403 4.386 0.0016
Step3 - Step17 0.133710 0.03 4403 4.459 0.0012
Step3 - Step18 0.152988 0.03 4403 5.101 0.0001
Step4 - Step5 0.012503 0.03 4403 0.417 1.0000
Step4 - Step6 0.031347 0.03 4403 1.045 0.9999
Step4 - Step7 0.055056 0.03 4403 1.836 0.9339
Step4 - Step8 0.041611 0.03 4403 1.388 0.9962
Step4 - Step9 0.048476 0.03 4403 1.616 0.9797
Step4 - Step10 0.055892 0.03 4403 1.864 0.9250
Step4 - Step11 0.047903 0.03 4403 1.597 0.9820
Step4 - Step12 0.041485 0.03 4403 1.383 0.9963
Step4 - Step13 0.059350 0.03 4403 1.979 0.8794
Step4 - Step14 0.075765 0.03 4403 2.526 0.5099
Step4 - Step15 0.120047 0.03 4403 4.003 0.0080
Step4 - Step16 0.120948 0.03 4403 4.033 0.0071
Step4 - Step17 0.123113 0.03 4403 4.105 0.0053
Step4 - Step18 0.142391 0.03 4403 4.748 0.0003
Step5 - Step6 0.018844 0.03 4403 0.628 1.0000
Step5 - Step7 0.042552 0.03 4403 1.419 0.9950
Step5 - Step8 0.029108 0.03 4403 0.971 1.0000
Step5 - Step9 0.035973 0.03 4403 1.200 0.9994
Step5 - Step10 0.043388 0.03 4403 1.447 0.9938
Step5 - Step11 0.035400 0.03 4403 1.180 0.9995
Step5 - Step12 0.028981 0.03 4403 0.966 1.0000
Step5 - Step13 0.046847 0.03 4403 1.562 0.9857
Step5 - Step14 0.063262 0.03 4403 2.110 0.8110
Step5 - Step15 0.107543 0.03 4403 3.586 0.0365
Step5 - Step16 0.108444 0.03 4403 3.616 0.0330
Step5 - Step17 0.110610 0.03 4403 3.688 0.0257
Step5 - Step18 0.129887 0.03 4403 4.331 0.0021
Step6 - Step7 0.023708 0.03 4403 0.791 1.0000
Step6 - Step8 0.010264 0.03 4403 0.342 1.0000
Step6 - Step9 0.017129 0.03 4403 0.571 1.0000
Step6 - Step10 0.024544 0.03 4403 0.818 1.0000
Step6 - Step11 0.016556 0.03 4403 0.552 1.0000
Step6 - Step12 0.010137 0.03 4403 0.338 1.0000
Step6 - Step13 0.028003 0.03 4403 0.934 1.0000
Step6 - Step14 0.044418 0.03 4403 1.481 0.9919
Step6 - Step15 0.088699 0.03 4403 2.958 0.2215
Step6 - Step16 0.089600 0.03 4403 2.988 0.2063
Step6 - Step17 0.091766 0.03 4403 3.060 0.1728
Step6 - Step18 0.111043 0.03 4403 3.703 0.0244
Step7 - Step8 -0.013444 0.03 4403 -0.448 1.0000
Step7 - Step9 -0.006579 0.03 4403 -0.219 1.0000
Step7 - Step10 0.000836 0.03 4403 0.028 1.0000
Step7 - Step11 -0.007152 0.03 4403 -0.238 1.0000
Step7 - Step12 -0.013571 0.03 4403 -0.453 1.0000
Step7 - Step13 0.004294 0.03 4403 0.143 1.0000
Step7 - Step14 0.020710 0.03 4403 0.691 1.0000
Step7 - Step15 0.064991 0.03 4403 2.167 0.7754
Step7 - Step16 0.065892 0.03 4403 2.197 0.7558
Step7 - Step17 0.068057 0.03 4403 2.269 0.7057
Step7 - Step18 0.087335 0.03 4403 2.912 0.2459
Step8 - Step9 0.006865 0.03 4403 0.229 1.0000
Step8 - Step10 0.014280 0.03 4403 0.476 1.0000
Step8 - Step11 0.006292 0.03 4403 0.210 1.0000
Step8 - Step12 -0.000126 0.03 4403 -0.004 1.0000
Step8 - Step13 0.017739 0.03 4403 0.592 1.0000
Step8 - Step14 0.034154 0.03 4403 1.139 0.9997
Step8 - Step15 0.078436 0.03 4403 2.615 0.4420
Step8 - Step16 0.079336 0.03 4403 2.646 0.4198
Step8 - Step17 0.081502 0.03 4403 2.718 0.3681
Step8 - Step18 0.100780 0.03 4403 3.361 0.0751
Step9 - Step10 0.007415 0.03 4403 0.247 1.0000
Step9 - Step11 -0.000573 0.03 4403 -0.019 1.0000
Step9 - Step12 -0.006992 0.03 4403 -0.233 1.0000
Step9 - Step13 0.010874 0.03 4403 0.363 1.0000
Step9 - Step14 0.027289 0.03 4403 0.910 1.0000
Step9 - Step15 0.071570 0.03 4403 2.387 0.6183
Step9 - Step16 0.072471 0.03 4403 2.417 0.5952
Step9 - Step17 0.074637 0.03 4403 2.489 0.5391
Step9 - Step18 0.093914 0.03 4403 3.132 0.1436
Step10 - Step11 -0.007988 0.03 4403 -0.266 1.0000
Step10 - Step12 -0.014407 0.03 4403 -0.480 1.0000
Step10 - Step13 0.003458 0.03 4403 0.115 1.0000
Step10 - Step14 0.019874 0.03 4403 0.663 1.0000
Step10 - Step15 0.064155 0.03 4403 2.139 0.7930
Step10 - Step16 0.065056 0.03 4403 2.169 0.7740
Step10 - Step17 0.067221 0.03 4403 2.242 0.7255
Step10 - Step18 0.086499 0.03 4403 2.884 0.2617
Step11 - Step12 -0.006419 0.03 4403 -0.214 1.0000
Step11 - Step13 0.011447 0.03 4403 0.382 1.0000
Step11 - Step14 0.027862 0.03 4403 0.929 1.0000
Step11 - Step15 0.072143 0.03 4403 2.406 0.6036
Step11 - Step16 0.073044 0.03 4403 2.436 0.5804
Step11 - Step17 0.075210 0.03 4403 2.508 0.5242
Step11 - Step18 0.094487 0.03 4403 3.151 0.1365
Step12 - Step13 0.017865 0.03 4403 0.596 1.0000
Step12 - Step14 0.034281 0.03 4403 1.143 0.9997
Step12 - Step15 0.078562 0.03 4403 2.620 0.4389
Step12 - Step16 0.079463 0.03 4403 2.650 0.4167
Step12 - Step17 0.081628 0.03 4403 2.722 0.3652
Step12 - Step18 0.100906 0.03 4403 3.365 0.0741
Step13 - Step14 0.016415 0.03 4403 0.547 1.0000
Step13 - Step15 0.060697 0.03 4403 2.024 0.8579
Step13 - Step16 0.061598 0.03 4403 2.054 0.8423
Step13 - Step17 0.063763 0.03 4403 2.126 0.8010
Step13 - Step18 0.083041 0.03 4403 2.769 0.3332
Step14 - Step15 0.044281 0.03 4403 1.477 0.9922
Step14 - Step16 0.045182 0.03 4403 1.507 0.9903
Step14 - Step17 0.047348 0.03 4403 1.579 0.9841
Step14 - Step18 0.066625 0.03 4403 2.222 0.7392
Step15 - Step16 0.000901 0.03 4403 0.030 1.0000
Step15 - Step17 0.003066 0.03 4403 0.102 1.0000
Step15 - Step18 0.022344 0.03 4403 0.745 1.0000
Step16 - Step17 0.002165 0.03 4403 0.072 1.0000
Step16 - Step18 0.021443 0.03 4403 0.715 1.0000
Step17 - Step18 0.019278 0.03 4403 0.643 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
--- Axis: Z ---Analysis of Deviance Table (Type II Wald chisquare tests)
Response: RMS
Chisq Df Pr(>Chisq)
Step 146.27 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Estimated Marginal Means:
Step emmean SE df lower.CL upper.CL
1 1.47 0.181 17.9 1.086 1.85
2 1.45 0.181 17.9 1.066 1.83
3 1.43 0.181 17.9 1.049 1.81
4 1.43 0.181 17.9 1.052 1.81
5 1.40 0.181 17.9 1.022 1.78
6 1.35 0.181 17.9 0.969 1.73
7 1.32 0.181 17.9 0.943 1.71
8 1.30 0.181 17.9 0.918 1.68
9 1.27 0.181 17.9 0.892 1.65
10 1.27 0.181 17.9 0.894 1.66
11 1.26 0.181 17.9 0.881 1.64
12 1.28 0.181 17.9 0.898 1.66
13 1.29 0.181 17.9 0.910 1.67
14 1.26 0.181 17.9 0.875 1.64
15 1.25 0.181 17.9 0.864 1.63
16 1.24 0.181 17.9 0.860 1.62
17 1.22 0.181 17.9 0.837 1.60
18 1.18 0.181 17.9 0.795 1.56
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.02021 0.0417 4403 0.484 1.0000
Step1 - Step3 0.03650 0.0417 4403 0.875 1.0000
Step1 - Step4 0.03412 0.0417 4403 0.818 1.0000
Step1 - Step5 0.06408 0.0417 4403 1.536 0.9881
Step1 - Step6 0.11679 0.0417 4403 2.799 0.3137
Step1 - Step7 0.14230 0.0417 4403 3.410 0.0644
Step1 - Step8 0.16778 0.0417 4403 4.021 0.0074
Step1 - Step9 0.19355 0.0417 4403 4.639 0.0005
Step1 - Step10 0.19213 0.0417 4403 4.605 0.0006
Step1 - Step11 0.20428 0.0417 4403 4.896 0.0001
Step1 - Step12 0.18757 0.0417 4403 4.495 0.0010
Step1 - Step13 0.17606 0.0417 4403 4.220 0.0033
Step1 - Step14 0.21042 0.0417 4403 5.043 0.0001
Step1 - Step15 0.22173 0.0417 4403 5.314 <.0001
Step1 - Step16 0.22604 0.0417 4403 5.417 <.0001
Step1 - Step17 0.24916 0.0417 4403 5.971 <.0001
Step1 - Step18 0.29054 0.0417 4403 6.963 <.0001
Step2 - Step3 0.01629 0.0417 4403 0.390 1.0000
Step2 - Step4 0.01391 0.0417 4403 0.333 1.0000
Step2 - Step5 0.04388 0.0417 4403 1.052 0.9999
Step2 - Step6 0.09659 0.0417 4403 2.315 0.6726
Step2 - Step7 0.12210 0.0417 4403 2.926 0.2383
Step2 - Step8 0.14757 0.0417 4403 3.537 0.0431
Step2 - Step9 0.17335 0.0417 4403 4.154 0.0043
Step2 - Step10 0.17192 0.0417 4403 4.120 0.0050
Step2 - Step11 0.18408 0.0417 4403 4.412 0.0014
Step2 - Step12 0.16737 0.0417 4403 4.011 0.0077
Step2 - Step13 0.15586 0.0417 4403 3.735 0.0218
Step2 - Step14 0.19021 0.0417 4403 4.559 0.0007
Step2 - Step15 0.20152 0.0417 4403 4.830 0.0002
Step2 - Step16 0.20583 0.0417 4403 4.933 0.0001
Step2 - Step17 0.22895 0.0417 4403 5.487 <.0001
Step2 - Step18 0.27033 0.0417 4403 6.479 <.0001
Step3 - Step4 -0.00238 0.0417 4403 -0.057 1.0000
Step3 - Step5 0.02758 0.0417 4403 0.661 1.0000
Step3 - Step6 0.08029 0.0417 4403 1.924 0.9028
Step3 - Step7 0.10580 0.0417 4403 2.536 0.5027
Step3 - Step8 0.13128 0.0417 4403 3.146 0.1381
Step3 - Step9 0.15705 0.0417 4403 3.764 0.0196
Step3 - Step10 0.15563 0.0417 4403 3.730 0.0222
Step3 - Step11 0.16778 0.0417 4403 4.021 0.0074
Step3 - Step12 0.15107 0.0417 4403 3.621 0.0325
Step3 - Step13 0.13956 0.0417 4403 3.345 0.0787
Step3 - Step14 0.17392 0.0417 4403 4.168 0.0041
Step3 - Step15 0.18523 0.0417 4403 4.439 0.0013
Step3 - Step16 0.18954 0.0417 4403 4.543 0.0008
Step3 - Step17 0.21266 0.0417 4403 5.097 0.0001
Step3 - Step18 0.25404 0.0417 4403 6.088 <.0001
Step4 - Step5 0.02996 0.0417 4403 0.718 1.0000
Step4 - Step6 0.08267 0.0417 4403 1.981 0.8784
Step4 - Step7 0.10818 0.0417 4403 2.593 0.4591
Step4 - Step8 0.13366 0.0417 4403 3.203 0.1183
Step4 - Step9 0.15943 0.0417 4403 3.821 0.0160
Step4 - Step10 0.15801 0.0417 4403 3.787 0.0181
Step4 - Step11 0.17016 0.0417 4403 4.078 0.0059
Step4 - Step12 0.15345 0.0417 4403 3.678 0.0267
Step4 - Step13 0.14194 0.0417 4403 3.402 0.0662
Step4 - Step14 0.17630 0.0417 4403 4.225 0.0032
Step4 - Step15 0.18761 0.0417 4403 4.496 0.0010
Step4 - Step16 0.19192 0.0417 4403 4.600 0.0006
Step4 - Step17 0.21504 0.0417 4403 5.154 <.0001
Step4 - Step18 0.25642 0.0417 4403 6.145 <.0001
Step5 - Step6 0.05271 0.0417 4403 1.263 0.9988
Step5 - Step7 0.07822 0.0417 4403 1.875 0.9213
Step5 - Step8 0.10370 0.0417 4403 2.485 0.5419
Step5 - Step9 0.12947 0.0417 4403 3.103 0.1548
Step5 - Step10 0.12804 0.0417 4403 3.069 0.1690
Step5 - Step11 0.14020 0.0417 4403 3.360 0.0752
Step5 - Step12 0.12349 0.0417 4403 2.960 0.2205
Step5 - Step13 0.11198 0.0417 4403 2.684 0.3920
Step5 - Step14 0.14634 0.0417 4403 3.507 0.0474
Step5 - Step15 0.15764 0.0417 4403 3.778 0.0187
Step5 - Step16 0.16196 0.0417 4403 3.882 0.0127
Step5 - Step17 0.18508 0.0417 4403 4.436 0.0013
Step5 - Step18 0.22646 0.0417 4403 5.427 <.0001
Step6 - Step7 0.02551 0.0417 4403 0.611 1.0000
Step6 - Step8 0.05099 0.0417 4403 1.222 0.9992
Step6 - Step9 0.07676 0.0417 4403 1.840 0.9327
Step6 - Step10 0.07533 0.0417 4403 1.805 0.9427
Step6 - Step11 0.08749 0.0417 4403 2.097 0.8184
Step6 - Step12 0.07078 0.0417 4403 1.696 0.9675
Step6 - Step13 0.05927 0.0417 4403 1.421 0.9950
Step6 - Step14 0.09363 0.0417 4403 2.244 0.7238
Step6 - Step15 0.10493 0.0417 4403 2.515 0.5188
Step6 - Step16 0.10925 0.0417 4403 2.618 0.4400
Step6 - Step17 0.13237 0.0417 4403 3.172 0.1288
Step6 - Step18 0.17375 0.0417 4403 4.164 0.0042
Step7 - Step8 0.02548 0.0417 4403 0.611 1.0000
Step7 - Step9 0.05125 0.0417 4403 1.228 0.9991
Step7 - Step10 0.04982 0.0417 4403 1.194 0.9994
Step7 - Step11 0.06198 0.0417 4403 1.485 0.9917
Step7 - Step12 0.04527 0.0417 4403 1.085 0.9998
Step7 - Step13 0.03376 0.0417 4403 0.809 1.0000
Step7 - Step14 0.06812 0.0417 4403 1.632 0.9777
Step7 - Step15 0.07942 0.0417 4403 1.903 0.9109
Step7 - Step16 0.08374 0.0417 4403 2.007 0.8663
Step7 - Step17 0.10686 0.0417 4403 2.561 0.4833
Step7 - Step18 0.14824 0.0417 4403 3.553 0.0408
Step8 - Step9 0.02578 0.0417 4403 0.618 1.0000
Step8 - Step10 0.02435 0.0417 4403 0.584 1.0000
Step8 - Step11 0.03650 0.0417 4403 0.875 1.0000
Step8 - Step12 0.01979 0.0417 4403 0.474 1.0000
Step8 - Step13 0.00829 0.0417 4403 0.199 1.0000
Step8 - Step14 0.04264 0.0417 4403 1.022 0.9999
Step8 - Step15 0.05395 0.0417 4403 1.293 0.9983
Step8 - Step16 0.05826 0.0417 4403 1.396 0.9959
Step8 - Step17 0.08138 0.0417 4403 1.950 0.8921
Step8 - Step18 0.12276 0.0417 4403 2.942 0.2297
Step9 - Step10 -0.00143 0.0417 4403 -0.034 1.0000
Step9 - Step11 0.01073 0.0417 4403 0.257 1.0000
Step9 - Step12 -0.00598 0.0417 4403 -0.143 1.0000
Step9 - Step13 -0.01749 0.0417 4403 -0.419 1.0000
Step9 - Step14 0.01686 0.0417 4403 0.404 1.0000
Step9 - Step15 0.02817 0.0417 4403 0.675 1.0000
Step9 - Step16 0.03249 0.0417 4403 0.779 1.0000
Step9 - Step17 0.05561 0.0417 4403 1.333 0.9976
Step9 - Step18 0.09699 0.0417 4403 2.324 0.6654
Step10 - Step11 0.01216 0.0417 4403 0.291 1.0000
Step10 - Step12 -0.00455 0.0417 4403 -0.109 1.0000
Step10 - Step13 -0.01606 0.0417 4403 -0.385 1.0000
Step10 - Step14 0.01829 0.0417 4403 0.438 1.0000
Step10 - Step15 0.02960 0.0417 4403 0.709 1.0000
Step10 - Step16 0.03391 0.0417 4403 0.813 1.0000
Step10 - Step17 0.05703 0.0417 4403 1.367 0.9968
Step10 - Step18 0.09841 0.0417 4403 2.359 0.6397
Step11 - Step12 -0.01671 0.0417 4403 -0.400 1.0000
Step11 - Step13 -0.02822 0.0417 4403 -0.676 1.0000
Step11 - Step14 0.00613 0.0417 4403 0.147 1.0000
Step11 - Step15 0.01744 0.0417 4403 0.418 1.0000
Step11 - Step16 0.02176 0.0417 4403 0.521 1.0000
Step11 - Step17 0.04488 0.0417 4403 1.076 0.9998
Step11 - Step18 0.08626 0.0417 4403 2.067 0.8351
Step12 - Step13 -0.01151 0.0417 4403 -0.276 1.0000
Step12 - Step14 0.02284 0.0417 4403 0.548 1.0000
Step12 - Step15 0.03415 0.0417 4403 0.819 1.0000
Step12 - Step16 0.03847 0.0417 4403 0.922 1.0000
Step12 - Step17 0.06159 0.0417 4403 1.476 0.9922
Step12 - Step18 0.10297 0.0417 4403 2.468 0.5554
Step13 - Step14 0.03435 0.0417 4403 0.823 1.0000
Step13 - Step15 0.04566 0.0417 4403 1.094 0.9998
Step13 - Step16 0.04998 0.0417 4403 1.198 0.9994
Step13 - Step17 0.07310 0.0417 4403 1.752 0.9562
Step13 - Step18 0.11448 0.0417 4403 2.744 0.3503
Step14 - Step15 0.01131 0.0417 4403 0.271 1.0000
Step14 - Step16 0.01562 0.0417 4403 0.374 1.0000
Step14 - Step17 0.03874 0.0417 4403 0.929 1.0000
Step14 - Step18 0.08012 0.0417 4403 1.920 0.9044
Step15 - Step16 0.00431 0.0417 4403 0.103 1.0000
Step15 - Step17 0.02743 0.0417 4403 0.657 1.0000
Step15 - Step18 0.06881 0.0417 4403 1.649 0.9753
Step16 - Step17 0.02312 0.0417 4403 0.554 1.0000
Step16 - Step18 0.06450 0.0417 4403 1.546 0.9872
Step17 - Step18 0.04138 0.0417 4403 0.992 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates plot_stepwise_rms_block45_faceted <- function(step_summary_block45, seq_length) {
step_levels <- as.character(1:seq_length)
step_ticks <- step_levels[as.numeric(step_levels) %% 2 == 1 | step_levels == "1"]
df <- step_summary_block45 %>%
filter(
Block %in% c("4", "5"),
step_count == seq_length,
Step %in% step_levels
) %>%
mutate(
Step = as.character(Step),
Block = factor(Block, levels = c("4", "5"), labels = c("Block 4", "Block 5"))
) %>%
group_by(Block, Step, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
sd_rms = sd(RMS, na.rm = TRUE),
.groups = "drop"
) %>%
mutate(
Step = factor(Step, levels = step_levels) # ✅ Enforce correct numeric order
)
ggplot(df, aes(x = Step, y = mean_rms, color = Block)) +
geom_point(position = position_dodge(width = 0.5), size = 2) +
geom_errorbar(
aes(ymin = mean_rms - sd_rms, ymax = mean_rms + sd_rms),
width = 0.3,
position = position_dodge(width = 0.5)
) +
facet_wrap(~ Axis, ncol = 3, scales = "free_y") +
scale_x_discrete(breaks = step_ticks) +
ylim(0, 3.25) +
labs(
title = paste(seq_length, "-Step Sequences: Step-wise RMS Acceleration — Block 4 vs Block 5"),
