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.
#Root mean square
#Root mean square (RMS) of acceleration is an often-used value in gait analysis research to quantify the magnitude of body segment accelerations(Menz et al., 2003; Mizuike et al., 2009; Sekine et al., 2013; Senden et al., 2012). RMS can be easily computed with the raw accelerometer data and is seen as an uncomplicated approach to analyse the magnitude of accelerations in each axis(Mizuike et al., 2009; Sekine et al., 2013)). Although this study does not directly analyses gait performance, the movements performed in the ds-dsp task resemble walking movements and therefore it is seen as a suitable approach for the following analysis. In the present study, RMS of the center of mass acceleration is used to evaluate the movement characteristics across task phases and sequence lengths, providing insights into movement control and paired with its standard deviation movement variability.# -------- 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"
)1 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),
TrialInBlock = interaction(subject, Block, 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 | TrialInBlock)"))
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
cat("\nANOVA table for fixed effects:\n")
print(anova(model))
}
-----------------------------
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 0.09683 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 0.78329 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 6423 -3.547 0.0036
Block1 - Block3 -0.10350 0.0159 6423 -6.510 <.0001
Block1 - Block4 -0.06026 0.0137 6423 -4.408 0.0001
Block1 - Block5 -0.06273 0.0136 6423 -4.608 <.0001
Block2 - Block3 -0.05048 0.0164 6423 -3.085 0.0174
Block2 - Block4 -0.00724 0.0142 6423 -0.508 0.9866
Block2 - Block5 -0.00971 0.0142 6423 -0.685 0.9599
Block3 - Block4 0.04324 0.0152 6423 2.839 0.0367
Block3 - Block5 0.04077 0.0152 6423 2.685 0.0563
Block4 - Block5 -0.00247 0.0128 6423 -0.193 0.9997
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.05975 0.0149 6423 3.997 0.0006
Block1 - Block3 0.18845 0.0159 6423 11.854 <.0001
Block1 - Block4 0.11650 0.0137 6423 8.522 <.0001
Block1 - Block5 0.27007 0.0136 6423 19.838 <.0001
Block2 - Block3 0.12870 0.0164 6423 7.867 <.0001
Block2 - Block4 0.05675 0.0142 6423 3.986 0.0007
Block2 - Block5 0.21032 0.0142 6423 14.828 <.0001
Block3 - Block4 -0.07195 0.0152 6423 -4.723 <.0001
Block3 - Block5 0.08162 0.0152 6423 5.376 <.0001
Block4 - Block5 0.15357 0.0128 6423 11.973 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
ANOVA table for fixed effects:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 10.24 2.56 4 6423.6 38.998 < 2.2e-16 ***
phase 563.26 563.26 1 6423.0 8577.798 < 2.2e-16 ***
Block:phase 23.64 5.91 4 6423.0 89.993 < 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 6423 -3.740 0.0017
Block1 - Block3 -0.112259 0.0189 6423 -5.954 <.0001
Block1 - Block4 -0.058741 0.0162 6423 -3.623 0.0027
Block1 - Block5 -0.058438 0.0161 6423 -3.620 0.0028
Block2 - Block3 -0.045966 0.0194 6423 -2.369 0.1240
Block2 - Block4 0.007552 0.0169 6423 0.447 0.9917
Block2 - Block5 0.007855 0.0168 6423 0.467 0.9903
Block3 - Block4 0.053518 0.0181 6423 2.962 0.0255
Block3 - Block5 0.053820 0.0180 6423 2.989 0.0235
Block4 - Block5 0.000303 0.0152 6423 0.020 1.0000
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.058482 0.0177 6423 3.299 0.0086
Block1 - Block3 0.205943 0.0189 6423 10.923 <.0001