x = "Step",
y = "Mean RMS Acceleration (m/s²)",
color = NULL
) +
theme_minimal() +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
text = element_text(size = 12),
plot.title = element_text(face = "bold"),
legend.position = "top"
)
}plot_stepwise_rms_block45_faceted(step_summary_block45, seq_length = 6)
plot_stepwise_rms_block45_faceted(step_summary_block45, seq_length = 12)
plot_stepwise_rms_block45_faceted(step_summary_block45, seq_length = 18)
#4 Behavioural analysis
RT <- read.csv("/Users/can/Documents/Uni/Thesis/Data/E-Prime/all_excluded2.csv", sep = ";")
# Filter only response procedure entries, remove subject 12, convert to numeric
RTR <- RT %>%
filter(procedure == "responsprocedure") %>%
mutate(
feedback.ACC = as.numeric(feedback.ACC),
feedback.RT = as.numeric(feedback.RT)
) %>%
filter(subject != 12)
# -------- Assign trial numbers dynamically --------
RTR <- RTR %>%
group_by(subject, session) %>%
mutate(trial = cumsum(sub.trial.number == 1)) %>%
ungroup()
# -------- Compute trial-level accuracy and mean RT --------
df <- RTR %>%
group_by(subject, session, trial) %>%
mutate(
trial.acc = sum(feedback.ACC, na.rm = TRUE) / n(),
trial.RT = mean(feedback.RT, na.rm = TRUE)
) %>%
ungroup()
# -------- Filter only trials with 80% accuracy --------
df_acc <- df %>%
filter(
(session %in% c(1, 2, 3) & trial.acc >= 0.8) |
(session %in% c(4, 5) & trial.acc == 1)
) %>%
mutate(
subject = as.factor(subject),
sub.trial.number = as.factor(sub.trial.number),
session = as.factor(session)
)
# -------- Add corr_trials per subject --------
df_acc5 <- df_acc %>%
distinct(subject, trial, session) %>%
count(subject, name = "corr_trials")
df_acc <- left_join(df_acc, df_acc5, by = "subject")
df_acc <- df_acc %>% select(-feedback.CRESP, -feedback.RESP, -cue.OnsetDelay, -cue.OnsetTime)#4.1.1 RT per block
# Ensure correct factor levels
df_acc$session <- factor(df_acc$session, levels = 1:5, labels = paste("Block", 1:5))
# -------- Training Blocks Only (1–3) --------
df_train <- df_acc %>% filter(session %in% c("Block 1", "Block 2", "Block 3"))
model_rt_train <- lmer(feedback.RT ~ session + (1 | subject), data = df_train)
cat("=== LMM Summary: Training Blocks (RT) ===\n")=== LMM Summary: Training Blocks (RT) ===print(summary(model_rt_train))Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ session + (1 | subject)
Data: df_train
REML criterion at convergence: 322915
Scaled residuals:
Min 1Q Median 3Q Max
-2.9479 -0.4784 -0.2247 0.1839 29.4415
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 46657 216.0
Residual 117302 342.5
Number of obs: 22248, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 5.034e+02 5.117e+01 1.727e+01 9.837 1.7e-08 ***
sessionBlock 2 4.255e-01 6.502e+00 2.223e+04 0.065 0.948
sessionBlock 3 3.553e+01 6.215e+00 2.223e+04 5.717 1.1e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) sssnB2
sessinBlck2 -0.080
sessinBlck3 -0.084 0.663cat("\n=== Type II ANOVA ===\n")
=== Type II ANOVA ===print(Anova(model_rt_train, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
session 57.47 2 3.316e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_train <- emmeans(model_rt_train, ~ session)
print(summary(emm_train)) session emmean SE df lower.CL upper.CL
Block 1 503 51.2 17.3 396 611
Block 2 504 51.1 17.1 396 612
Block 3 539 51.0 17.1 431 647
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(summary(pairs(emm_train), infer = c(TRUE, TRUE))) contrast estimate SE df lower.CL upper.CL t.ratio p.value
Block 1 - Block 2 -0.425 6.50 22229 -15.7 14.8 -0.065 0.9976
Block 1 - Block 3 -35.532 6.21 22230 -50.1 -21.0 -5.717 <.0001
Block 2 - Block 3 -35.107 5.23 22230 -47.4 -22.9 -6.719 <.0001
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 3 estimates
P value adjustment: tukey method for comparing a family of 3 estimates plot_rt_train <- df_train %>%
group_by(session) %>%
summarise(mean_RT = mean(feedback.RT), sd_RT = sd(feedback.RT), n = n())
ggplot(plot_rt_train, aes(x = session, y = mean_RT)) +
geom_point(size = 4, color = "steelblue") +
geom_errorbar(aes(ymin = mean_RT - sd_RT, ymax = mean_RT + sd_RT), width = 0.2, color = "steelblue") +
labs(title = "Mean RT – Training Blocks ", x = "Block", y = "Mean RT (ms)") +
theme_minimal(base_size = 13) +
theme(panel.grid = element_blank())
# -------- Test Blocks Only (4–5) --------
df_test <- df_acc %>% filter(session %in% c("Block 4", "Block 5"))
model_rt_test <- lmer(feedback.RT ~ session + (1 | subject), data = df_test)
cat("\n\n=== LMM Summary: Test Blocks (RT) ===\n")
=== LMM Summary: Test Blocks (RT) ===print(summary(model_rt_test))Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ session + (1 | subject)
Data: df_test
REML criterion at convergence: 180713.6
Scaled residuals:
Min 1Q Median 3Q Max
-2.0432 -0.4163 -0.2051 0.1536 28.0193
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 30386 174.3
Residual 134940 367.3
Number of obs: 12330, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 465.809 41.315 17.110 11.28 2.42e-09 ***
sessionBlock 5 116.233 6.977 12321.235 16.66 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
sessinBlck5 -0.066cat("\n=== Type II ANOVA ===\n")
=== Type II ANOVA ===print(Anova(model_rt_test, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
session 277.5 1 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_test <- emmeans(model_rt_test, ~ session)
print(summary(emm_test)) session emmean SE df lower.CL upper.CL
Block 4 466 41.3 17.1 379 553
Block 5 582 41.4 17.4 495 669
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(summary(pairs(emm_test), infer = c(TRUE, TRUE))) contrast estimate SE df lower.CL upper.CL t.ratio p.value
Block 4 - Block 5 -116 6.98 12321 -130 -103 -16.657 <.0001
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 plot_rt_test <- df_test %>%
group_by(session) %>%
summarise(mean_RT = mean(feedback.RT), sd_RT = sd(feedback.RT), n = n())
ggplot(plot_rt_test, aes(x = session, y = mean_RT)) +
geom_point(size = 4, color = "darkgreen") +
geom_errorbar(aes(ymin = mean_RT - sd_RT, ymax = mean_RT + sd_RT), width = 0.2, color = "darkgreen") +
labs(title = "Mean RT – Test Blocks (± SD)", x = "Block", y = "Mean RT (ms)") +
theme_minimal(base_size = 13) +
theme(panel.grid = element_blank())
#4.1.2 RT per block divided into sequence lengths for test phase
# ====== Preparation ======
# Filter for test blocks (Block 4 & 5)
df_test_all <- df_acc %>%
filter(session %in% c("Block 4", "Block 5")) %>%
group_by(subject, session, trial) %>%
mutate(seq_length_trial = n_distinct(sub.trial.number)) %>%
ungroup() %>%
mutate(
subject = as.factor(subject),
session = as.factor(session),
seq_length_trial = as.factor(seq_length_trial) # 6, 12, 18
)
# ====== Linear Mixed Model ======
model_rt <- lmer(feedback.RT ~ session * seq_length_trial + (1 | subject), data = df_test_all)
cat("=== LMM Summary: feedback.RT ~ session * seq_length_trial ===\n")=== LMM Summary: feedback.RT ~ session * seq_length_trial ===print(summary(model_rt))Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ session * seq_length_trial + (1 | subject)
Data: df_test_all
REML criterion at convergence: 180663.8
Scaled residuals:
Min 1Q Median 3Q Max
-2.1100 -0.4184 -0.2072 0.1509 28.0496
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 30532 174.7
Residual 134729 367.1
Number of obs: 12330, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value
(Intercept) 447.108 42.260 18.551 10.580
sessionBlock 5 105.253 13.922 12308.336 7.560
seq_length_trial12 21.682 11.827 12307.363 1.833
seq_length_trial18 25.308 11.516 12308.455 2.198
sessionBlock 5:seq_length_trial12 36.256 18.104 12307.695 2.003
sessionBlock 5:seq_length_trial18 1.587 17.441 12308.629 0.091
Pr(>|t|)
(Intercept) 2.71e-09 ***
sessionBlock 5 4.30e-14 ***
seq_length_trial12 0.0668 .
seq_length_trial18 0.0280 *
sessionBlock 5:seq_length_trial12 0.0452 *
sessionBlock 5:seq_length_trial18 0.9275
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) sssnB5 sq__12 sq__18 sB5:__12
sessinBlck5 -0.152
sq_lngth_12 -0.179 0.543
sq_lngth_18 -0.184 0.554 0.658
sssnB5:__12 0.117 -0.763 -0.653 -0.429
sssnB5:__18 0.121 -0.789 -0.434 -0.657 0.613 cat("\n=== Type II ANOVA ===\n")
=== Type II ANOVA ===print(Anova(model_rt, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
session 286.7283 1 < 2.2e-16 ***
seq_length_trial 17.1089 2 0.0001927 ***
session:seq_length_trial 6.0764 2 0.0479200 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1cat("\n=== Estimated Marginal Means ===\n")
=== Estimated Marginal Means ===emm_rt <- emmeans(model_rt, ~ session * seq_length_trial)
print(summary(emm_rt)) session seq_length_trial emmean SE df lower.CL upper.CL
Block 4 6 447 42.3 18.6 359 536
Block 5 6 552 42.4 18.9 464 641
Block 4 12 469 41.8 17.8 381 557
Block 5 12 610 42.2 18.5 522 699
Block 4 18 472 41.7 17.6 385 560
Block 5 18 579 42.0 18.2 491 668
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 cat("\n=== Pairwise Comparisons ===\n")
=== Pairwise Comparisons ===print(summary(pairs(emm_rt), infer = c(TRUE, TRUE))) contrast estimate SE df
Block 4 seq_length_trial6 - Block 5 seq_length_trial6 -105.25 13.90 12308
Block 4 seq_length_trial6 - Block 4 seq_length_trial12 -21.68 11.80 12307
Block 4 seq_length_trial6 - Block 5 seq_length_trial12 -163.19 13.30 12310
Block 4 seq_length_trial6 - Block 4 seq_length_trial18 -25.31 11.50 12308
Block 4 seq_length_trial6 - Block 5 seq_length_trial18 -132.15 12.70 12312
Block 5 seq_length_trial6 - Block 4 seq_length_trial12 83.57 12.40 12309
Block 5 seq_length_trial6 - Block 5 seq_length_trial12 -57.94 13.70 12308
Block 5 seq_length_trial6 - Block 4 seq_length_trial18 79.94 12.20 12311
Block 5 seq_length_trial6 - Block 5 seq_length_trial18 -26.90 13.10 12310
Block 4 seq_length_trial12 - Block 5 seq_length_trial12 -141.51 11.70 12311
Block 4 seq_length_trial12 - Block 4 seq_length_trial18 -3.63 9.66 12309
Block 4 seq_length_trial12 - Block 5 seq_length_trial18 -110.47 11.10 12314
Block 5 seq_length_trial12 - Block 4 seq_length_trial18 137.88 11.40 12313
Block 5 seq_length_trial12 - Block 5 seq_length_trial18 31.04 12.40 12309
Block 4 seq_length_trial18 - Block 5 seq_length_trial18 -106.84 10.70 12316
lower.CL upper.CL t.ratio p.value
-144.93 -65.57 -7.560 <.0001
-55.39 12.03 -1.833 0.4443
-200.99 -125.39 -12.305 <.0001
-58.13 7.52 -2.198 0.2388
-168.35 -95.94 -10.403 <.0001
48.10 119.04 6.716 <.0001
-97.01 -18.87 -4.226 0.0003
45.19 114.70 6.557 <.0001
-64.37 10.58 -2.046 0.3164
-174.85 -108.17 -12.096 <.0001
-31.15 23.90 -0.376 0.9990
-141.97 -78.96 -9.995 <.0001
105.33 170.44 12.071 <.0001
-4.17 66.26 2.512 0.1205
-137.39 -76.29 -9.967 <.0001
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 6 estimates
P value adjustment: tukey method for comparing a family of 6 estimates # ====== Plot: Combined plot per sequence length ======
plot_data_rt <- df_test_all %>%
group_by(session, seq_length_trial) %>%
summarise(
mean_RT = mean(feedback.RT, na.rm = TRUE),
sd_RT = sd(feedback.RT, na.rm = TRUE),
n = n()
)`summarise()` has grouped output by 'session'. You can override using the
`.groups` argument.ggplot(plot_data_rt, aes(x = seq_length_trial, y = mean_RT, color = session, group = session)) +
geom_point(size = 4, position = position_dodge(width = 0.4)) +
geom_errorbar(aes(ymin = mean_RT - sd_RT, ymax = mean_RT + sd_RT),
width = 0.2, position = position_dodge(width = 0.4)) +
labs(
title = "Mean Reaction Time by Block and Sequence Length",
x = "Sequence Length (Steps)",
y = "Mean RT (ms)",
color = "Block"
) +
theme_minimal(base_size = 13) +
theme(panel.grid = element_blank())
#4.2.1 correct trials per block
# --------- Step 1: Ensure correct filtering logic ---------
df_acc <- df %>%
filter(
(session %in% c(1, 2, 3) & trial.acc >= 0.8) |
(session %in% c(4, 5) & trial.acc == 1)
) %>%
mutate(
subject = as.factor(subject),
sub.trial.number = as.factor(sub.trial.number),
session = as.factor(session)
)
# --------- Step 2: Count correct trials per subject × session ---------
correct_trials_df <- df_acc %>%
distinct(subject, session, trial) %>%
count(subject, session, name = "correct_trials") %>%
mutate(session = factor(session, levels = 1:5, labels = paste("Block", 1:5)))
# --------- Step 3a: Training Blocks Only (Block 1–3) ---------
train_trials <- correct_trials_df %>%
filter(session %in% c("Block 1", "Block 2", "Block 3"))
if (nrow(train_trials) > 0) {
model_train <- lmer(correct_trials ~ session + (1 | subject), data = train_trials)
cat("=== LMM Summary: Training Blocks (Block 1–3) ===\n")
print(summary(model_train))
cat("\n=== Type II ANOVA (Chi-square) ===\n")
print(Anova(model_train, type = 2))
cat("\n=== Estimated Marginal Means (Training) ===\n")
emm_train <- emmeans(model_train, ~ session)
print(summary(emm_train))
cat("\n=== Pairwise Comparisons Between Training Blocks ===\n")
print(summary(pairs(emm_train), infer = c(TRUE, TRUE)))
# Plot for training blocks
plot_train <- train_trials %>%
group_by(session) %>%
summarise(
mean_corr_trials = mean(correct_trials),
sd_corr_trials = sd(correct_trials),
n = n()
)
ggplot(plot_train, aes(x = session, y = mean_corr_trials)) +
geom_point(size = 4, color = "firebrick") +
geom_errorbar(aes(ymin = mean_corr_trials - sd_corr_trials,
ymax = mean_corr_trials + sd_corr_trials),
width = 0.2, color = "firebrick") +
labs(
title = "Correct Trials – Training Blocks ",
x = "Block",
y = "Correct Trials"
) +
theme_minimal(base_size = 13) +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank()
)
} else {
cat("⚠️ No valid training block data (Block 1–3)\n")
}=== LMM Summary: Training Blocks (Block 1–3) ===
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: correct_trials ~ session + (1 | subject)
Data: train_trials
REML criterion at convergence: 352.3
Scaled residuals:
Min 1Q Median 3Q Max
-2.4185 -0.4628 0.0811 0.5994 1.5145
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 22.25 4.716
Residual 34.49 5.872
Number of obs: 54, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 40.833 1.775 39.005 23.001 < 2e-16 ***
sessionBlock 2 -5.667 1.957 34.000 -2.895 0.00658 **
sessionBlock 3 -9.222 1.957 34.000 -4.711 4.05e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) sssnB2
sessinBlck2 -0.551
sessinBlck3 -0.551 0.500
=== Type II ANOVA (Chi-square) ===
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: correct_trials
Chisq Df Pr(>Chisq)
session 22.584 2 1.247e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
=== Estimated Marginal Means (Training) ===
session emmean SE df lower.CL upper.CL
Block 1 40.8 1.78 39 37.2 44.4
Block 2 35.2 1.78 39 31.6 38.8
Block 3 31.6 1.78 39 28.0 35.2
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
=== Pairwise Comparisons Between Training Blocks ===
contrast estimate SE df lower.CL upper.CL t.ratio p.value
Block 1 - Block 2 5.67 1.96 34 0.87 10.46 2.895 0.0176
Block 1 - Block 3 9.22 1.96 34 4.43 14.02 4.711 0.0001
Block 2 - Block 3 3.56 1.96 34 -1.24 8.35 1.816 0.1795
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 3 estimates
P value adjustment: tukey method for comparing a family of 3 estimates 
# --------- Step 3b: Test Blocks Only (Block 4–5) ---------
test_trials <- correct_trials_df %>%
filter(session %in% c("Block 4", "Block 5"))
if (nrow(test_trials) > 0) {
model_test <- lmer(correct_trials ~ session + (1 | subject), data = test_trials)
cat("\n\n=== LMM Summary: Test Blocks (Block 4–5) ===\n")
print(summary(model_test))
cat("\n=== Type II ANOVA (Chi-square) ===\n")
print(Anova(model_test, type = 2))
cat("\n=== Estimated Marginal Means (Test) ===\n")
emm_test <- emmeans(model_test, ~ session)
print(summary(emm_test))
cat("\n=== Pairwise Comparisons Between Test Blocks ===\n")
print(summary(pairs(emm_test), infer = c(TRUE, TRUE)))
# Plot for test blocks
plot_test <- test_trials %>%
group_by(session) %>%
summarise(
mean_corr_trials = mean(correct_trials),
sd_corr_trials = sd(correct_trials),
n = n()
)
ggplot(plot_test, aes(x = session, y = mean_corr_trials)) +
geom_point(size = 4, color = "darkred") +
geom_errorbar(aes(ymin = mean_corr_trials - sd_corr_trials,
ymax = mean_corr_trials + sd_corr_trials),
width = 0.2, color = "darkred") +
labs(
title = "Correct Trials – Test Blocks",
x = "Block",
y = "Correct Trials"
) +
theme_minimal(base_size = 13) +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank()
)
} else {
cat("⚠️ No valid test block data (Block 4–5)\n")
}
=== LMM Summary: Test Blocks (Block 4–5) ===
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: correct_trials ~ session + (1 | subject)
Data: test_trials
REML criterion at convergence: 227.6
Scaled residuals:
Min 1Q Median 3Q Max
-2.22385 -0.42259 0.01505 0.61002 1.34895
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 11.58 3.403
Residual 38.38 6.195
Number of obs: 35, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 36.278 1.666 31.311 21.775 < 2e-16 ***
sessionBlock 5 -8.865 2.102 16.286 -4.217 0.000632 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr)
sessinBlck5 -0.609
=== Type II ANOVA (Chi-square) ===
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: correct_trials
Chisq Df Pr(>Chisq)
session 17.782 1 2.478e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
=== Estimated Marginal Means (Test) ===
session emmean SE df lower.CL upper.CL
Block 4 36.3 1.67 31.4 32.9 39.7
Block 5 27.4 1.72 31.7 23.9 30.9
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
=== Pairwise Comparisons Between Test Blocks ===
contrast estimate SE df lower.CL upper.CL t.ratio p.value
Block 4 - Block 5 8.86 2.11 16.6 4.41 13.3 4.208 0.0006
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 
#4.2.2 correct trials per block divided into sequence lengths for test phase
# ====== Step 1: Prepare Full Accuracy-Filtered Data ======
df_acc <- df %>%
filter(
(session %in% c(1, 2, 3) & trial.acc >= 0.8) |
(session %in% c(4, 5) & trial.acc == 1)
) %>%
mutate(
subject = as.factor(subject),
session = factor(session, levels = 1:5, labels = paste("Block", 1:5))
)
# ====== Step 2: Add seq_length_trial variable ======
df_acc <- df_acc %>%
group_by(subject, session, trial) %>%
mutate(seq_length_trial = n_distinct(sub.trial.number)) %>%
ungroup() %>%
mutate(seq_length_trial = as.factor(seq_length_trial))
# ====== Step 3: Count correct trials per subject × session × sequence length ======
correct_trials_df <- df_acc %>%
distinct(subject, session, trial, seq_length_trial) %>%
count(subject, session, seq_length_trial, name = "correct_trials")
# ====== Step 4: Run LMM for Test Blocks Only (Block 4 & 5) ======
test_trials <- correct_trials_df %>%
filter(session %in% c("Block 4", "Block 5"))
if (nrow(test_trials) > 0) {
model_test <- lmer(correct_trials ~ session * seq_length_trial + (1 | subject), data = test_trials)
cat("\n=== LMM Summary: Correct Trials – Test Blocks ===\n")
print(summary(model_test))
cat("\n=== Type II ANOVA (Chi-square) ===\n")
print(Anova(model_test, type = 2))
cat("\n=== Estimated Marginal Means ===\n")
emm_test <- emmeans(model_test, ~ session * seq_length_trial)
print(summary(emm_test))
cat("\n=== Pairwise Comparisons (Session × Sequence Length) ===\n")
print(summary(pairs(emm_test), infer = c(TRUE, TRUE)))
# ====== Step 5: Plot Combined Accuracy by Sequence Length ======
plot_test <- test_trials %>%
group_by(session, seq_length_trial) %>%
summarise(
mean_corr_trials = mean(correct_trials),
sd_corr_trials = sd(correct_trials),
n = n(),
.groups = "drop"
)
ggplot(plot_test, aes(x = seq_length_trial, y = mean_corr_trials, color = session, group = session)) +
geom_point(size = 4, position = position_dodge(width = 0.4)) +
geom_errorbar(aes(ymin = mean_corr_trials - sd_corr_trials,
ymax = mean_corr_trials + sd_corr_trials),
width = 0.2, position = position_dodge(width = 0.4)) +
labs(
title = "Correct Trials – Test Blocks by Sequence Length",
x = "Sequence Length (Steps)",
y = "Correct Trials",
color = "Block"
) +
theme_minimal(base_size = 13) +
theme(panel.grid = element_blank())
} else {
cat("⚠️ No valid test block data (Block 4–5)\n")
}
=== LMM Summary: Correct Trials – Test Blocks ===
Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: correct_trials ~ session * seq_length_trial + (1 | subject)
Data: test_trials
REML criterion at convergence: 485.2
Scaled residuals:
Min 1Q Median 3Q Max
-2.07486 -0.52085 0.03835 0.54790 2.11017
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 2.327 1.526
Residual 5.631 2.373
Number of obs: 104, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 13.9444 0.6649 68.7570 20.971 < 2e-16
sessionBlock 5 -1.0262 0.8047 81.1751 -1.275 0.20581
seq_length_trial12 -1.5000 0.7910 80.6262 -1.896 0.06150
seq_length_trial18 -4.0556 0.7910 80.6262 -5.127 1.98e-06
sessionBlock 5:seq_length_trial12 -3.4412 1.1350 80.6262 -3.032 0.00327
sessionBlock 5:seq_length_trial18 -1.8478 1.1453 80.7892 -1.613 0.11056
(Intercept) ***
sessionBlock 5
seq_length_trial12 .
seq_length_trial18 ***
sessionBlock 5:seq_length_trial12 **
sessionBlock 5:seq_length_trial18
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) sssnB5 sq__12 sq__18 sB5:__12
sessinBlck5 -0.585
sq_lngth_12 -0.595 0.492
sq_lngth_18 -0.595 0.492 0.500
sssnB5:__12 0.415 -0.705 -0.697 -0.348
sssnB5:__18 0.411 -0.699 -0.345 -0.691 0.496
=== Type II ANOVA (Chi-square) ===
Analysis of Deviance Table (Type II Wald chisquare tests)
Response: correct_trials
Chisq Df Pr(>Chisq)
session 35.2349 1 2.922e-09 ***
seq_length_trial 77.1714 2 < 2.2e-16 ***
session:seq_length_trial 9.2091 2 0.01001 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
=== Estimated Marginal Means ===
session seq_length_trial emmean SE df lower.CL upper.CL
Block 4 6 13.94 0.665 69.4 12.62 15.27
Block 5 6 12.92 0.681 71.9 11.56 14.28
Block 4 12 12.44 0.665 69.4 11.12 13.77
Block 5 12 7.98 0.681 71.9 6.62 9.34
Block 4 18 9.89 0.665 69.4 8.56 11.22
Block 5 18 7.01 0.699 74.7 5.62 8.41
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
=== Pairwise Comparisons (Session × Sequence Length) ===
contrast estimate SE df
Block 4 seq_length_trial6 - Block 5 seq_length_trial6 1.026 0.805 81.6
Block 4 seq_length_trial6 - Block 4 seq_length_trial12 1.500 0.791 81.0
Block 4 seq_length_trial6 - Block 5 seq_length_trial12 5.967 0.805 81.6
Block 4 seq_length_trial6 - Block 4 seq_length_trial18 4.056 0.791 81.0
Block 4 seq_length_trial6 - Block 5 seq_length_trial18 6.930 0.820 81.9
Block 5 seq_length_trial6 - Block 4 seq_length_trial12 0.474 0.805 81.6
Block 5 seq_length_trial6 - Block 5 seq_length_trial12 4.941 0.814 81.0
Block 5 seq_length_trial6 - Block 4 seq_length_trial18 3.029 0.805 81.6
Block 5 seq_length_trial6 - Block 5 seq_length_trial18 5.903 0.828 81.4
Block 4 seq_length_trial12 - Block 5 seq_length_trial12 4.467 0.805 81.6
Block 4 seq_length_trial12 - Block 4 seq_length_trial18 2.556 0.791 81.0
Block 4 seq_length_trial12 - Block 5 seq_length_trial18 5.430 0.820 81.9
Block 5 seq_length_trial12 - Block 4 seq_length_trial18 -1.912 0.805 81.6
Block 5 seq_length_trial12 - Block 5 seq_length_trial18 0.962 0.828 81.4
Block 4 seq_length_trial18 - Block 5 seq_length_trial18 2.874 0.820 81.9
lower.CL upper.CL t.ratio p.value
-1.323 3.376 1.275 0.7977
-0.809 3.809 1.896 0.4119
3.618 8.317 7.413 <.0001
1.747 6.364 5.127 <.0001
4.538 9.322 8.454 <.0001
-1.876 2.823 0.589 0.9915
2.565 7.317 6.071 <.0001
0.680 5.379 3.763 0.0041
3.485 8.321 7.126 <.0001
2.118 6.817 5.550 <.0001
0.247 4.864 3.231 0.0213
3.038 7.822 6.624 <.0001
-4.261 0.437 -2.375 0.1773
-1.456 3.380 1.161 0.8537
0.482 5.266 3.506 0.0093
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95
Conf-level adjustment: tukey method for comparing a family of 6 estimates
P value adjustment: tukey method for comparing a family of 6 estimates 
#4.3 concatenation training blocks
RT <- read.csv("/Users/can/Documents/Uni/Thesis/Data/E-Prime/all_excluded2.csv", sep = ";")
# Filter only response procedure entries, remove subject 12, convert to numeric
RTR <- RT %>%
filter(procedure == "responsprocedure") %>%
mutate(
feedback.ACC = as.numeric(feedback.ACC),
feedback.RT = as.numeric(feedback.RT)
) %>%
filter(subject != 12)
# -------- Assign trial numbers dynamically --------
RTR <- RTR %>%
group_by(subject, session) %>%
mutate(trial = cumsum(sub.trial.number == 1)) %>%
ungroup()
# -------- Compute trial-level accuracy and mean RT --------
df <- RTR %>%
group_by(subject, session, trial) %>%
mutate(
trial.acc = sum(feedback.ACC, na.rm = TRUE) / n(),
trial.RT = mean(feedback.RT, na.rm = TRUE)
) %>%
ungroup()
# -------- Filter only trials with 80% accuracy --------
df_acc <- df %>%
filter(
(session %in% c(1, 2, 3) & trial.acc >= 0.8) |
(session %in% c(4, 5) & trial.acc == 1)
) %>%
mutate(
subject = as.factor(subject),
sub.trial.number = as.factor(sub.trial.number),
session = as.factor(session)
)
# -------- Add corr_trials per subject --------
df_acc5 <- df_acc %>%
distinct(subject, trial, session) %>%
count(subject, name = "corr_trials")
df_acc <- left_join(df_acc, df_acc5, by = "subject")
df_acc <- df_acc %>% select(-feedback.CRESP, -feedback.RESP, -cue.OnsetDelay, -cue.OnsetTime)# Ensure session is treated as factor again
df_acc$session <- factor(df_acc$session)
# -------- Block 1: 6-step sequences --------
df_B1_steps <- df_acc %>% filter(session == 1)
model_B1 <- lmer(feedback.RT ~ sub.trial.number + (1 | subject), data = df_B1_steps)
cat("=== Block 1: Stepwise RT Model Summary ===\n")=== Block 1: Stepwise RT Model Summary ===print(summary(model_B1))Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ sub.trial.number + (1 | subject)
Data: df_B1_steps
REML criterion at convergence: 63902.2
Scaled residuals:
Min 1Q Median 3Q Max
-4.2550 -0.4120 -0.1512 0.2137 28.3250
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 66052 257.0
Residual 114010 337.7
Number of obs: 4410, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 752.57 61.85 18.20 12.17 3.52e-10 ***
sub.trial.number2 -296.25 17.61 4386.99 -16.82 < 2e-16 ***
sub.trial.number3 -318.39 17.61 4386.99 -18.08 < 2e-16 ***
sub.trial.number4 -307.24 17.61 4386.99 -17.44 < 2e-16 ***
sub.trial.number5 -288.44 17.61 4386.99 -16.38 < 2e-16 ***
sub.trial.number6 -280.70 17.61 4386.99 -15.94 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) sb.t.2 sb.t.3 sb.t.4 sb.t.5
sb.trl.nmb2 -0.142
sb.trl.nmb3 -0.142 0.500
sb.trl.nmb4 -0.142 0.500 0.500
sb.trl.nmb5 -0.142 0.500 0.500 0.500
sb.trl.nmb6 -0.142 0.500 0.500 0.500 0.500cat("\n=== Chi-square ANOVA (Block 1) ===\n")
=== Chi-square ANOVA (Block 1) ===print(Anova(model_B1, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 483.51 5 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_B1 <- emmeans(model_B1, ~ sub.trial.number)
cat("\n=== Estimated Marginal Means per Step (Block 1) ===\n")
=== Estimated Marginal Means per Step (Block 1) ===print(summary(emm_B1)) sub.trial.number emmean SE df lower.CL upper.CL
1 753 61.8 18.2 623 882
2 456 61.8 18.2 326 586
3 434 61.8 18.2 304 564
4 445 61.8 18.2 315 575
5 464 61.8 18.2 334 594
6 472 61.8 18.2 342 602
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 step_comparisons_B1 <- contrast(emm_B1, method = "pairwise", adjust = "none")
cat("\n=== Stepwise Pairwise Comparisons (Block 1) ===\n")
=== Stepwise Pairwise Comparisons (Block 1) ===print(summary(step_comparisons_B1, infer = c(TRUE, TRUE))) contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 296.25 17.6 4387 261.7 330.78
sub.trial.number1 - sub.trial.number3 318.39 17.6 4387 283.9 352.92
sub.trial.number1 - sub.trial.number4 307.24 17.6 4387 272.7 341.77
sub.trial.number1 - sub.trial.number5 288.44 17.6 4387 253.9 322.97
sub.trial.number1 - sub.trial.number6 280.70 17.6 4387 246.2 315.23
sub.trial.number2 - sub.trial.number3 22.14 17.6 4387 -12.4 56.67
sub.trial.number2 - sub.trial.number4 10.99 17.6 4387 -23.5 45.52
sub.trial.number2 - sub.trial.number5 -7.81 17.6 4387 -42.3 26.72
sub.trial.number2 - sub.trial.number6 -15.55 17.6 4387 -50.1 18.98
sub.trial.number3 - sub.trial.number4 -11.15 17.6 4387 -45.7 23.38
sub.trial.number3 - sub.trial.number5 -29.95 17.6 4387 -64.5 4.58
sub.trial.number3 - sub.trial.number6 -37.69 17.6 4387 -72.2 -3.16
sub.trial.number4 - sub.trial.number5 -18.80 17.6 4387 -53.3 15.73
sub.trial.number4 - sub.trial.number6 -26.54 17.6 4387 -61.1 7.99
sub.trial.number5 - sub.trial.number6 -7.74 17.6 4387 -42.3 26.79
t.ratio p.value
16.820 <.0001
18.077 <.0001
17.444 <.0001
16.376 <.0001
15.937 <.0001
1.257 0.2088
0.624 0.5326
-0.443 0.6575
-0.883 0.3774
-0.633 0.5267
-1.701 0.0891
-2.140 0.0324
-1.067 0.2858
-1.507 0.1319
-0.439 0.6604
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 # -------- Block 2: 12-step sequences --------
df_B2_steps <- df_acc %>% filter(session == 2)
model_B2 <- lmer(feedback.RT ~ sub.trial.number + (1 | subject), data = df_B2_steps)
cat("\n\n=== Block 2: Stepwise RT Model Summary ===\n")
=== Block 2: Stepwise RT Model Summary ===print(summary(model_B2))Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ sub.trial.number + (1 | subject)
Data: df_B2_steps