Block1 - Block4 0.132968 0.0162 6423 8.202 <.0001
Block1 - Block5 0.293955 0.0161 6423 18.207 <.0001
Block2 - Block3 0.147461 0.0194 6423 7.600 <.0001
Block2 - Block4 0.074486 0.0169 6423 4.411 0.0001
Block2 - Block5 0.235473 0.0168 6423 13.998 <.0001
Block3 - Block4 -0.072975 0.0181 6423 -4.039 0.0005
Block3 - Block5 0.088011 0.0180 6423 4.888 <.0001
Block4 - Block5 0.160986 0.0152 6423 10.583 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
ANOVA table for fixed effects:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 13.80 3.45 4 6423.7 37.343 < 2.2e-16 ***
phase 628.92 628.92 1 6423.0 6809.556 < 2.2e-16 ***
Block:phase 26.71 6.68 4 6423.0 72.292 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
-----------------------------
Axis: z boundary (singular) fit: see help('isSingular') Block phase emmean SE df lower.CL upper.CL
1 Preparation 0.0678 0.0646 20.2 -0.0669 0.203
2 Preparation 0.1726 0.0651 20.7 0.0371 0.308
3 Preparation 0.2492 0.0659 21.8 0.1125 0.386
4 Preparation 0.1635 0.0640 19.4 0.0296 0.297
5 Preparation 0.1609 0.0640 19.4 0.0272 0.295
1 Execution 1.4006 0.0646 20.2 1.2659 1.535
2 Execution 1.3898 0.0651 20.7 1.2543 1.525
3 Execution 1.1905 0.0659 21.8 1.0538 1.327
4 Execution 1.2873 0.0640 19.4 1.1534 1.421
5 Execution 1.0224 0.0640 19.4 0.8886 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 -0.10478 0.0286 6423 -3.663 0.0023
Block1 - Block3 -0.18139 0.0304 6423 -5.962 <.0001
Block1 - Block4 -0.09563 0.0262 6423 -3.656 0.0024
Block1 - Block5 -0.09312 0.0261 6423 -3.574 0.0033
Block2 - Block3 -0.07661 0.0313 6423 -2.447 0.1032
Block2 - Block4 0.00915 0.0273 6423 0.336 0.9973
Block2 - Block5 0.01166 0.0271 6423 0.430 0.9929
Block3 - Block4 0.08576 0.0292 6423 2.942 0.0271
Block3 - Block5 0.08828 0.0291 6423 3.038 0.0202
Block4 - Block5 0.00251 0.0245 6423 0.102 1.0000
phase = Execution:
contrast estimate SE df t.ratio p.value
Block1 - Block2 0.01088 0.0286 6423 0.380 0.9956
Block1 - Block3 0.21009 0.0304 6423 6.906 <.0001
Block1 - Block4 0.11334 0.0262 6423 4.333 0.0001
Block1 - Block5 0.37822 0.0261 6423 14.517 <.0001
Block2 - Block3 0.19921 0.0313 6423 6.363 <.0001
Block2 - Block4 0.10246 0.0273 6423 3.760 0.0016
Block2 - Block5 0.36734 0.0271 6423 13.532 <.0001
Block3 - Block4 -0.09675 0.0292 6423 -3.319 0.0081
Block3 - Block5 0.16813 0.0291 6423 5.786 <.0001
Block4 - Block5 0.26488 0.0245 6423 10.791 <.0001
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 5 estimates
ANOVA table for fixed effects:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 28.89 7.22 4 6423.6 30.027 < 2.2e-16 ***
phase 1839.64 1839.64 1 6423.0 7649.547 < 2.2e-16 ***
Block:phase 49.52 12.38 4 6423.0 51.479 < 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 #3. step wise RMS analysis and Difficulty comparison #3.1 6 steps Block 1,4 & 5
# --- 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
3.2 -0.1671991428
4.2 0.0840589302
5.2 -0.0272489593
7.2 -0.0093849254
8.2 -0.3098901263
10.2 0.2445621236
11.2 -0.1726072429
13.2 0.0349961870
14.2 -0.1113606675
15.2 0.2560216920
16.2 -0.0105412199
17.2 0.0158435567
18.2 -0.3014491414
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
14.3 -0.1125153613
15.3 0.1121603029
16.3 0.0477317826
17.3 -0.1204963768
18.3 0.0264114170
19.3 -0.0062586830
22.3 0.0634685103
23.3 0.0127806815
2.4 -0.2108775310
3.4 -0.1515624121
4.4 -0.0532072369
5.4 -0.0058353467
7.4 -0.1913619731
8.4 -0.2178064043
10.4 -0.4698513704
11.4 -0.4775652851
13.4 0.0394805740
14.4 0.1157207475
15.4 0.1997862197
16.4 -0.0982597779
17.4 -0.0915791656
18.4 -0.0962530786
19.4 0.1317614630
20.4 -0.1115260795
22.4 0.1725189791
23.4 -0.0772204817
2.5 -0.0053147333
3.5 0.0278462145
4.5 -0.0712078149
5.5 -0.0319068216
7.5 -0.0601610989
8.5 -0.2081448562
10.5 -0.3901011094
11.5 -0.5040226684
13.5 -0.0349908994
14.5 0.1809234646
15.5 0.1371233345
16.5 -0.0903140910
17.5 0.1274249313
18.5 -0.0699732385
19.5 -0.1583602249
20.5 -0.1568036544
22.5 -0.0667260336
23.5 -0.2116332830
2.6 -0.0136826981
3.6 0.0040040266
4.6 -0.0370470482
5.6 -0.0165190802
7.6 0.1346135815
8.6 0.1919760965
10.6 0.0727777418
11.6 0.0286932495
13.6 0.0793052692
14.6 0.0664008446
15.6 0.1373489634
16.6 0.0364559443
17.6 -0.2207002446
18.6 -0.0935419592
19.6 -0.0217620692
20.6 -0.0754658532
22.6 0.0481480569
23.6 0.0274854824
2.7 -0.0563742988
3.7 0.0819953948
4.7 -0.0175268584
5.7 -0.1361321718
7.7 0.1304425743
8.7 -0.1661622149
10.7 -0.2502992808
11.7 0.0805977911
13.7 -0.0202435879
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15.7 0.0139673332
16.7 0.1075444065
17.7 -0.0500113096
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19.7 0.0700799083
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22.7 -0.0904059356
23.7 0.3310065258
2.8 -0.1876581233
3.8 0.0447738638
4.8 0.1720205797
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7.8 0.0338277742
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10.8 0.3651378486
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16.8 0.0527220093
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20.8 0.0268527665
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2.9 -0.1503064715
3.9 0.2188944543
4.9 -0.0894039782
5.9 -0.0430642176
7.9 -0.2316201204
8.9 -0.2770739116
10.9 0.1282263278
11.9 0.0092995955
13.9 -0.1193505853
14.9 -0.0658660700
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17.9 -0.0515088410
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19.9 0.0836375092
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22.9 0.0267231199
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2.10 -0.1475801969
3.10 0.3233484664
4.10 0.0503739670
5.10 -0.0490087151
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10.10 0.3558932232
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14.10 0.1367017467
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18.10 0.0380882803
19.10 0.1433064625
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22.10 0.2201194044
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2.11 0.3318366394
3.11 0.0663996889
4.11 0.0285237005
5.11 -0.0501558025
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10.11 0.4049274235
11.11 0.0784171327
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14.11 0.0015227541
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20.11 0.0846239862
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2.12 0.0902404110
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5.12 -0.0098248194
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13.12 0.0350174135
14.12 0.0370965146
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18.12 -0.0587881106
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22.12 0.0372140237
23.12 0.1383137538
2.13 0.0479691556
3.13 0.0919016236
4.13 -0.0489711287
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7.13 -0.1038983566
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13.13 0.0160230858
14.13 0.0977784949