REML criterion at convergence: 107721.7
Scaled residuals:
Min 1Q Median 3Q Max
-3.5089 -0.4615 -0.1869 0.1857 12.1535
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 61848 248.7
Residual 84366 290.5
Number of obs: 7596, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 763.10 59.75 18.17 12.77 1.62e-10 ***
sub.trial.number2 -288.81 16.33 7566.95 -17.69 < 2e-16 ***
sub.trial.number3 -318.54 16.33 7566.95 -19.51 < 2e-16 ***
sub.trial.number4 -349.02 16.33 7566.95 -21.38 < 2e-16 ***
sub.trial.number5 -238.88 16.33 7566.95 -14.63 < 2e-16 ***
sub.trial.number6 -276.63 16.33 7566.95 -16.94 < 2e-16 ***
sub.trial.number7 -230.88 16.33 7566.95 -14.14 < 2e-16 ***
sub.trial.number8 -262.55 16.33 7566.95 -16.08 < 2e-16 ***
sub.trial.number9 -238.26 16.33 7566.95 -14.59 < 2e-16 ***
sub.trial.number10 -265.18 16.33 7566.95 -16.24 < 2e-16 ***
sub.trial.number11 -302.70 16.33 7566.95 -18.54 < 2e-16 ***
sub.trial.number12 -281.80 16.33 7566.95 -17.26 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) sb.t.2 sb.t.3 sb.t.4 sb.t.5 sb.t.6 sb.t.7 sb.t.8 sb.t.9
sb.trl.nmb2 -0.137
sb.trl.nmb3 -0.137 0.500
sb.trl.nmb4 -0.137 0.500 0.500
sb.trl.nmb5 -0.137 0.500 0.500 0.500
sb.trl.nmb6 -0.137 0.500 0.500 0.500 0.500
sb.trl.nmb7 -0.137 0.500 0.500 0.500 0.500 0.500
sb.trl.nmb8 -0.137 0.500 0.500 0.500 0.500 0.500 0.500
sb.trl.nmb9 -0.137 0.500 0.500 0.500 0.500 0.500 0.500 0.500
sb.trl.nm10 -0.137 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
sb.trl.nm11 -0.137 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
sb.trl.nm12 -0.137 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
sb..10 sb..11
sb.trl.nmb2
sb.trl.nmb3
sb.trl.nmb4
sb.trl.nmb5
sb.trl.nmb6
sb.trl.nmb7
sb.trl.nmb8
sb.trl.nmb9
sb.trl.nm10
sb.trl.nm11 0.500
sb.trl.nm12 0.500 0.500cat("\n=== Chi-square ANOVA (Block 2) ===\n")
=== Chi-square ANOVA (Block 2) ===print(Anova(model_B2, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 628.64 11 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_B2 <- emmeans(model_B2, ~ sub.trial.number)
cat("\n=== Estimated Marginal Means per Step (Block 2) ===\n")
=== Estimated Marginal Means per Step (Block 2) ===print(summary(emm_B2)) sub.trial.number emmean SE df lower.CL upper.CL
1 763 59.7 18.2 638 889
2 474 59.7 18.2 349 600
3 445 59.7 18.2 319 570
4 414 59.7 18.2 289 539
5 524 59.7 18.2 399 650
6 486 59.7 18.2 361 612
7 532 59.7 18.2 407 658
8 501 59.7 18.2 375 626
9 525 59.7 18.2 399 650
10 498 59.7 18.2 373 623
11 460 59.7 18.2 335 586
12 481 59.7 18.2 356 607
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 step_comparisons_B2 <- contrast(emm_B2, method = "pairwise", adjust = "none")
cat("\n=== Stepwise Pairwise Comparisons (Block 2) ===\n")
=== Stepwise Pairwise Comparisons (Block 2) ===print(summary(step_comparisons_B2, infer = c(TRUE, TRUE))) contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 288.807 16.3 7567 256.803 320.81
sub.trial.number1 - sub.trial.number3 318.537 16.3 7567 286.532 350.54
sub.trial.number1 - sub.trial.number4 349.021 16.3 7567 317.016 381.03
sub.trial.number1 - sub.trial.number5 238.880 16.3 7567 206.875 270.88
sub.trial.number1 - sub.trial.number6 276.632 16.3 7567 244.627 308.64
sub.trial.number1 - sub.trial.number7 230.885 16.3 7567 198.880 262.89
sub.trial.number1 - sub.trial.number8 262.545 16.3 7567 230.540 294.55
sub.trial.number1 - sub.trial.number9 238.256 16.3 7567 206.251 270.26
sub.trial.number1 - sub.trial.number10 265.180 16.3 7567 233.175 297.18
sub.trial.number1 - sub.trial.number11 302.703 16.3 7567 270.698 334.71
sub.trial.number1 - sub.trial.number12 281.799 16.3 7567 249.795 313.80
sub.trial.number2 - sub.trial.number3 29.730 16.3 7567 -2.275 61.73
sub.trial.number2 - sub.trial.number4 60.213 16.3 7567 28.209 92.22
sub.trial.number2 - sub.trial.number5 -49.927 16.3 7567 -81.932 -17.92
sub.trial.number2 - sub.trial.number6 -12.175 16.3 7567 -44.180 19.83
sub.trial.number2 - sub.trial.number7 -57.923 16.3 7567 -89.927 -25.92
sub.trial.number2 - sub.trial.number8 -26.262 16.3 7567 -58.267 5.74
sub.trial.number2 - sub.trial.number9 -50.551 16.3 7567 -82.556 -18.55
sub.trial.number2 - sub.trial.number10 -23.627 16.3 7567 -55.632 8.38
sub.trial.number2 - sub.trial.number11 13.896 16.3 7567 -18.109 45.90
sub.trial.number2 - sub.trial.number12 -7.008 16.3 7567 -39.013 25.00
sub.trial.number3 - sub.trial.number4 30.483 16.3 7567 -1.521 62.49
sub.trial.number3 - sub.trial.number5 -79.657 16.3 7567 -111.662 -47.65
sub.trial.number3 - sub.trial.number6 -41.905 16.3 7567 -73.910 -9.90
sub.trial.number3 - sub.trial.number7 -87.652 16.3 7567 -119.657 -55.65
sub.trial.number3 - sub.trial.number8 -55.992 16.3 7567 -87.997 -23.99
sub.trial.number3 - sub.trial.number9 -80.281 16.3 7567 -112.286 -48.28
sub.trial.number3 - sub.trial.number10 -53.357 16.3 7567 -85.362 -21.35
sub.trial.number3 - sub.trial.number11 -15.834 16.3 7567 -47.839 16.17
sub.trial.number3 - sub.trial.number12 -36.738 16.3 7567 -68.743 -4.73
sub.trial.number4 - sub.trial.number5 -110.141 16.3 7567 -142.145 -78.14
sub.trial.number4 - sub.trial.number6 -72.389 16.3 7567 -104.393 -40.38
sub.trial.number4 - sub.trial.number7 -118.136 16.3 7567 -150.141 -86.13
sub.trial.number4 - sub.trial.number8 -86.475 16.3 7567 -118.480 -54.47
sub.trial.number4 - sub.trial.number9 -110.765 16.3 7567 -142.769 -78.76
sub.trial.number4 - sub.trial.number10 -83.840 16.3 7567 -115.845 -51.84
sub.trial.number4 - sub.trial.number11 -46.318 16.3 7567 -78.322 -14.31
sub.trial.number4 - sub.trial.number12 -67.221 16.3 7567 -99.226 -35.22
sub.trial.number5 - sub.trial.number6 37.752 16.3 7567 5.747 69.76
sub.trial.number5 - sub.trial.number7 -7.995 16.3 7567 -40.000 24.01
sub.trial.number5 - sub.trial.number8 23.665 16.3 7567 -8.340 55.67
sub.trial.number5 - sub.trial.number9 -0.624 16.3 7567 -32.629 31.38
sub.trial.number5 - sub.trial.number10 26.300 16.3 7567 -5.705 58.30
sub.trial.number5 - sub.trial.number11 63.823 16.3 7567 31.818 95.83
sub.trial.number5 - sub.trial.number12 42.919 16.3 7567 10.915 74.92
sub.trial.number6 - sub.trial.number7 -45.747 16.3 7567 -77.752 -13.74
sub.trial.number6 - sub.trial.number8 -14.087 16.3 7567 -46.092 17.92
sub.trial.number6 - sub.trial.number9 -38.376 16.3 7567 -70.381 -6.37
sub.trial.number6 - sub.trial.number10 -11.452 16.3 7567 -43.456 20.55
sub.trial.number6 - sub.trial.number11 26.071 16.3 7567 -5.934 58.08
sub.trial.number6 - sub.trial.number12 5.168 16.3 7567 -26.837 37.17
sub.trial.number7 - sub.trial.number8 31.660 16.3 7567 -0.344 63.66
sub.trial.number7 - sub.trial.number9 7.371 16.3 7567 -24.633 39.38
sub.trial.number7 - sub.trial.number10 34.295 16.3 7567 2.291 66.30
sub.trial.number7 - sub.trial.number11 71.818 16.3 7567 39.814 103.82
sub.trial.number7 - sub.trial.number12 50.915 16.3 7567 18.910 82.92
sub.trial.number8 - sub.trial.number9 -24.289 16.3 7567 -56.294 7.72
sub.trial.number8 - sub.trial.number10 2.635 16.3 7567 -29.370 34.64
sub.trial.number8 - sub.trial.number11 40.158 16.3 7567 8.153 72.16
sub.trial.number8 - sub.trial.number12 19.254 16.3 7567 -12.750 51.26
sub.trial.number9 - sub.trial.number10 26.924 16.3 7567 -5.080 58.93
sub.trial.number9 - sub.trial.number11 64.447 16.3 7567 32.442 96.45
sub.trial.number9 - sub.trial.number12 43.543 16.3 7567 11.539 75.55
sub.trial.number10 - sub.trial.number11 37.523 16.3 7567 5.518 69.53
sub.trial.number10 - sub.trial.number12 16.619 16.3 7567 -15.385 48.62
sub.trial.number11 - sub.trial.number12 -20.904 16.3 7567 -52.908 11.10
t.ratio p.value
17.689 <.0001
19.510 <.0001
21.377 <.0001
14.631 <.0001
16.944 <.0001
14.142 <.0001
16.081 <.0001
14.593 <.0001
16.242 <.0001
18.540 <.0001
17.260 <.0001
1.821 0.0687
3.688 0.0002
-3.058 0.0022
-0.746 0.4558
-3.548 0.0004
-1.609 0.1078
-3.096 0.0020
-1.447 0.1479
0.851 0.3947
-0.429 0.6678
1.867 0.0619
-4.879 <.0001
-2.567 0.0103
-5.369 <.0001
-3.429 0.0006
-4.917 <.0001
-3.268 0.0011
-0.970 0.3322
-2.250 0.0245
-6.746 <.0001
-4.434 <.0001
-7.236 <.0001
-5.297 <.0001
-6.784 <.0001
-5.135 <.0001
-2.837 0.0046
-4.117 <.0001
2.312 0.0208
-0.490 0.6244
1.449 0.1472
-0.038 0.9695
1.611 0.1072
3.909 0.0001
2.629 0.0086
-2.802 0.0051
-0.863 0.3883
-2.351 0.0188
-0.701 0.4831
1.597 0.1103
0.317 0.7516
1.939 0.0525
0.451 0.6517
2.101 0.0357
4.399 <.0001
3.119 0.0018
-1.488 0.1369
0.161 0.8718
2.460 0.0139
1.179 0.2383
1.649 0.0992
3.947 0.0001
2.667 0.0077
2.298 0.0216
1.018 0.3087
-1.280 0.2005
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 # -------- Block 3: 18-step sequences --------
df_B3_steps <- df_acc %>% filter(session == 3)
model_B3 <- lmer(feedback.RT ~ sub.trial.number + (1 | subject), data = df_B3_steps)
cat("\n\n=== Block 3: Stepwise RT Model Summary ===\n")
=== Block 3: Stepwise RT Model Summary ===print(summary(model_B3))Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ sub.trial.number + (1 | subject)
Data: df_B3_steps
REML criterion at convergence: 148515.2
Scaled residuals:
Min 1Q Median 3Q Max
-2.6869 -0.4308 -0.1755 0.1673 29.5780
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 41978 204.9
Residual 116815 341.8
Number of obs: 10242, groups: subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 818.91 50.39 19.89 16.251 6.02e-13 ***
sub.trial.number2 -325.33 20.26 10206.97 -16.055 < 2e-16 ***
sub.trial.number3 -352.76 20.26 10206.97 -17.409 < 2e-16 ***
sub.trial.number4 -371.41 20.26 10206.97 -18.329 < 2e-16 ***
sub.trial.number5 -266.14 20.26 10206.97 -13.134 < 2e-16 ***
sub.trial.number6 -287.47 20.26 10206.97 -14.187 < 2e-16 ***
sub.trial.number7 -293.04 20.26 10206.97 -14.462 < 2e-16 ***
sub.trial.number8 -308.28 20.26 10206.97 -15.214 < 2e-16 ***
sub.trial.number9 -259.58 20.26 10206.97 -12.810 < 2e-16 ***
sub.trial.number10 -246.68 20.26 10206.97 -12.174 < 2e-16 ***
sub.trial.number11 -278.51 20.26 10206.97 -13.745 < 2e-16 ***
sub.trial.number12 -339.40 20.26 10206.97 -16.749 < 2e-16 ***
sub.trial.number13 -92.33 20.26 10206.97 -4.556 5.27e-06 ***
sub.trial.number14 -234.44 20.26 10206.97 -11.570 < 2e-16 ***
sub.trial.number15 -284.38 20.26 10206.97 -14.034 < 2e-16 ***
sub.trial.number16 -339.54 20.26 10206.97 -16.756 < 2e-16 ***
sub.trial.number17 -299.99 20.26 10206.97 -14.805 < 2e-16 ***
sub.trial.number18 -285.92 20.26 10206.97 -14.110 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation matrix not shown by default, as p = 18 > 12.
Use print(summary(model_B3), correlation=TRUE) or
vcov(summary(model_B3)) if you need itcat("\n=== Chi-square ANOVA (Block 3) ===\n")
=== Chi-square ANOVA (Block 3) ===print(Anova(model_B3, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 681.83 17 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_B3 <- emmeans(model_B3, ~ sub.trial.number)
cat("\n=== Estimated Marginal Means per Step (Block 3) ===\n")
=== Estimated Marginal Means per Step (Block 3) ===print(summary(emm_B3)) sub.trial.number emmean SE df lower.CL upper.CL
1 819 50.4 19.9 714 924
2 494 50.4 19.9 388 599
3 466 50.4 19.9 361 571
4 447 50.4 19.9 342 553
5 553 50.4 19.9 448 658
6 531 50.4 19.9 426 637
7 526 50.4 19.9 421 631
8 511 50.4 19.9 405 616
9 559 50.4 19.9 454 664
10 572 50.4 19.9 467 677
11 540 50.4 19.9 435 646
12 480 50.4 19.9 374 585
13 727 50.4 19.9 621 832
14 584 50.4 19.9 479 690
15 535 50.4 19.9 429 640
16 479 50.4 19.9 374 585
17 519 50.4 19.9 414 624
18 533 50.4 19.9 428 638
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 step_comparisons_B3 <- contrast(emm_B3, method = "pairwise", adjust = "none")
cat("\n=== Stepwise Pairwise Comparisons (Block 3) ===\n")
=== Stepwise Pairwise Comparisons (Block 3) ===print(summary(step_comparisons_B3, infer = c(TRUE, TRUE))) contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 325.330 20.3 10207 285.611 365.050
sub.trial.number1 - sub.trial.number3 352.761 20.3 10207 313.041 392.481
sub.trial.number1 - sub.trial.number4 371.413 20.3 10207 331.693 411.133
sub.trial.number1 - sub.trial.number5 266.135 20.3 10207 226.416 305.855
sub.trial.number1 - sub.trial.number6 287.473 20.3 10207 247.753 327.193
sub.trial.number1 - sub.trial.number7 293.037 20.3 10207 253.317 332.757
sub.trial.number1 - sub.trial.number8 308.276 20.3 10207 268.556 347.996
sub.trial.number1 - sub.trial.number9 259.576 20.3 10207 219.857 299.296
sub.trial.number1 - sub.trial.number10 246.677 20.3 10207 206.957 286.397
sub.trial.number1 - sub.trial.number11 278.510 20.3 10207 238.790 318.229
sub.trial.number1 - sub.trial.number12 339.397 20.3 10207 299.677 379.117
sub.trial.number1 - sub.trial.number13 92.325 20.3 10207 52.605 132.045
sub.trial.number1 - sub.trial.number14 234.438 20.3 10207 194.718 274.158
sub.trial.number1 - sub.trial.number15 284.378 20.3 10207 244.658 324.098
sub.trial.number1 - sub.trial.number16 339.539 20.3 10207 299.820 379.259
sub.trial.number1 - sub.trial.number17 299.988 20.3 10207 260.268 339.708
sub.trial.number1 - sub.trial.number18 285.919 20.3 10207 246.199 325.639
sub.trial.number2 - sub.trial.number3 27.431 20.3 10207 -12.289 67.150
sub.trial.number2 - sub.trial.number4 46.083 20.3 10207 6.363 85.802
sub.trial.number2 - sub.trial.number5 -59.195 20.3 10207 -98.915 -19.475
sub.trial.number2 - sub.trial.number6 -37.858 20.3 10207 -77.578 1.862
sub.trial.number2 - sub.trial.number7 -32.294 20.3 10207 -72.013 7.426
sub.trial.number2 - sub.trial.number8 -17.055 20.3 10207 -56.774 22.665
sub.trial.number2 - sub.trial.number9 -65.754 20.3 10207 -105.474 -26.034
sub.trial.number2 - sub.trial.number10 -78.654 20.3 10207 -118.374 -38.934
sub.trial.number2 - sub.trial.number11 -46.821 20.3 10207 -86.541 -7.101
sub.trial.number2 - sub.trial.number12 14.067 20.3 10207 -25.653 53.787
sub.trial.number2 - sub.trial.number13 -233.005 20.3 10207 -272.725 -193.285
sub.trial.number2 - sub.trial.number14 -90.893 20.3 10207 -130.613 -51.173
sub.trial.number2 - sub.trial.number15 -40.953 20.3 10207 -80.672 -1.233
sub.trial.number2 - sub.trial.number16 14.209 20.3 10207 -25.511 53.929
sub.trial.number2 - sub.trial.number17 -25.343 20.3 10207 -65.063 14.377
sub.trial.number2 - sub.trial.number18 -39.411 20.3 10207 -79.131 0.309
sub.trial.number3 - sub.trial.number4 18.652 20.3 10207 -21.068 58.372
sub.trial.number3 - sub.trial.number5 -86.626 20.3 10207 -126.346 -46.906
sub.trial.number3 - sub.trial.number6 -65.288 20.3 10207 -105.008 -25.568
sub.trial.number3 - sub.trial.number7 -59.724 20.3 10207 -99.444 -20.004
sub.trial.number3 - sub.trial.number8 -44.485 20.3 10207 -84.205 -4.765
sub.trial.number3 - sub.trial.number9 -93.184 20.3 10207 -132.904 -53.465
sub.trial.number3 - sub.trial.number10 -106.084 20.3 10207 -145.804 -66.365
sub.trial.number3 - sub.trial.number11 -74.251 20.3 10207 -113.971 -34.532
sub.trial.number3 - sub.trial.number12 -13.364 20.3 10207 -53.084 26.356
sub.trial.number3 - sub.trial.number13 -260.436 20.3 10207 -300.156 -220.716
sub.trial.number3 - sub.trial.number14 -118.323 20.3 10207 -158.043 -78.603
sub.trial.number3 - sub.trial.number15 -68.383 20.3 10207 -108.103 -28.663
sub.trial.number3 - sub.trial.number16 -13.221 20.3 10207 -52.941 26.498
sub.trial.number3 - sub.trial.number17 -52.773 20.3 10207 -92.493 -13.053
sub.trial.number3 - sub.trial.number18 -66.842 20.3 10207 -106.562 -27.122
sub.trial.number4 - sub.trial.number5 -105.278 20.3 10207 -144.998 -65.558
sub.trial.number4 - sub.trial.number6 -83.940 20.3 10207 -123.660 -44.220
sub.trial.number4 - sub.trial.number7 -78.376 20.3 10207 -118.096 -38.656
sub.trial.number4 - sub.trial.number8 -63.137 20.3 10207 -102.857 -23.417
sub.trial.number4 - sub.trial.number9 -111.837 20.3 10207 -151.556 -72.117
sub.trial.number4 - sub.trial.number10 -124.736 20.3 10207 -164.456 -85.016
sub.trial.number4 - sub.trial.number11 -92.903 20.3 10207 -132.623 -53.184
sub.trial.number4 - sub.trial.number12 -32.016 20.3 10207 -71.736 7.704
sub.trial.number4 - sub.trial.number13 -279.088 20.3 10207 -318.808 -239.368
sub.trial.number4 - sub.trial.number14 -136.975 20.3 10207 -176.695 -97.255
sub.trial.number4 - sub.trial.number15 -87.035 20.3 10207 -126.755 -47.315
sub.trial.number4 - sub.trial.number16 -31.873 20.3 10207 -71.593 7.846
sub.trial.number4 - sub.trial.number17 -71.425 20.3 10207 -111.145 -31.705
sub.trial.number4 - sub.trial.number18 -85.494 20.3 10207 -125.214 -45.774
sub.trial.number5 - sub.trial.number6 21.337 20.3 10207 -18.382 61.057
sub.trial.number5 - sub.trial.number7 26.902 20.3 10207 -12.818 66.621
sub.trial.number5 - sub.trial.number8 42.141 20.3 10207 2.421 81.861
sub.trial.number5 - sub.trial.number9 -6.559 20.3 10207 -46.279 33.161
sub.trial.number5 - sub.trial.number10 -19.459 20.3 10207 -59.179 20.261
sub.trial.number5 - sub.trial.number11 12.374 20.3 10207 -27.346 52.094
sub.trial.number5 - sub.trial.number12 73.262 20.3 10207 33.542 112.982
sub.trial.number5 - sub.trial.number13 -173.810 20.3 10207 -213.530 -134.090
sub.trial.number5 - sub.trial.number14 -31.698 20.3 10207 -71.418 8.022
sub.trial.number5 - sub.trial.number15 18.242 20.3 10207 -21.477 57.962
sub.trial.number5 - sub.trial.number16 73.404 20.3 10207 33.684 113.124
sub.trial.number5 - sub.trial.number17 33.852 20.3 10207 -5.867 73.572
sub.trial.number5 - sub.trial.number18 19.784 20.3 10207 -19.936 59.504
sub.trial.number6 - sub.trial.number7 5.564 20.3 10207 -34.156 45.284
sub.trial.number6 - sub.trial.number8 20.803 20.3 10207 -18.917 60.523
sub.trial.number6 - sub.trial.number9 -27.896 20.3 10207 -67.616 11.824
sub.trial.number6 - sub.trial.number10 -40.796 20.3 10207 -80.516 -1.076
sub.trial.number6 - sub.trial.number11 -8.963 20.3 10207 -48.683 30.757
sub.trial.number6 - sub.trial.number12 51.924 20.3 10207 12.205 91.644
sub.trial.number6 - sub.trial.number13 -195.148 20.3 10207 -234.868 -155.428
sub.trial.number6 - sub.trial.number14 -53.035 20.3 10207 -92.755 -13.315
sub.trial.number6 - sub.trial.number15 -3.095 20.3 10207 -42.815 36.625
sub.trial.number6 - sub.trial.number16 52.067 20.3 10207 12.347 91.787
sub.trial.number6 - sub.trial.number17 12.515 20.3 10207 -27.205 52.235
sub.trial.number6 - sub.trial.number18 -1.554 20.3 10207 -41.273 38.166
sub.trial.number7 - sub.trial.number8 15.239 20.3 10207 -24.481 54.959
sub.trial.number7 - sub.trial.number9 -33.461 20.3 10207 -73.180 6.259
sub.trial.number7 - sub.trial.number10 -46.360 20.3 10207 -86.080 -6.640
sub.trial.number7 - sub.trial.number11 -14.527 20.3 10207 -54.247 25.193
sub.trial.number7 - sub.trial.number12 46.360 20.3 10207 6.640 86.080
sub.trial.number7 - sub.trial.number13 -200.712 20.3 10207 -240.432 -160.992
sub.trial.number7 - sub.trial.number14 -58.599 20.3 10207 -98.319 -18.879
sub.trial.number7 - sub.trial.number15 -8.659 20.3 10207 -48.379 31.061
sub.trial.number7 - sub.trial.number16 46.503 20.3 10207 6.783 86.222
sub.trial.number7 - sub.trial.number17 6.951 20.3 10207 -32.769 46.671
sub.trial.number7 - sub.trial.number18 -7.118 20.3 10207 -46.838 32.602
sub.trial.number8 - sub.trial.number9 -48.700 20.3 10207 -88.419 -8.980
sub.trial.number8 - sub.trial.number10 -61.599 20.3 10207 -101.319 -21.879
sub.trial.number8 - sub.trial.number11 -29.766 20.3 10207 -69.486 9.954
sub.trial.number8 - sub.trial.number12 31.121 20.3 10207 -8.599 70.841
sub.trial.number8 - sub.trial.number13 -215.951 20.3 10207 -255.671 -176.231
sub.trial.number8 - sub.trial.number14 -73.838 20.3 10207 -113.558 -34.118
sub.trial.number8 - sub.trial.number15 -23.898 20.3 10207 -63.618 15.822
sub.trial.number8 - sub.trial.number16 31.264 20.3 10207 -8.456 70.984
sub.trial.number8 - sub.trial.number17 -8.288 20.3 10207 -48.008 31.432
sub.trial.number8 - sub.trial.number18 -22.357 20.3 10207 -62.077 17.363
sub.trial.number9 - sub.trial.number10 -12.900 20.3 10207 -52.620 26.820
sub.trial.number9 - sub.trial.number11 18.933 20.3 10207 -20.787 58.653
sub.trial.number9 - sub.trial.number12 79.821 20.3 10207 40.101 119.541
sub.trial.number9 - sub.trial.number13 -167.251 20.3 10207 -206.971 -127.531
sub.trial.number9 - sub.trial.number14 -25.139 20.3 10207 -64.859 14.581
sub.trial.number9 - sub.trial.number15 24.801 20.3 10207 -14.918 64.521
sub.trial.number9 - sub.trial.number16 79.963 20.3 10207 40.243 119.683
sub.trial.number9 - sub.trial.number17 40.411 20.3 10207 0.691 80.131
sub.trial.number9 - sub.trial.number18 26.343 20.3 10207 -13.377 66.063
sub.trial.number10 - sub.trial.number11 31.833 20.3 10207 -7.887 71.553
sub.trial.number10 - sub.trial.number12 92.721 20.3 10207 53.001 132.440
sub.trial.number10 - sub.trial.number13 -154.351 20.3 10207 -194.071 -114.632
sub.trial.number10 - sub.trial.number14 -12.239 20.3 10207 -51.959 27.481
sub.trial.number10 - sub.trial.number15 37.701 20.3 10207 -2.019 77.421
sub.trial.number10 - sub.trial.number16 92.863 20.3 10207 53.143 132.583
sub.trial.number10 - sub.trial.number17 53.311 20.3 10207 13.591 93.031
sub.trial.number10 - sub.trial.number18 39.242 20.3 10207 -0.477 78.962
sub.trial.number11 - sub.trial.number12 60.888 20.3 10207 21.168 100.607
sub.trial.number11 - sub.trial.number13 -186.185 20.3 10207 -225.904 -146.465
sub.trial.number11 - sub.trial.number14 -44.072 20.3 10207 -83.792 -4.352
sub.trial.number11 - sub.trial.number15 5.868 20.3 10207 -33.852 45.588
sub.trial.number11 - sub.trial.number16 61.030 20.3 10207 21.310 100.750
sub.trial.number11 - sub.trial.number17 21.478 20.3 10207 -18.242 61.198
sub.trial.number11 - sub.trial.number18 7.410 20.3 10207 -32.310 47.129
sub.trial.number12 - sub.trial.number13 -247.072 20.3 10207 -286.792 -207.352
sub.trial.number12 - sub.trial.number14 -104.960 20.3 10207 -144.679 -65.240
sub.trial.number12 - sub.trial.number15 -55.019 20.3 10207 -94.739 -15.300
sub.trial.number12 - sub.trial.number16 0.142 20.3 10207 -39.578 39.862
sub.trial.number12 - sub.trial.number17 -39.410 20.3 10207 -79.129 0.310
sub.trial.number12 - sub.trial.number18 -53.478 20.3 10207 -93.198 -13.758
sub.trial.number13 - sub.trial.number14 142.113 20.3 10207 102.393 181.832
sub.trial.number13 - sub.trial.number15 192.053 20.3 10207 152.333 231.773
sub.trial.number13 - sub.trial.number16 247.214 20.3 10207 207.494 286.934
sub.trial.number13 - sub.trial.number17 207.663 20.3 10207 167.943 247.382
sub.trial.number13 - sub.trial.number18 193.594 20.3 10207 153.874 233.314
sub.trial.number14 - sub.trial.number15 49.940 20.3 10207 10.220 89.660
sub.trial.number14 - sub.trial.number16 105.102 20.3 10207 65.382 144.822
sub.trial.number14 - sub.trial.number17 65.550 20.3 10207 25.830 105.270
sub.trial.number14 - sub.trial.number18 51.481 20.3 10207 11.762 91.201
sub.trial.number15 - sub.trial.number16 55.162 20.3 10207 15.442 94.882
sub.trial.number15 - sub.trial.number17 15.610 20.3 10207 -24.110 55.330
sub.trial.number15 - sub.trial.number18 1.541 20.3 10207 -38.179 41.261
sub.trial.number16 - sub.trial.number17 -39.552 20.3 10207 -79.272 0.168
sub.trial.number16 - sub.trial.number18 -53.620 20.3 10207 -93.340 -13.900
sub.trial.number17 - sub.trial.number18 -14.069 20.3 10207 -53.788 25.651
t.ratio p.value
16.055 <.0001
17.409 <.0001
18.329 <.0001
13.134 <.0001
14.187 <.0001
14.462 <.0001
15.214 <.0001
12.810 <.0001
12.174 <.0001
13.745 <.0001
16.749 <.0001
4.556 <.0001
11.570 <.0001
14.034 <.0001
16.756 <.0001
14.805 <.0001
14.110 <.0001
1.354 0.1759
2.274 0.0230
-2.921 0.0035
-1.868 0.0617
-1.594 0.1110
-0.842 0.4000
-3.245 0.0012
-3.882 0.0001
-2.311 0.0209
0.694 0.4876
-11.499 <.0001
-4.486 <.0001
-2.021 0.0433
0.701 0.4832
-1.251 0.2111
-1.945 0.0518
0.920 0.3573
-4.275 <.0001
-3.222 0.0013
-2.947 0.0032
-2.195 0.0282
-4.599 <.0001
-5.235 <.0001
-3.664 0.0002
-0.660 0.5096
-12.853 <.0001
-5.839 <.0001
-3.375 0.0007
-0.652 0.5141
-2.604 0.0092
-3.299 0.0010
-5.196 <.0001
-4.142 <.0001
-3.868 0.0001
-3.116 0.0018
-5.519 <.0001
-6.156 <.0001
-4.585 <.0001
-1.580 0.1141
-13.773 <.0001
-6.760 <.0001
-4.295 <.0001
-1.573 0.1158
-3.525 0.0004
-4.219 <.0001
1.053 0.2924
1.328 0.1843
2.080 0.0376
-0.324 0.7462
-0.960 0.3369
0.611 0.5414
3.616 0.0003
-8.578 <.0001
-1.564 0.1178
0.900 0.3680
3.623 0.0003
1.671 0.0948
0.976 0.3289
0.275 0.7836
1.027 0.3046
-1.377 0.1686
-2.013 0.0441
-0.442 0.6583
2.562 0.0104
-9.631 <.0001
-2.617 0.0089
-0.153 0.8786
2.570 0.0102
0.618 0.5368
-0.077 0.9389
0.752 0.4520
-1.651 0.0987
-2.288 0.0222
-0.717 0.4734
2.288 0.0222
-9.905 <.0001
-2.892 0.0038
-0.427 0.6691
2.295 0.0218
0.343 0.7316
-0.351 0.7254
-2.403 0.0163
-3.040 0.0024
-1.469 0.1419
1.536 0.1246
-10.657 <.0001
-3.644 0.0003
-1.179 0.2383
1.543 0.1229
-0.409 0.6825
-1.103 0.2699
-0.637 0.5244
0.934 0.3501
3.939 0.0001
-8.254 <.0001
-1.241 0.2148
1.224 0.2210
3.946 0.0001
1.994 0.0461
1.300 0.1936
1.571 0.1162
4.576 <.0001
-7.617 <.0001
-0.604 0.5459
1.861 0.0628
4.583 <.0001
2.631 0.0085
1.937 0.0528
3.005 0.0027
-9.188 <.0001
-2.175 0.0297
0.290 0.7721
3.012 0.0026
1.060 0.2892
0.366 0.7146
-12.193 <.0001
-5.180 <.0001
-2.715 0.0066
0.007 0.9944
-1.945 0.0518
-2.639 0.0083
7.013 <.0001
9.478 <.0001
12.200 <.0001
10.248 <.0001
9.554 <.0001
2.465 0.0137
5.187 <.0001
3.235 0.0012
2.541 0.0111
2.722 0.0065
0.770 0.4411
0.076 0.9394
-1.952 0.0510
-2.646 0.0082
-0.694 0.4875
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 # Combine EMMs for all three blocks
emm_B1_df <- as.data.frame(emm_B1) %>% mutate(Block = "Block 1")
emm_B2_df <- as.data.frame(emm_B2) %>% mutate(Block = "Block 2")
emm_B3_df <- as.data.frame(emm_B3) %>% mutate(Block = "Block 3")
emm_all <- bind_rows(emm_B1_df, emm_B2_df, emm_B3_df) %>%
mutate(
sub.trial.number = as.numeric(as.character(sub.trial.number)),
Block = factor(Block, levels = c("Block 1", "Block 2", "Block 3"))
)
# Plot
ggplot(emm_all, aes(x = sub.trial.number, y = emmean, color = Block, group = Block)) +
geom_point(size = 2) +
geom_line(linewidth = 0.9) +
geom_errorbar(aes(ymin = emmean - SE, ymax = emmean + SE), width = 0.3) +
labs(
title = "Reaction Times per step",
x = "Step Number",
y = "RT (ms)"
) +
scale_x_continuous(breaks = scales::pretty_breaks()) +
theme_minimal(base_size = 13) +
theme(
panel.grid = element_blank(),
legend.title = element_blank()
)
#4.4 concatenation test blocks
# Ensure session is a factor
df_acc$session <- factor(df_acc$session)
# === Add sequence length per trial ===
df_acc <- df_acc %>%
group_by(subject, session, trial) %>%
mutate(seq_length = n()) %>%
ungroup()
# ========== 1. 6-step sequences in Block 4 vs 5 ==========
df_6 <- df_acc %>%
filter(session %in% c(4, 5), seq_length == 6)
model_6 <- lmer(feedback.RT ~ sub.trial.number * session + (1 | subject), data = df_6)
cat("=== Chi-square ANOVA: 6-step sequences ===\n")=== Chi-square ANOVA: 6-step sequences ===print(Anova(model_6, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 623.9439 5 <2e-16 ***
session 89.7160 1 <2e-16 ***
sub.trial.number:session 3.1762 5 0.6728
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_6 <- emmeans(model_6, ~ sub.trial.number | session)
cat("\n=== EMMs per Step: 6-step ===\n")
=== EMMs per Step: 6-step ===print(summary(emm_6))session = 4:
sub.trial.number emmean SE df lower.CL upper.CL
1 764 43.7 23.9 674 855
2 415 43.7 23.9 325 506
3 374 43.7 23.9 283 464
4 362 43.7 23.9 272 452
5 382 43.7 23.9 291 472
6 388 43.7 23.9 298 478
session = 5:
sub.trial.number emmean SE df lower.CL upper.CL
1 839 44.3 25.3 747 930
2 503 44.3 25.3 412 594
3 497 44.3 25.3 405 588
4 493 44.3 25.3 402 584
5 492 44.3 25.3 401 583
6 492 44.3 25.3 401 583
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 cat("\n=== Stepwise Pairwise Comparisons (within block): 6-step ===\n")
=== Stepwise Pairwise Comparisons (within block): 6-step ===step_comparisons_6 <- contrast(emm_6, method = "pairwise", adjust = "none")
print(summary(step_comparisons_6, infer = c(TRUE, TRUE)))session = 4:
contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 348.940 25.7 2785 298.51 399.4
sub.trial.number1 - sub.trial.number3 390.669 25.7 2785 340.24 441.1
sub.trial.number1 - sub.trial.number4 402.183 25.7 2785 351.76 452.6
sub.trial.number1 - sub.trial.number5 382.510 25.7 2785 332.08 432.9
sub.trial.number1 - sub.trial.number6 376.163 25.7 2785 325.74 426.6
sub.trial.number2 - sub.trial.number3 41.729 25.7 2785 -8.70 92.2
sub.trial.number2 - sub.trial.number4 53.243 25.7 2785 2.82 103.7
sub.trial.number2 - sub.trial.number5 33.570 25.7 2785 -16.86 84.0
sub.trial.number2 - sub.trial.number6 27.223 25.7 2785 -23.20 77.6
sub.trial.number3 - sub.trial.number4 11.514 25.7 2785 -38.91 61.9
sub.trial.number3 - sub.trial.number5 -8.159 25.7 2785 -58.59 42.3
sub.trial.number3 - sub.trial.number6 -14.506 25.7 2785 -64.93 35.9
sub.trial.number4 - sub.trial.number5 -19.673 25.7 2785 -70.10 30.8
sub.trial.number4 - sub.trial.number6 -26.020 25.7 2785 -76.45 24.4
sub.trial.number5 - sub.trial.number6 -6.347 25.7 2785 -56.77 44.1
t.ratio p.value
13.568 <.0001
15.191 <.0001
15.639 <.0001
14.874 <.0001
14.627 <.0001
1.623 0.1048
2.070 0.0385
1.305 0.1919
1.059 0.2899
0.448 0.6544
-0.317 0.7511
-0.564 0.5728
-0.765 0.4443
-1.012 0.3117
-0.247 0.8051
session = 5:
contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 335.693 27.6 2785 281.58 389.8
sub.trial.number1 - sub.trial.number3 342.060 27.6 2785 287.95 396.2