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19.13 0.0023689690
20.13 0.2281982278
22.13 -0.0313518911
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2.14 -0.1089657986
3.14 0.0356337375
4.14 -0.0170156649
5.14 -0.0997473726
7.14 -0.0162800611
8.14 0.0062217642
10.14 0.2481914834
11.14 0.0471107913
13.14 -0.0636379863
14.14 -0.1411166199
15.14 -0.1856605207
16.14 -0.0907871562
17.14 0.2118912921
18.14 -0.0649949019
19.14 0.1833268349
20.14 -0.0278250233
22.14 -0.0129618816
23.14 0.4265270483
2.15 -0.0310321276
3.15 -0.1255453464
4.15 -0.0370206198
5.15 0.0114209252
7.15 -0.0637963221
8.15 -0.2827883897
10.15 0.0285703992
11.15 -0.2100021391
13.15 0.1570660793
14.15 -0.2823610579
15.15 -0.0039585043
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20.15 0.0549166059
22.15 0.1084516134
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2.16 0.0138862982
3.16 -0.0470287604
4.16 0.0041432204
5.16 0.0224206926
7.16 0.0062018726
8.16 -0.2181449499
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23.17 0.5883923499
2.18 -0.1072072553
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7.18 0.0451657504
8.18 0.7128053000
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3.19 0.1316410153
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7.20 -0.1145734053
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10.20 0.0004379728
11.20 -0.3851125042
13.20 -0.1625353659
14.20 -0.1129034951
15.20 0.0059847033
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17.20 -0.0288660914
18.20 0.0276082916
19.20 -0.0473335682
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22.20 -0.1153716344
23.20 0.4447624368
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3.21 -0.1578967809
4.21 0.1846219034
5.21 -0.0913180412
7.21 -0.0894921250
8.21 0.2520624519
10.21 0.2795877088
11.21 -0.3641344426
13.21 -0.0408792425
14.21 -0.0334263813
15.21 -0.0751491596
16.21 0.0310086273
17.21 0.0008318191
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22.21 0.1019493499
23.21 0.0823669039
2.22 -0.2304788558
3.22 -0.1535617795
4.22 0.0383224618
5.22 0.0867338426
7.22 0.0208645865
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20.23 0.1117132194
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2.24 0.0098183320
3.24 0.1136220695
4.24 0.0536950073
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13.25 0.0265340614
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16.25 0.0491645057
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20.25 0.0050710228
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7.27 0.0675901264
8.27 1.1501790442
10.27 0.3389440563
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3.29 0.0182326468
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5.29 -0.0607642276
7.29 0.0517348075
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11.29 0.0817158392
13.29 0.3117846855
14.29 0.0832203001
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22.29 0.0118450337
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3.30 0.1780344820
4.30 -0.0664466638
5.30 0.0062434184
7.30 0.1030836762
8.30 0.0324831350
10.30 0.3965182061
11.30 0.5071631396
13.30 0.0041561995
14.30 0.0816095035
15.30 -0.0279950062
16.30 0.5190248311
17.30 0.1977070333
18.30 0.2637680269
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22.30 -0.0830985418
23.30 -0.1278287480
2.31 -0.0887935897
3.31 -0.0006673297
4.31 -0.0745864012
5.31 -0.0470061028
7.31 -0.0188602404
8.31 0.1205741965
10.31 0.3533753374