sub.trial.number1 - sub.trial.number4 345.762 27.6 2785 291.65 399.9
sub.trial.number1 - sub.trial.number5 346.459 27.6 2785 292.35 400.6
sub.trial.number1 - sub.trial.number6 346.725 27.6 2785 292.62 400.8
sub.trial.number2 - sub.trial.number3 6.367 27.6 2785 -47.74 60.5
sub.trial.number2 - sub.trial.number4 10.069 27.6 2785 -44.04 64.2
sub.trial.number2 - sub.trial.number5 10.766 27.6 2785 -43.34 64.9
sub.trial.number2 - sub.trial.number6 11.032 27.6 2785 -43.08 65.1
sub.trial.number3 - sub.trial.number4 3.702 27.6 2785 -50.41 57.8
sub.trial.number3 - sub.trial.number5 4.399 27.6 2785 -49.71 58.5
sub.trial.number3 - sub.trial.number6 4.665 27.6 2785 -49.44 58.8
sub.trial.number4 - sub.trial.number5 0.697 27.6 2785 -53.41 54.8
sub.trial.number4 - sub.trial.number6 0.963 27.6 2785 -53.15 55.1
sub.trial.number5 - sub.trial.number6 0.266 27.6 2785 -53.84 54.4
t.ratio p.value
12.165 <.0001
12.396 <.0001
12.530 <.0001
12.555 <.0001
12.565 <.0001
0.231 0.8175
0.365 0.7152
0.390 0.6965
0.400 0.6893
0.134 0.8933
0.159 0.8734
0.169 0.8658
0.025 0.9798
0.035 0.9722
0.010 0.9923
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 emm_6_df <- as.data.frame(emm_6) %>%
mutate(seq_length = "6", sub.trial.number = as.numeric(as.character(sub.trial.number)))
# ========== 2. 12-step sequences in Block 4 vs 5 ==========
df_12 <- df_acc %>%
filter(session %in% c(4, 5), seq_length == 12)
model_12 <- lmer(feedback.RT ~ sub.trial.number * session + (1 | subject), data = df_12)
cat("\n\n=== Chi-square ANOVA: 12-step sequences ===\n")
=== Chi-square ANOVA: 12-step sequences ===print(Anova(model_12, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 424.13 11 < 2.2e-16 ***
session 162.02 1 < 2.2e-16 ***
sub.trial.number:session 34.28 11 0.0003255 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_12 <- emmeans(model_12, ~ sub.trial.number | session)
cat("\n=== EMMs per Step: 12-step ===\n")
=== EMMs per Step: 12-step ===print(summary(emm_12))session = 4:
sub.trial.number emmean SE df lower.CL upper.CL
1 739 49.6 27.0 637 840
2 435 49.6 27.0 333 537
3 395 49.6 27.0 293 497
4 397 49.6 27.0 295 499
5 438 49.6 27.0 336 540
6 472 49.6 27.0 370 574
7 584 49.6 27.0 482 686
8 405 49.6 27.0 303 507
9 492 49.6 27.0 390 593
10 452 49.6 27.0 350 554
11 422 49.6 27.0 320 523
12 405 49.6 27.0 303 506
session = 5:
sub.trial.number emmean SE df lower.CL upper.CL
1 970 53.2 35.5 862 1078
2 536 53.2 35.5 428 644
3 516 53.2 35.5 408 623
4 538 53.2 35.5 430 646
5 542 53.2 35.5 434 649
6 596 53.2 35.5 488 704
7 717 53.2 35.5 609 825
8 615 53.2 35.5 507 723
9 768 53.2 35.5 661 876
10 598 53.2 35.5 490 706
11 450 53.2 35.5 342 558
12 509 53.2 35.5 401 616
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 cat("\n=== Stepwise Pairwise Comparisons (within block): 12-step ===\n")
=== Stepwise Pairwise Comparisons (within block): 12-step ===step_comparisons_12 <- contrast(emm_12, method = "pairwise", adjust = "none")
print(summary(step_comparisons_12, infer = c(TRUE, TRUE)))session = 4:
contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 303.513 32.7 4255 239.35 367.675
sub.trial.number1 - sub.trial.number3 343.759 32.7 4255 279.60 407.921
sub.trial.number1 - sub.trial.number4 341.710 32.7 4255 277.55 405.872
sub.trial.number1 - sub.trial.number5 300.915 32.7 4255 236.75 365.077
sub.trial.number1 - sub.trial.number6 266.804 32.7 4255 202.64 330.965
sub.trial.number1 - sub.trial.number7 154.647 32.7 4255 90.49 218.809
sub.trial.number1 - sub.trial.number8 333.433 32.7 4255 269.27 397.595
sub.trial.number1 - sub.trial.number9 247.138 32.7 4255 182.98 311.300
sub.trial.number1 - sub.trial.number10 286.696 32.7 4255 222.53 350.858
sub.trial.number1 - sub.trial.number11 317.045 32.7 4255 252.88 381.206
sub.trial.number1 - sub.trial.number12 334.058 32.7 4255 269.90 398.220
sub.trial.number2 - sub.trial.number3 40.245 32.7 4255 -23.92 104.407
sub.trial.number2 - sub.trial.number4 38.196 32.7 4255 -25.97 102.358
sub.trial.number2 - sub.trial.number5 -2.598 32.7 4255 -66.76 61.563
sub.trial.number2 - sub.trial.number6 -36.710 32.7 4255 -100.87 27.452
sub.trial.number2 - sub.trial.number7 -148.866 32.7 4255 -213.03 -84.704
sub.trial.number2 - sub.trial.number8 29.920 32.7 4255 -34.24 94.081
sub.trial.number2 - sub.trial.number9 -56.375 32.7 4255 -120.54 7.787
sub.trial.number2 - sub.trial.number10 -16.817 32.7 4255 -80.98 47.345
sub.trial.number2 - sub.trial.number11 13.531 32.7 4255 -50.63 77.693
sub.trial.number2 - sub.trial.number12 30.545 32.7 4255 -33.62 94.706
sub.trial.number3 - sub.trial.number4 -2.049 32.7 4255 -66.21 62.113
sub.trial.number3 - sub.trial.number5 -42.844 32.7 4255 -107.01 21.318
sub.trial.number3 - sub.trial.number6 -76.955 32.7 4255 -141.12 -12.794
sub.trial.number3 - sub.trial.number7 -189.112 32.7 4255 -253.27 -124.950
sub.trial.number3 - sub.trial.number8 -10.326 32.7 4255 -74.49 53.836
sub.trial.number3 - sub.trial.number9 -96.621 32.7 4255 -160.78 -32.459
sub.trial.number3 - sub.trial.number10 -57.062 32.7 4255 -121.22 7.099
sub.trial.number3 - sub.trial.number11 -26.714 32.7 4255 -90.88 37.447
sub.trial.number3 - sub.trial.number12 -9.701 32.7 4255 -73.86 54.461
sub.trial.number4 - sub.trial.number5 -40.795 32.7 4255 -104.96 23.367
sub.trial.number4 - sub.trial.number6 -74.906 32.7 4255 -139.07 -10.745
sub.trial.number4 - sub.trial.number7 -187.062 32.7 4255 -251.22 -122.901
sub.trial.number4 - sub.trial.number8 -8.277 32.7 4255 -72.44 55.885
sub.trial.number4 - sub.trial.number9 -94.571 32.7 4255 -158.73 -30.410
sub.trial.number4 - sub.trial.number10 -55.013 32.7 4255 -119.18 9.148
sub.trial.number4 - sub.trial.number11 -24.665 32.7 4255 -88.83 39.496
sub.trial.number4 - sub.trial.number12 -7.652 32.7 4255 -71.81 56.510
sub.trial.number5 - sub.trial.number6 -34.112 32.7 4255 -98.27 30.050
sub.trial.number5 - sub.trial.number7 -146.268 32.7 4255 -210.43 -82.106
sub.trial.number5 - sub.trial.number8 32.518 32.7 4255 -31.64 96.680
sub.trial.number5 - sub.trial.number9 -53.777 32.7 4255 -117.94 10.385
sub.trial.number5 - sub.trial.number10 -14.219 32.7 4255 -78.38 49.943
sub.trial.number5 - sub.trial.number11 16.130 32.7 4255 -48.03 80.291
sub.trial.number5 - sub.trial.number12 33.143 32.7 4255 -31.02 97.305
sub.trial.number6 - sub.trial.number7 -112.156 32.7 4255 -176.32 -47.995
sub.trial.number6 - sub.trial.number8 66.629 32.7 4255 2.47 130.791
sub.trial.number6 - sub.trial.number9 -19.665 32.7 4255 -83.83 44.496
sub.trial.number6 - sub.trial.number10 19.893 32.7 4255 -44.27 84.055
sub.trial.number6 - sub.trial.number11 50.241 32.7 4255 -13.92 114.403
sub.trial.number6 - sub.trial.number12 67.254 32.7 4255 3.09 131.416
sub.trial.number7 - sub.trial.number8 178.786 32.7 4255 114.62 242.947
sub.trial.number7 - sub.trial.number9 92.491 32.7 4255 28.33 156.653
sub.trial.number7 - sub.trial.number10 132.049 32.7 4255 67.89 196.211
sub.trial.number7 - sub.trial.number11 162.397 32.7 4255 98.24 226.559
sub.trial.number7 - sub.trial.number12 179.411 32.7 4255 115.25 243.572
sub.trial.number8 - sub.trial.number9 -86.295 32.7 4255 -150.46 -22.133
sub.trial.number8 - sub.trial.number10 -46.737 32.7 4255 -110.90 17.425
sub.trial.number8 - sub.trial.number11 -16.388 32.7 4255 -80.55 47.773
sub.trial.number8 - sub.trial.number12 0.625 32.7 4255 -63.54 64.787
sub.trial.number9 - sub.trial.number10 39.558 32.7 4255 -24.60 103.720
sub.trial.number9 - sub.trial.number11 69.906 32.7 4255 5.74 134.068
sub.trial.number9 - sub.trial.number12 86.920 32.7 4255 22.76 151.081
sub.trial.number10 - sub.trial.number11 30.348 32.7 4255 -33.81 94.510
sub.trial.number10 - sub.trial.number12 47.362 32.7 4255 -16.80 111.523
sub.trial.number11 - sub.trial.number12 17.013 32.7 4255 -47.15 81.175
t.ratio p.value
9.274 <.0001
10.504 <.0001
10.441 <.0001
9.195 <.0001
8.152 <.0001
4.725 <.0001
10.188 <.0001
7.552 <.0001
8.760 <.0001
9.688 <.0001
10.207 <.0001
1.230 0.2189
1.167 0.2432
-0.079 0.9367
-1.122 0.2621
-4.549 <.0001
0.914 0.3607
-1.723 0.0850
-0.514 0.6074
0.413 0.6793
0.933 0.3507
-0.063 0.9501
-1.309 0.1906
-2.351 0.0187
-5.778 <.0001
-0.316 0.7524
-2.952 0.0032
-1.744 0.0813
-0.816 0.4144
-0.296 0.7669
-1.247 0.2126
-2.289 0.0221
-5.716 <.0001
-0.253 0.8004
-2.890 0.0039
-1.681 0.0928
-0.754 0.4511
-0.234 0.8151
-1.042 0.2973
-4.469 <.0001
0.994 0.3205
-1.643 0.1004
-0.434 0.6640
0.493 0.6221
1.013 0.3113
-3.427 0.0006
2.036 0.0418
-0.601 0.5479
0.608 0.5433
1.535 0.1248
2.055 0.0399
5.463 <.0001
2.826 0.0047
4.035 0.0001
4.962 <.0001
5.482 <.0001
-2.637 0.0084
-1.428 0.1533
-0.501 0.6166
0.019 0.9848
1.209 0.2268
2.136 0.0327
2.656 0.0079
0.927 0.3538
1.447 0.1479
0.520 0.6032
session = 5:
contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 433.813 42.3 4255 350.86 516.769
sub.trial.number1 - sub.trial.number3 454.306 42.3 4255 371.35 537.262
sub.trial.number1 - sub.trial.number4 432.090 42.3 4255 349.13 515.045
sub.trial.number1 - sub.trial.number5 428.366 42.3 4255 345.41 511.322
sub.trial.number1 - sub.trial.number6 373.672 42.3 4255 290.72 456.628
sub.trial.number1 - sub.trial.number7 252.813 42.3 4255 169.86 335.769
sub.trial.number1 - sub.trial.number8 355.052 42.3 4255 272.10 438.008
sub.trial.number1 - sub.trial.number9 201.515 42.3 4255 118.56 284.471
sub.trial.number1 - sub.trial.number10 371.978 42.3 4255 289.02 454.934
sub.trial.number1 - sub.trial.number11 519.828 42.3 4255 436.87 602.784
sub.trial.number1 - sub.trial.number12 461.276 42.3 4255 378.32 544.232
sub.trial.number2 - sub.trial.number3 20.492 42.3 4255 -62.46 103.448
sub.trial.number2 - sub.trial.number4 -1.724 42.3 4255 -84.68 81.232
sub.trial.number2 - sub.trial.number5 -5.448 42.3 4255 -88.40 77.508
sub.trial.number2 - sub.trial.number6 -60.142 42.3 4255 -143.10 22.814
sub.trial.number2 - sub.trial.number7 -181.000 42.3 4255 -263.96 -98.044
sub.trial.number2 - sub.trial.number8 -78.761 42.3 4255 -161.72 4.195
sub.trial.number2 - sub.trial.number9 -232.298 42.3 4255 -315.25 -149.343
sub.trial.number2 - sub.trial.number10 -61.836 42.3 4255 -144.79 21.120
sub.trial.number2 - sub.trial.number11 86.015 42.3 4255 3.06 168.971
sub.trial.number2 - sub.trial.number12 27.463 42.3 4255 -55.49 110.419
sub.trial.number3 - sub.trial.number4 -22.216 42.3 4255 -105.17 60.739
sub.trial.number3 - sub.trial.number5 -25.940 42.3 4255 -108.90 57.016
sub.trial.number3 - sub.trial.number6 -80.634 42.3 4255 -163.59 2.322
sub.trial.number3 - sub.trial.number7 -201.493 42.3 4255 -284.45 -118.537
sub.trial.number3 - sub.trial.number8 -99.254 42.3 4255 -182.21 -16.298
sub.trial.number3 - sub.trial.number9 -252.791 42.3 4255 -335.75 -169.835
sub.trial.number3 - sub.trial.number10 -82.328 42.3 4255 -165.28 0.628
sub.trial.number3 - sub.trial.number11 65.522 42.3 4255 -17.43 148.478
sub.trial.number3 - sub.trial.number12 6.970 42.3 4255 -75.99 89.926
sub.trial.number4 - sub.trial.number5 -3.724 42.3 4255 -86.68 79.232
sub.trial.number4 - sub.trial.number6 -58.418 42.3 4255 -141.37 24.538
sub.trial.number4 - sub.trial.number7 -179.276 42.3 4255 -262.23 -96.320
sub.trial.number4 - sub.trial.number8 -77.037 42.3 4255 -159.99 5.919
sub.trial.number4 - sub.trial.number9 -230.575 42.3 4255 -313.53 -147.619
sub.trial.number4 - sub.trial.number10 -60.112 42.3 4255 -143.07 22.844
sub.trial.number4 - sub.trial.number11 87.739 42.3 4255 4.78 170.695
sub.trial.number4 - sub.trial.number12 29.187 42.3 4255 -53.77 112.142
sub.trial.number5 - sub.trial.number6 -54.694 42.3 4255 -137.65 28.262
sub.trial.number5 - sub.trial.number7 -175.552 42.3 4255 -258.51 -92.596
sub.trial.number5 - sub.trial.number8 -73.313 42.3 4255 -156.27 9.643
sub.trial.number5 - sub.trial.number9 -226.851 42.3 4255 -309.81 -143.895
sub.trial.number5 - sub.trial.number10 -56.388 42.3 4255 -139.34 26.568
sub.trial.number5 - sub.trial.number11 91.463 42.3 4255 8.51 174.419
sub.trial.number5 - sub.trial.number12 32.910 42.3 4255 -50.05 115.866
sub.trial.number6 - sub.trial.number7 -120.858 42.3 4255 -203.81 -37.902
sub.trial.number6 - sub.trial.number8 -18.619 42.3 4255 -101.58 64.337
sub.trial.number6 - sub.trial.number9 -172.157 42.3 4255 -255.11 -89.201
sub.trial.number6 - sub.trial.number10 -1.694 42.3 4255 -84.65 81.262
sub.trial.number6 - sub.trial.number11 146.157 42.3 4255 63.20 229.113
sub.trial.number6 - sub.trial.number12 87.605 42.3 4255 4.65 170.560
sub.trial.number7 - sub.trial.number8 102.239 42.3 4255 19.28 185.195
sub.trial.number7 - sub.trial.number9 -51.298 42.3 4255 -134.25 31.657
sub.trial.number7 - sub.trial.number10 119.164 42.3 4255 36.21 202.120
sub.trial.number7 - sub.trial.number11 267.015 42.3 4255 184.06 349.971
sub.trial.number7 - sub.trial.number12 208.463 42.3 4255 125.51 291.419
sub.trial.number8 - sub.trial.number9 -153.537 42.3 4255 -236.49 -70.581
sub.trial.number8 - sub.trial.number10 16.925 42.3 4255 -66.03 99.881
sub.trial.number8 - sub.trial.number11 164.776 42.3 4255 81.82 247.732
sub.trial.number8 - sub.trial.number12 106.224 42.3 4255 23.27 189.180
sub.trial.number9 - sub.trial.number10 170.463 42.3 4255 87.51 253.419
sub.trial.number9 - sub.trial.number11 318.313 42.3 4255 235.36 401.269
sub.trial.number9 - sub.trial.number12 259.761 42.3 4255 176.81 342.717
sub.trial.number10 - sub.trial.number11 147.851 42.3 4255 64.89 230.807
sub.trial.number10 - sub.trial.number12 89.299 42.3 4255 6.34 172.255
sub.trial.number11 - sub.trial.number12 -58.552 42.3 4255 -141.51 24.404
t.ratio p.value
10.252 <.0001
10.737 <.0001
10.212 <.0001
10.124 <.0001
8.831 <.0001
5.975 <.0001
8.391 <.0001
4.762 <.0001
8.791 <.0001
12.285 <.0001
10.901 <.0001
0.484 0.6282
-0.041 0.9675
-0.129 0.8976
-1.421 0.1553
-4.278 <.0001
-1.861 0.0628
-5.490 <.0001
-1.461 0.1440
2.033 0.0421
0.649 0.5164
-0.525 0.5996
-0.613 0.5399
-1.906 0.0568
-4.762 <.0001
-2.346 0.0190
-5.974 <.0001
-1.946 0.0518
1.549 0.1216
0.165 0.8692
-0.088 0.9299
-1.381 0.1675
-4.237 <.0001
-1.821 0.0687
-5.449 <.0001
-1.421 0.1555
2.074 0.0382
0.690 0.4904
-1.293 0.1962
-4.149 <.0001
-1.733 0.0832
-5.361 <.0001
-1.333 0.1827
2.162 0.0307
0.778 0.4367
-2.856 0.0043
-0.440 0.6599
-4.069 <.0001
-0.040 0.9681
3.454 0.0006
2.070 0.0385
2.416 0.0157
-1.212 0.2254
2.816 0.0049
6.310 <.0001
4.927 <.0001
-3.629 0.0003
0.400 0.6892
3.894 0.0001
2.510 0.0121
4.029 0.0001
7.523 <.0001
6.139 <.0001
3.494 0.0005
2.110 0.0349
-1.384 0.1665
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 emm_12_df <- as.data.frame(emm_12) %>%
mutate(seq_length = "12", sub.trial.number = as.numeric(as.character(sub.trial.number)))
# ========== 3. 18-step sequences in Block 4 vs 5 ==========
df_18 <- df_acc %>%
filter(session %in% c(4, 5), seq_length == 18)
model_18 <- lmer(feedback.RT ~ sub.trial.number * session + (1 | subject), data = df_18)
cat("\n\n=== Chi-square ANOVA: 18-step sequences ===\n")
=== Chi-square ANOVA: 18-step sequences ===print(Anova(model_18, type = 2))Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 385.211 17 < 2.2e-16 ***
session 86.629 1 < 2.2e-16 ***
sub.trial.number:session 54.881 17 7.161e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1emm_18 <- emmeans(model_18, ~ sub.trial.number | session)
cat("\n=== EMMs per Step: 18-step ===\n")
=== EMMs per Step: 18-step ===print(summary(emm_18))session = 4:
sub.trial.number emmean SE df lower.CL upper.CL
1 814 50.3 35.3 712 916
2 449 50.3 35.3 347 551
3 402 50.3 35.3 300 504
4 394 50.3 35.3 292 496
5 442 50.3 35.3 340 544
6 459 50.3 35.3 357 561
7 502 50.3 35.3 400 604
8 449 50.3 35.3 347 551
9 489 50.3 35.3 387 591
10 485 50.3 35.3 383 587
11 455 50.3 35.3 353 557
12 419 50.3 35.3 317 521
13 579 50.3 35.3 477 681
14 552 50.3 35.3 450 654
15 420 50.3 35.3 318 522
16 399 50.3 35.3 297 501
17 390 50.3 35.3 288 492
18 460 50.3 35.3 358 562
session = 5:
sub.trial.number emmean SE df lower.CL upper.CL
1 850 54.8 49.9 740 960
2 494 54.8 49.9 384 604
3 509 54.8 49.9 398 619
4 540 54.8 49.9 430 650
5 557 54.8 49.9 447 667
6 560 54.8 49.9 449 670
7 627 54.8 49.9 516 737
8 515 54.8 49.9 404 625
9 747 54.8 49.9 637 858
10 714 54.8 49.9 603 824
11 474 54.8 49.9 364 584
12 490 54.8 49.9 380 600
13 872 54.8 49.9 762 982
14 625 54.8 49.9 515 735
15 436 54.8 49.9 326 546
16 473 54.8 49.9 363 583
17 519 54.8 49.9 409 629
18 473 54.8 49.9 363 584
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 cat("\n=== Stepwise Pairwise Comparisons (within block): 18-step ===\n")
=== Stepwise Pairwise Comparisons (within block): 18-step ===step_comparisons_18 <- contrast(emm_18, method = "pairwise", adjust = "none")
print(summary(step_comparisons_18, infer = c(TRUE, TRUE)))session = 4:
contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 365.528 40.0 5167 287.10 443.95
sub.trial.number1 - sub.trial.number3 412.410 40.0 5167 333.98 490.84
sub.trial.number1 - sub.trial.number4 420.022 40.0 5167 341.60 498.45
sub.trial.number1 - sub.trial.number5 371.730 40.0 5167 293.30 450.16
sub.trial.number1 - sub.trial.number6 354.888 40.0 5167 276.46 433.31
sub.trial.number1 - sub.trial.number7 311.910 40.0 5167 233.48 390.34
sub.trial.number1 - sub.trial.number8 365.180 40.0 5167 286.75 443.61
sub.trial.number1 - sub.trial.number9 325.522 40.0 5167 247.10 403.95
sub.trial.number1 - sub.trial.number10 329.511 40.0 5167 251.08 407.94
sub.trial.number1 - sub.trial.number11 359.242 40.0 5167 280.82 437.67
sub.trial.number1 - sub.trial.number12 394.910 40.0 5167 316.48 473.34
sub.trial.number1 - sub.trial.number13 235.354 40.0 5167 156.93 313.78
sub.trial.number1 - sub.trial.number14 261.719 40.0 5167 183.29 340.15
sub.trial.number1 - sub.trial.number15 393.916 40.0 5167 315.49 472.34
sub.trial.number1 - sub.trial.number16 415.433 40.0 5167 337.01 493.86
sub.trial.number1 - sub.trial.number17 424.135 40.0 5167 345.71 502.56
sub.trial.number1 - sub.trial.number18 354.539 40.0 5167 276.11 432.97
sub.trial.number2 - sub.trial.number3 46.882 40.0 5167 -31.54 125.31
sub.trial.number2 - sub.trial.number4 54.494 40.0 5167 -23.93 132.92
sub.trial.number2 - sub.trial.number5 6.202 40.0 5167 -72.22 84.63
sub.trial.number2 - sub.trial.number6 -10.640 40.0 5167 -89.07 67.79
sub.trial.number2 - sub.trial.number7 -53.618 40.0 5167 -132.04 24.81
sub.trial.number2 - sub.trial.number8 -0.348 40.0 5167 -78.77 78.08
sub.trial.number2 - sub.trial.number9 -40.006 40.0 5167 -118.43 38.42
sub.trial.number2 - sub.trial.number10 -36.017 40.0 5167 -114.44 42.41
sub.trial.number2 - sub.trial.number11 -6.287 40.0 5167 -84.71 72.14
sub.trial.number2 - sub.trial.number12 29.382 40.0 5167 -49.04 107.81
sub.trial.number2 - sub.trial.number13 -130.174 40.0 5167 -208.60 -51.75
sub.trial.number2 - sub.trial.number14 -103.809 40.0 5167 -182.24 -25.38
sub.trial.number2 - sub.trial.number15 28.388 40.0 5167 -50.04 106.81
sub.trial.number2 - sub.trial.number16 49.904 40.0 5167 -28.52 128.33
sub.trial.number2 - sub.trial.number17 58.607 40.0 5167 -19.82 137.03
sub.trial.number2 - sub.trial.number18 -10.989 40.0 5167 -89.42 67.44
sub.trial.number3 - sub.trial.number4 7.612 40.0 5167 -70.81 86.04
sub.trial.number3 - sub.trial.number5 -40.680 40.0 5167 -119.11 37.75
sub.trial.number3 - sub.trial.number6 -57.523 40.0 5167 -135.95 20.90
sub.trial.number3 - sub.trial.number7 -100.500 40.0 5167 -178.93 -22.07
sub.trial.number3 - sub.trial.number8 -47.230 40.0 5167 -125.66 31.20
sub.trial.number3 - sub.trial.number9 -86.888 40.0 5167 -165.31 -8.46
sub.trial.number3 - sub.trial.number10 -82.899 40.0 5167 -161.33 -4.47
sub.trial.number3 - sub.trial.number11 -53.169 40.0 5167 -131.59 25.26
sub.trial.number3 - sub.trial.number12 -17.500 40.0 5167 -95.93 60.93
sub.trial.number3 - sub.trial.number13 -177.056 40.0 5167 -255.48 -98.63
sub.trial.number3 - sub.trial.number14 -150.691 40.0 5167 -229.12 -72.26
sub.trial.number3 - sub.trial.number15 -18.494 40.0 5167 -96.92 59.93
sub.trial.number3 - sub.trial.number16 3.022 40.0 5167 -75.40 81.45
sub.trial.number3 - sub.trial.number17 11.725 40.0 5167 -66.70 90.15
sub.trial.number3 - sub.trial.number18 -57.871 40.0 5167 -136.30 20.56
sub.trial.number4 - sub.trial.number5 -48.292 40.0 5167 -126.72 30.13
sub.trial.number4 - sub.trial.number6 -65.135 40.0 5167 -143.56 13.29
sub.trial.number4 - sub.trial.number7 -108.112 40.0 5167 -186.54 -29.69
sub.trial.number4 - sub.trial.number8 -54.843 40.0 5167 -133.27 23.58
sub.trial.number4 - sub.trial.number9 -94.500 40.0 5167 -172.93 -16.07
sub.trial.number4 - sub.trial.number10 -90.511 40.0 5167 -168.94 -12.08
sub.trial.number4 - sub.trial.number11 -60.781 40.0 5167 -139.21 17.65
sub.trial.number4 - sub.trial.number12 -25.112 40.0 5167 -103.54 53.31
sub.trial.number4 - sub.trial.number13 -184.668 40.0 5167 -263.09 -106.24
sub.trial.number4 - sub.trial.number14 -158.303 40.0 5167 -236.73 -79.88
sub.trial.number4 - sub.trial.number15 -26.107 40.0 5167 -104.53 52.32
sub.trial.number4 - sub.trial.number16 -4.590 40.0 5167 -83.02 73.84
sub.trial.number4 - sub.trial.number17 4.112 40.0 5167 -74.31 82.54
sub.trial.number4 - sub.trial.number18 -65.483 40.0 5167 -143.91 12.94
sub.trial.number5 - sub.trial.number6 -16.843 40.0 5167 -95.27 61.58
sub.trial.number5 - sub.trial.number7 -59.820 40.0 5167 -138.25 18.61
sub.trial.number5 - sub.trial.number8 -6.551 40.0 5167 -84.98 71.88
sub.trial.number5 - sub.trial.number9 -46.208 40.0 5167 -124.63 32.22
sub.trial.number5 - sub.trial.number10 -42.219 40.0 5167 -120.65 36.21
sub.trial.number5 - sub.trial.number11 -12.489 40.0 5167 -90.92 65.94
sub.trial.number5 - sub.trial.number12 23.180 40.0 5167 -55.25 101.61
sub.trial.number5 - sub.trial.number13 -136.376 40.0 5167 -214.80 -57.95
sub.trial.number5 - sub.trial.number14 -110.011 40.0 5167 -188.44 -31.58
sub.trial.number5 - sub.trial.number15 22.185 40.0 5167 -56.24 100.61
sub.trial.number5 - sub.trial.number16 43.702 40.0 5167 -34.72 122.13
sub.trial.number5 - sub.trial.number17 52.404 40.0 5167 -26.02 130.83
sub.trial.number5 - sub.trial.number18 -17.191 40.0 5167 -95.62 61.24
sub.trial.number6 - sub.trial.number7 -42.977 40.0 5167 -121.40 35.45
sub.trial.number6 - sub.trial.number8 10.292 40.0 5167 -68.13 88.72
sub.trial.number6 - sub.trial.number9 -29.365 40.0 5167 -107.79 49.06
sub.trial.number6 - sub.trial.number10 -25.376 40.0 5167 -103.80 53.05
sub.trial.number6 - sub.trial.number11 4.354 40.0 5167 -74.07 82.78
sub.trial.number6 - sub.trial.number12 40.023 40.0 5167 -38.40 118.45
sub.trial.number6 - sub.trial.number13 -119.534 40.0 5167 -197.96 -41.11
sub.trial.number6 - sub.trial.number14 -93.168 40.0 5167 -171.59 -14.74
sub.trial.number6 - sub.trial.number15 39.028 40.0 5167 -39.40 117.45
sub.trial.number6 - sub.trial.number16 60.545 40.0 5167 -17.88 138.97
sub.trial.number6 - sub.trial.number17 69.247 40.0 5167 -9.18 147.67
sub.trial.number6 - sub.trial.number18 -0.348 40.0 5167 -78.77 78.08
sub.trial.number7 - sub.trial.number8 53.270 40.0 5167 -25.16 131.70
sub.trial.number7 - sub.trial.number9 13.612 40.0 5167 -64.81 92.04
sub.trial.number7 - sub.trial.number10 17.601 40.0 5167 -60.83 96.03
sub.trial.number7 - sub.trial.number11 47.331 40.0 5167 -31.09 125.76
sub.trial.number7 - sub.trial.number12 83.000 40.0 5167 4.57 161.43
sub.trial.number7 - sub.trial.number13 -76.556 40.0 5167 -154.98 1.87
sub.trial.number7 - sub.trial.number14 -50.191 40.0 5167 -128.62 28.24
sub.trial.number7 - sub.trial.number15 82.006 40.0 5167 3.58 160.43
sub.trial.number7 - sub.trial.number16 103.522 40.0 5167 25.10 181.95
sub.trial.number7 - sub.trial.number17 112.225 40.0 5167 33.80 190.65
sub.trial.number7 - sub.trial.number18 42.629 40.0 5167 -35.80 121.06
sub.trial.number8 - sub.trial.number9 -39.657 40.0 5167 -118.08 38.77
sub.trial.number8 - sub.trial.number10 -35.669 40.0 5167 -114.09 42.76
sub.trial.number8 - sub.trial.number11 -5.938 40.0 5167 -84.36 72.49
sub.trial.number8 - sub.trial.number12 29.730 40.0 5167 -48.70 108.16
sub.trial.number8 - sub.trial.number13 -129.826 40.0 5167 -208.25 -51.40
sub.trial.number8 - sub.trial.number14 -103.461 40.0 5167 -181.89 -25.03
sub.trial.number8 - sub.trial.number15 28.736 40.0 5167 -49.69 107.16
sub.trial.number8 - sub.trial.number16 50.253 40.0 5167 -28.17 128.68
sub.trial.number8 - sub.trial.number17 58.955 40.0 5167 -19.47 137.38
sub.trial.number8 - sub.trial.number18 -10.640 40.0 5167 -89.07 67.79
sub.trial.number9 - sub.trial.number10 3.989 40.0 5167 -74.44 82.42
sub.trial.number9 - sub.trial.number11 33.719 40.0 5167 -44.71 112.15
sub.trial.number9 - sub.trial.number12 69.388 40.0 5167 -9.04 147.81
sub.trial.number9 - sub.trial.number13 -90.168 40.0 5167 -168.59 -11.74
sub.trial.number9 - sub.trial.number14 -63.803 40.0 5167 -142.23 14.62
sub.trial.number9 - sub.trial.number15 68.393 40.0 5167 -10.03 146.82
sub.trial.number9 - sub.trial.number16 89.910 40.0 5167 11.48 168.34
sub.trial.number9 - sub.trial.number17 98.612 40.0 5167 20.19 177.04
sub.trial.number9 - sub.trial.number18 29.017 40.0 5167 -49.41 107.44
sub.trial.number10 - sub.trial.number11 29.730 40.0 5167 -48.70 108.16
sub.trial.number10 - sub.trial.number12 65.399 40.0 5167 -13.03 143.83
sub.trial.number10 - sub.trial.number13 -94.157 40.0 5167 -172.58 -15.73
sub.trial.number10 - sub.trial.number14 -67.792 40.0 5167 -146.22 10.63
sub.trial.number10 - sub.trial.number15 64.404 40.0 5167 -14.02 142.83
sub.trial.number10 - sub.trial.number16 85.921 40.0 5167 7.50 164.35
sub.trial.number10 - sub.trial.number17 94.624 40.0 5167 16.20 173.05
sub.trial.number10 - sub.trial.number18 25.028 40.0 5167 -53.40 103.45
sub.trial.number11 - sub.trial.number12 35.669 40.0 5167 -42.76 114.09
sub.trial.number11 - sub.trial.number13 -123.888 40.0 5167 -202.31 -45.46
sub.trial.number11 - sub.trial.number14 -97.522 40.0 5167 -175.95 -19.10
sub.trial.number11 - sub.trial.number15 34.674 40.0 5167 -43.75 113.10
sub.trial.number11 - sub.trial.number16 56.191 40.0 5167 -22.24 134.62
sub.trial.number11 - sub.trial.number17 64.893 40.0 5167 -13.53 143.32
sub.trial.number11 - sub.trial.number18 -4.702 40.0 5167 -83.13 73.72
sub.trial.number12 - sub.trial.number13 -159.556 40.0 5167 -237.98 -81.13
sub.trial.number12 - sub.trial.number14 -133.191 40.0 5167 -211.62 -54.76
sub.trial.number12 - sub.trial.number15 -0.994 40.0 5167 -79.42 77.43
sub.trial.number12 - sub.trial.number16 20.523 40.0 5167 -57.90 98.95
sub.trial.number12 - sub.trial.number17 29.225 40.0 5167 -49.20 107.65
sub.trial.number12 - sub.trial.number18 -40.371 40.0 5167 -118.80 38.06
sub.trial.number13 - sub.trial.number14 26.365 40.0 5167 -52.06 104.79
sub.trial.number13 - sub.trial.number15 158.562 40.0 5167 80.14 236.99
sub.trial.number13 - sub.trial.number16 180.079 40.0 5167 101.65 258.50
sub.trial.number13 - sub.trial.number17 188.781 40.0 5167 110.35 267.21
sub.trial.number13 - sub.trial.number18 119.185 40.0 5167 40.76 197.61
sub.trial.number14 - sub.trial.number15 132.197 40.0 5167 53.77 210.62
sub.trial.number14 - sub.trial.number16 153.714 40.0 5167 75.29 232.14
sub.trial.number14 - sub.trial.number17 162.416 40.0 5167 83.99 240.84
sub.trial.number14 - sub.trial.number18 92.820 40.0 5167 14.39 171.25
sub.trial.number15 - sub.trial.number16 21.517 40.0 5167 -56.91 99.94
sub.trial.number15 - sub.trial.number17 30.219 40.0 5167 -48.21 108.65
sub.trial.number15 - sub.trial.number18 -39.376 40.0 5167 -117.80 39.05
sub.trial.number16 - sub.trial.number17 8.702 40.0 5167 -69.72 87.13
sub.trial.number16 - sub.trial.number18 -60.893 40.0 5167 -139.32 17.53
sub.trial.number17 - sub.trial.number18 -69.596 40.0 5167 -148.02 8.83
t.ratio p.value
9.137 <.0001
10.309 <.0001
10.499 <.0001
9.292 <.0001
8.871 <.0001
7.797 <.0001
9.128 <.0001
8.137 <.0001
8.237 <.0001
8.980 <.0001
9.872 <.0001
5.883 <.0001
6.542 <.0001
9.847 <.0001
10.385 <.0001
10.602 <.0001
8.862 <.0001
1.172 0.2413
1.362 0.1732
0.155 0.8768
-0.266 0.7903
-1.340 0.1802
-0.009 0.9931
-1.000 0.3173
-0.900 0.3680
-0.157 0.8751
0.734 0.4627
-3.254 0.0011
-2.595 0.0095
0.710 0.4780
1.247 0.2123
1.465 0.1430
-0.275 0.7836
0.190 0.8491
-1.017 0.3093
-1.438 0.1505
-2.512 0.0120
-1.181 0.2378
-2.172 0.0299
-2.072 0.0383
-1.329 0.1839
-0.437 0.6618
-4.426 <.0001
-3.767 0.0002
-0.462 0.6439
0.076 0.9398
0.293 0.7695
-1.447 0.1481
-1.207 0.2274
-1.628 0.1035
-2.702 0.0069
-1.371 0.1705
-2.362 0.0182
-2.263 0.0237
-1.519 0.1287
-0.628 0.5302
-4.616 <.0001
-3.957 0.0001
-0.653 0.5140
-0.115 0.9087
0.103 0.9181
-1.637 0.1017
-0.421 0.6738
-1.495 0.1349
-0.164 0.8699
-1.155 0.2481
-1.055 0.2913
-0.312 0.7549
0.579 0.5623
-3.409 0.0007
-2.750 0.0060
0.555 0.5792
1.092 0.2747
1.310 0.1903
-0.430 0.6674
-1.074 0.2827
0.257 0.7970
-0.734 0.4630
-0.634 0.5259
0.109 0.9133
1.000 0.3171
-2.988 0.0028
-2.329 0.0199
0.976 0.3293
1.513 0.1302
1.731 0.0835
-0.009 0.9931
1.332 0.1831
0.340 0.7337
0.440 0.6600
1.183 0.2368
2.075 0.0381
-1.914 0.0557
-1.255 0.2097
2.050 0.0404
2.588 0.0097
2.805 0.0050
1.066 0.2867
-0.991 0.3216
-0.892 0.3726
-0.148 0.8820
0.743 0.4574
-3.245 0.0012
-2.586 0.0097
0.718 0.4726
1.256 0.2091
1.474 0.1406
-0.266 0.7903
0.100 0.9206
0.843 0.3993
1.734 0.0829
-2.254 0.0242
-1.595 0.1108
1.710 0.0874
2.247 0.0247
2.465 0.0137
0.725 0.4683
0.743 0.4574
1.635 0.1022
-2.354 0.0186
-1.695 0.0902
1.610 0.1075
2.148 0.0318
2.365 0.0181
0.626 0.5316
0.892 0.3726
-3.097 0.0020
-2.438 0.0148
0.867 0.3861
1.405 0.1602
1.622 0.1048
-0.118 0.9064
-3.988 0.0001
-3.329 0.0009
-0.025 0.9802
0.513 0.6080
0.731 0.4651
-1.009 0.3130
0.659 0.5099
3.964 0.0001
4.501 <.0001
4.719 <.0001
2.979 0.0029
3.305 0.0010
3.842 0.0001
4.060 <.0001
2.320 0.0204
0.538 0.5907
0.755 0.4501
-0.984 0.3250
0.218 0.8278
-1.522 0.1280
-1.740 0.0820
session = 5:
contrast estimate SE df lower.CL upper.CL
sub.trial.number1 - sub.trial.number2 355.848 50.4 5167 256.98 454.72
sub.trial.number1 - sub.trial.number3 341.438 50.4 5167 242.57 440.31
sub.trial.number1 - sub.trial.number4 310.366 50.4 5167 211.50 409.24
sub.trial.number1 - sub.trial.number5 292.821 50.4 5167 193.95 391.69
sub.trial.number1 - sub.trial.number6 290.509 50.4 5167 191.64 389.38
sub.trial.number1 - sub.trial.number7 223.491 50.4 5167 124.62 322.36
sub.trial.number1 - sub.trial.number8 335.482 50.4 5167 236.61 434.35
sub.trial.number1 - sub.trial.number9 102.696 50.4 5167 3.83 201.57
sub.trial.number1 - sub.trial.number10 136.536 50.4 5167 37.67 235.41
sub.trial.number1 - sub.trial.number11 376.054 50.4 5167 277.18 474.92
sub.trial.number1 - sub.trial.number12 360.339 50.4 5167 261.47 459.21
sub.trial.number1 - sub.trial.number13 -21.875 50.4 5167 -120.74 76.99
sub.trial.number1 - sub.trial.number14 225.152 50.4 5167 126.28 324.02
sub.trial.number1 - sub.trial.number15 413.830 50.4 5167 314.96 512.70
sub.trial.number1 - sub.trial.number16 376.973 50.4 5167 278.10 475.84
sub.trial.number1 - sub.trial.number17 331.062 50.4 5167 232.19 429.93
sub.trial.number1 - sub.trial.number18 376.580 50.4 5167 277.71 475.45
sub.trial.number2 - sub.trial.number3 -14.411 50.4 5167 -113.28 84.46
sub.trial.number2 - sub.trial.number4 -45.482 50.4 5167 -144.35 53.39
sub.trial.number2 - sub.trial.number5 -63.027 50.4 5167 -161.90 35.84
sub.trial.number2 - sub.trial.number6 -65.339 50.4 5167 -164.21 33.53
sub.trial.number2 - sub.trial.number7 -132.357 50.4 5167 -231.23 -33.49
sub.trial.number2 - sub.trial.number8 -20.366 50.4 5167 -119.24 78.50
sub.trial.number2 - sub.trial.number9 -253.152 50.4 5167 -352.02 -154.28
sub.trial.number2 - sub.trial.number10 -219.312 50.4 5167 -318.18 -120.44
sub.trial.number2 - sub.trial.number11 20.205 50.4 5167 -78.66 119.07
sub.trial.number2 - sub.trial.number12 4.491 50.4 5167 -94.38 103.36
sub.trial.number2 - sub.trial.number13 -377.723 50.4 5167 -476.59 -278.85
sub.trial.number2 - sub.trial.number14 -130.696 50.4 5167 -229.57 -31.83
sub.trial.number2 - sub.trial.number15 57.982 50.4 5167 -40.89 156.85
sub.trial.number2 - sub.trial.number16 21.125 50.4 5167 -77.74 119.99
sub.trial.number2 - sub.trial.number17 -24.786 50.4 5167 -123.66 74.08
sub.trial.number2 - sub.trial.number18 20.732 50.4 5167 -78.14 119.60
sub.trial.number3 - sub.trial.number4 -31.071 50.4 5167 -129.94 67.80
sub.trial.number3 - sub.trial.number5 -48.616 50.4 5167 -147.49 50.25
sub.trial.number3 - sub.trial.number6 -50.929 50.4 5167 -149.80 47.94
sub.trial.number3 - sub.trial.number7 -117.946 50.4 5167 -216.82 -19.08
sub.trial.number3 - sub.trial.number8 -5.955 50.4 5167 -104.82 92.91
sub.trial.number3 - sub.trial.number9 -238.741 50.4 5167 -337.61 -139.87
sub.trial.number3 - sub.trial.number10 -204.902 50.4 5167 -303.77 -106.03
sub.trial.number3 - sub.trial.number11 34.616 50.4 5167 -64.25 133.49
sub.trial.number3 - sub.trial.number12 18.902 50.4 5167 -79.97 117.77
sub.trial.number3 - sub.trial.number13 -363.312 50.4 5167 -462.18 -264.44
sub.trial.number3 - sub.trial.number14 -116.286 50.4 5167 -215.16 -17.42
sub.trial.number3 - sub.trial.number15 72.393 50.4 5167 -26.48 171.26
sub.trial.number3 - sub.trial.number16 35.536 50.4 5167 -63.33 134.41
sub.trial.number3 - sub.trial.number17 -10.375 50.4 5167 -109.24 88.49
sub.trial.number3 - sub.trial.number18 35.143 50.4 5167 -63.73 134.01
sub.trial.number4 - sub.trial.number5 -17.545 50.4 5167 -116.41 81.32
sub.trial.number4 - sub.trial.number6 -19.857 50.4 5167 -118.73 79.01
sub.trial.number4 - sub.trial.number7 -86.875 50.4 5167 -185.74 11.99
sub.trial.number4 - sub.trial.number8 25.116 50.4 5167 -73.75 123.99
sub.trial.number4 - sub.trial.number9 -207.670 50.4 5167 -306.54 -108.80
sub.trial.number4 - sub.trial.number10 -173.830 50.4 5167 -272.70 -74.96
sub.trial.number4 - sub.trial.number11 65.688 50.4 5167 -33.18 164.56
sub.trial.number4 - sub.trial.number12 49.973 50.4 5167 -48.90 148.84
sub.trial.number4 - sub.trial.number13 -332.241 50.4 5167 -431.11 -233.37
sub.trial.number4 - sub.trial.number14 -85.214 50.4 5167 -184.08 13.66
sub.trial.number4 - sub.trial.number15 103.464 50.4 5167 4.59 202.33
sub.trial.number4 - sub.trial.number16 66.607 50.4 5167 -32.26 165.48
sub.trial.number4 - sub.trial.number17 20.696 50.4 5167 -78.17 119.57
sub.trial.number4 - sub.trial.number18 66.214 50.4 5167 -32.66 165.08
sub.trial.number5 - sub.trial.number6 -2.312 50.4 5167 -101.18 96.56
sub.trial.number5 - sub.trial.number7 -69.330 50.4 5167 -168.20 29.54
sub.trial.number5 - sub.trial.number8 42.661 50.4 5167 -56.21 141.53
sub.trial.number5 - sub.trial.number9 -190.125 50.4 5167 -288.99 -91.26
sub.trial.number5 - sub.trial.number10 -156.286 50.4 5167 -255.16 -57.42
sub.trial.number5 - sub.trial.number11 83.232 50.4 5167 -15.64 182.10
sub.trial.number5 - sub.trial.number12 67.518 50.4 5167 -31.35 166.39
sub.trial.number5 - sub.trial.number13 -314.696 50.4 5167 -413.57 -215.83
sub.trial.number5 - sub.trial.number14 -67.670 50.4 5167 -166.54 31.20
sub.trial.number5 - sub.trial.number15 121.009 50.4 5167 22.14 219.88
sub.trial.number5 - sub.trial.number16 84.152 50.4 5167 -14.72 183.02
sub.trial.number5 - sub.trial.number17 38.241 50.4 5167 -60.63 137.11
sub.trial.number5 - sub.trial.number18 83.759 50.4 5167 -15.11 182.63
sub.trial.number6 - sub.trial.number7 -67.018 50.4 5167 -165.89 31.85
sub.trial.number6 - sub.trial.number8 44.973 50.4 5167 -53.90 143.84
sub.trial.number6 - sub.trial.number9 -187.812 50.4 5167 -286.68 -88.94
sub.trial.number6 - sub.trial.number10 -153.973 50.4 5167 -252.84 -55.10
sub.trial.number6 - sub.trial.number11 85.545 50.4 5167 -13.32 184.41
sub.trial.number6 - sub.trial.number12 69.830 50.4 5167 -29.04 168.70
sub.trial.number6 - sub.trial.number13 -312.384 50.4 5167 -411.25 -213.51
sub.trial.number6 - sub.trial.number14 -65.357 50.4 5167 -164.23 33.51
sub.trial.number6 - sub.trial.number15 123.321 50.4 5167 24.45 222.19
sub.trial.number6 - sub.trial.number16 86.464 50.4 5167 -12.41 185.33
sub.trial.number6 - sub.trial.number17 40.554 50.4 5167 -58.32 139.42
sub.trial.number6 - sub.trial.number18 86.071 50.4 5167 -12.80 184.94
sub.trial.number7 - sub.trial.number8 111.991 50.4 5167 13.12 210.86
sub.trial.number7 - sub.trial.number9 -120.795 50.4 5167 -219.66 -21.93
sub.trial.number7 - sub.trial.number10 -86.955 50.4 5167 -185.82 11.91
sub.trial.number7 - sub.trial.number11 152.562 50.4 5167 53.69 251.43
sub.trial.number7 - sub.trial.number12 136.848 50.4 5167 37.98 235.72
sub.trial.number7 - sub.trial.number13 -245.366 50.4 5167 -344.24 -146.50
sub.trial.number7 - sub.trial.number14 1.661 50.4 5167 -97.21 100.53
sub.trial.number7 - sub.trial.number15 190.339 50.4 5167 91.47 289.21
sub.trial.number7 - sub.trial.number16 153.482 50.4 5167 54.61 252.35
sub.trial.number7 - sub.trial.number17 107.571 50.4 5167 8.70 206.44
sub.trial.number7 - sub.trial.number18 153.089 50.4 5167 54.22 251.96
sub.trial.number8 - sub.trial.number9 -232.786 50.4 5167 -331.66 -133.92
sub.trial.number8 - sub.trial.number10 -198.946 50.4 5167 -297.82 -100.08
sub.trial.number8 - sub.trial.number11 40.571 50.4 5167 -58.30 139.44
sub.trial.number8 - sub.trial.number12 24.857 50.4 5167 -74.01 123.73
sub.trial.number8 - sub.trial.number13 -357.357 50.4 5167 -456.23 -258.49
sub.trial.number8 - sub.trial.number14 -110.330 50.4 5167 -209.20 -11.46
sub.trial.number8 - sub.trial.number15 78.348 50.4 5167 -20.52 177.22
sub.trial.number8 - sub.trial.number16 41.491 50.4 5167 -57.38 140.36
sub.trial.number8 - sub.trial.number17 -4.420 50.4 5167 -103.29 94.45
sub.trial.number8 - sub.trial.number18 41.098 50.4 5167 -57.77 139.97
sub.trial.number9 - sub.trial.number10 33.839 50.4 5167 -65.03 132.71
sub.trial.number9 - sub.trial.number11 273.357 50.4 5167 174.49 372.23
sub.trial.number9 - sub.trial.number12 257.643 50.4 5167 158.77 356.51
sub.trial.number9 - sub.trial.number13 -124.571 50.4 5167 -223.44 -25.70
sub.trial.number9 - sub.trial.number14 122.455 50.4 5167 23.59 221.32
sub.trial.number9 - sub.trial.number15 311.134 50.4 5167 212.26 410.00
sub.trial.number9 - sub.trial.number16 274.277 50.4 5167 175.41 373.15
sub.trial.number9 - sub.trial.number17 228.366 50.4 5167 129.50 327.24
sub.trial.number9 - sub.trial.number18 273.884 50.4 5167 175.01 372.75
sub.trial.number10 - sub.trial.number11 239.518 50.4 5167 140.65 338.39
sub.trial.number10 - sub.trial.number12 223.804 50.4 5167 124.93 322.67
sub.trial.number10 - sub.trial.number13 -158.411 50.4 5167 -257.28 -59.54
sub.trial.number10 - sub.trial.number14 88.616 50.4 5167 -10.25 187.49
sub.trial.number10 - sub.trial.number15 277.295 50.4 5167 178.43 376.16
sub.trial.number10 - sub.trial.number16 240.438 50.4 5167 141.57 339.31
sub.trial.number10 - sub.trial.number17 194.527 50.4 5167 95.66 293.40
sub.trial.number10 - sub.trial.number18 240.045 50.4 5167 141.18 338.91
sub.trial.number11 - sub.trial.number12 -15.714 50.4 5167 -114.58 83.16
sub.trial.number11 - sub.trial.number13 -397.929 50.4 5167 -496.80 -299.06
sub.trial.number11 - sub.trial.number14 -150.902 50.4 5167 -249.77 -52.03
sub.trial.number11 - sub.trial.number15 37.777 50.4 5167 -61.09 136.65
sub.trial.number11 - sub.trial.number16 0.920 50.4 5167 -97.95 99.79
sub.trial.number11 - sub.trial.number17 -44.991 50.4 5167 -143.86 53.88
sub.trial.number11 - sub.trial.number18 0.527 50.4 5167 -98.34 99.40
sub.trial.number12 - sub.trial.number13 -382.214 50.4 5167 -481.08 -283.34
sub.trial.number12 - sub.trial.number14 -135.188 50.4 5167 -234.06 -36.32
sub.trial.number12 - sub.trial.number15 53.491 50.4 5167 -45.38 152.36
sub.trial.number12 - sub.trial.number16 16.634 50.4 5167 -82.24 115.50
sub.trial.number12 - sub.trial.number17 -29.277 50.4 5167 -128.15 69.59
sub.trial.number12 - sub.trial.number18 16.241 50.4 5167 -82.63 115.11
sub.trial.number13 - sub.trial.number14 247.027 50.4 5167 148.16 345.90
sub.trial.number13 - sub.trial.number15 435.705 50.4 5167 336.84 534.57
sub.trial.number13 - sub.trial.number16 398.848 50.4 5167 299.98 497.72
sub.trial.number13 - sub.trial.number17 352.938 50.4 5167 254.07 451.81
sub.trial.number13 - sub.trial.number18 398.455 50.4 5167 299.59 497.32
sub.trial.number14 - sub.trial.number15 188.679 50.4 5167 89.81 287.55
sub.trial.number14 - sub.trial.number16 151.821 50.4 5167 52.95 250.69
sub.trial.number14 - sub.trial.number17 105.911 50.4 5167 7.04 204.78
sub.trial.number14 - sub.trial.number18 151.429 50.4 5167 52.56 250.30
sub.trial.number15 - sub.trial.number16 -36.857 50.4 5167 -135.73 62.01
sub.trial.number15 - sub.trial.number17 -82.768 50.4 5167 -181.64 16.10
sub.trial.number15 - sub.trial.number18 -37.250 50.4 5167 -136.12 61.62
sub.trial.number16 - sub.trial.number17 -45.911 50.4 5167 -144.78 52.96
sub.trial.number16 - sub.trial.number18 -0.393 50.4 5167 -99.26 98.48
sub.trial.number17 - sub.trial.number18 45.518 50.4 5167 -53.35 144.39
t.ratio p.value
7.056 <.0001
6.770 <.0001
6.154 <.0001
5.806 <.0001
5.760 <.0001
4.431 <.0001
6.652 <.0001
2.036 0.0418
2.707 0.0068
7.457 <.0001
7.145 <.0001
-0.434 0.6645
4.464 <.0001
8.206 <.0001
7.475 <.0001
6.564 <.0001
7.467 <.0001
-0.286 0.7751
-0.902 0.3672
-1.250 0.2115
-1.296 0.1952
-2.624 0.0087
-0.404 0.6864
-5.020 <.0001
-4.349 <.0001
0.401 0.6887
0.089 0.9290
-7.490 <.0001
-2.591 0.0096
1.150 0.2503
0.419 0.6753
-0.491 0.6231
0.411 0.6810
-0.616 0.5379
-0.964 0.3351
-1.010 0.3126
-2.339 0.0194
-0.118 0.9060
-4.734 <.0001
-4.063 <.0001
0.686 0.4925
0.375 0.7078
-7.204 <.0001
-2.306 0.0212
1.435 0.1512
0.705 0.4811
-0.206 0.8370
0.697 0.4859
-0.348 0.7279
-0.394 0.6938
-1.723 0.0850
0.498 0.6185
-4.118 <.0001
-3.447 0.0006
1.302 0.1928
0.991 0.3218
-6.588 <.0001
-1.690 0.0912
2.052 0.0403
1.321 0.1867
0.410 0.6815
1.313 0.1893
-0.046 0.9634
-1.375 0.1693
0.846 0.3977
-3.770 0.0002
-3.099 0.0020
1.650 0.0989
1.339 0.1807
-6.240 <.0001
-1.342 0.1797
2.399 0.0165
1.669 0.0953
0.758 0.4483
1.661 0.0968
-1.329 0.1840
0.892 0.3726
-3.724 0.0002
-3.053 0.0023
1.696 0.0899
1.385 0.1662
-6.194 <.0001
-1.296 0.1951
2.445 0.0145
1.714 0.0865
0.804 0.4214
1.707 0.0879
2.221 0.0264
-2.395 0.0166
-1.724 0.0847
3.025 0.0025
2.713 0.0067
-4.865 <.0001
0.033 0.9737
3.774 0.0002
3.043 0.0024
2.133 0.0330
3.036 0.0024
-4.616 <.0001
-3.945 0.0001
0.804 0.4212
0.493 0.6221
-7.086 <.0001
-2.188 0.0287
1.554 0.1204
0.823 0.4107
-0.088 0.9302
0.815 0.4152
0.671 0.5023
5.420 <.0001
5.109 <.0001
-2.470 0.0135
2.428 0.0152
6.169 <.0001
5.438 <.0001
4.528 <.0001
5.431 <.0001
4.749 <.0001
4.438 <.0001
-3.141 0.0017
1.757 0.0790
5.498 <.0001
4.767 <.0001
3.857 0.0001
4.760 <.0001
-0.312 0.7554
-7.890 <.0001
-2.992 0.0028
0.749 0.4539
0.018 0.9855
-0.892 0.3724
0.010 0.9917
-7.579 <.0001
-2.681 0.0074
1.061 0.2889
0.330 0.7415
-0.581 0.5616
0.322 0.7474
4.898 <.0001
8.639 <.0001
7.909 <.0001
6.998 <.0001
7.901 <.0001
3.741 0.0002
3.010 0.0026
2.100 0.0358
3.003 0.0027
-0.731 0.4649
-1.641 0.1008
-0.739 0.4602
-0.910 0.3627
-0.008 0.9938
0.903 0.3668
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 emm_18_df <- as.data.frame(emm_18) %>%
mutate(seq_length = "18", sub.trial.number = as.numeric(as.character(sub.trial.number)))emm_all <- bind_rows(emm_6_df, emm_12_df, emm_18_df) %>%
mutate(session = factor(session, labels = c("Block 4", "Block 5")))
plot_seq <- function(data, seq_len) {
ggplot(data %>% filter(seq_length == seq_len),
aes(x = sub.trial.number, y = emmean, color = session, group = session)) +
geom_point(size = 2) +
geom_line(linewidth = 0.9) +
geom_errorbar(aes(ymin = emmean - SE, ymax = emmean + SE), width = 0.2) +
scale_x_continuous(breaks = function(x) seq(floor(min(x)), ceiling(max(x)), by = 1)) +
labs(
title = paste0("RT – ", seq_len, "-step Sequences"),
x = "Step Number",
y = "Estimated RT (ms)"
) +
theme_minimal(base_size = 13) +
theme(panel.grid = element_blank(),
legend.title = element_blank())
}
plot_seq(emm_all, "6")
plot_seq(emm_all, "12")
plot_seq(emm_all, "18")