11.31 0.3411727000
13.31 -0.0546407249
14.31 0.1542977736
15.31 -0.1768275461
16.31 0.1969176557
17.31 0.0206024540
18.31 0.0902199150
19.31 -0.0654602229
20.31 -0.0025888289
22.31 -0.0149241618
23.31 0.0916750854
2.32 -0.0710196667
3.32 0.0687231806
4.32 0.1166260791
5.32 -0.0506704971
7.32 0.1113436462
8.32 0.4584114321
10.32 -0.0140336260
11.32 0.3624978988
13.32 -0.0715313829
14.32 -0.0819111893
15.32 0.5812305560
16.32 0.1147941913
17.32 0.0063407279
18.32 -0.0188982605
19.32 -0.0665468900
20.32 0.0189212533
22.32 0.0620300447
23.32 0.8829171291
2.33 -0.1291092769
3.33 -0.1701510418
4.33 -0.0352067015
5.33 0.0029834502
7.33 -0.0194729429
8.33 0.0677425203
10.33 0.8326449602
11.33 0.7345084275
13.33 0.1413648710
14.33 -0.1292743610
15.33 0.0330235167
16.33 0.0687152312
17.33 -0.0245632514
18.33 -0.0356465658
19.33 -0.1311661848
20.33 0.1854833329
22.33 0.0672488423
23.33 -0.2731100127
2.34 0.0289262966
3.34 0.0397096291
4.34 0.1130909543
5.34 0.2549985401
7.34 0.0439430113
8.34 -0.0626014254
10.34 0.7621541101
11.34 0.5195858867
13.34 0.2723114666
14.34 -0.0804284529
15.34 0.0199700737
16.34 0.2348870941
17.34 0.1033754450
18.34 -0.2171221455
19.34 -0.0488430338
20.34 0.1713999443
22.34 0.0959851564
23.34 -0.1910400913
2.35 0.0204540631
3.35 -0.0207958880
4.35 -0.1516115575
5.35 0.0037015298
7.35 0.1821805154
8.35 0.1222448714
10.35 0.1397204386
11.35 0.1473663067
13.35 0.0631240919
14.35 0.2026872596
15.35 -0.1575833133
16.35 0.1237953526
17.35 0.0148452216
18.35 0.0207312204
19.35 -0.0313711225
20.35 -0.0024722693
22.35 0.0367229676
23.35 -0.4266207460
2.36 0.1976316246
3.36 0.0551866534
4.36 0.0947837958
5.36 -0.0797259800
7.36 0.1014065188
8.36 -0.0058315012
10.36 -0.2677776404
11.36 0.3577614211
13.36 0.2147559080
14.36 0.2797418957
15.36 0.0444377217
16.36 0.2237485973
17.36 0.2702899569
18.36 -0.0881239466
19.36 0.1621286231
20.36 0.0170894875
22.36 0.1297813818
23.36 0.3626002307
2.37 0.1503802705
3.37 -0.0889889782
4.37 0.0079685862
5.37 -0.0433495187
7.37 0.1790644619
8.37 0.0880009198
10.37 -0.0304923454
11.37 -0.0111892102
13.37 -0.2346330214
14.37 0.2033326275
15.37 -0.0105737177
16.37 0.1879408590
17.37 0.0453884770
18.37 -0.0706900862
19.37 -0.0634691343
20.37 -0.1054133932
22.37 -0.0207091368
23.37 0.0385238975
2.38 0.4262476367
3.38 0.1505283741
4.38 -0.0852099208
5.38 -0.1097981715
7.38 -0.1579772790
8.38 -0.0146485941
10.38 -0.5253500316
11.38 0.1106903555
13.38 -0.2354407873
14.38 0.1577397721
15.38 -0.1029349239
16.38 -0.0992370588
17.38 0.1208171406
18.38 -0.0693234998
19.38 0.1839290461
20.38 -0.0936776119
22.38 -0.0666373262
23.38 -0.1499105042
2.39 1.1401044300
3.39 0.0561797587
4.39 -0.1351763855
5.39 0.0222744796
7.39 -0.1008850145
8.39 -0.3402674796
10.39 -0.0760019469
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
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3.40 2.571848e-01
4.40 2.477936e-01
5.40 2.926763e-03
7.40 -4.227186e-01
8.40 1.922108e-01
10.40 -4.167169e-01
11.40 1.106394e+00
13.40 -1.023160e+00
14.40 7.781499e-02
15.40 -4.216507e-01
16.40 1.657891e-01
17.40 3.252859e-01
18.40 4.197009e-01
19.40 -1.301005e-01
20.40 -1.194646e-02
22.40 -1.745729e-01
23.40 3.562989e-02
2.41 2.263375e-01
3.41 1.535321e-02
4.41 -2.829009e-03
5.41 2.772282e-02
7.41 -4.477450e-01
8.41 -7.335962e-01
10.41 -1.880667e+00
11.41 -5.968171e-01
13.41 -9.721078e-01
14.41 -9.079569e-02
15.41 2.811367e-01
16.41 -1.290724e-01
17.41 1.128712e-02
18.41 6.299503e-01
19.41 -4.417408e-03
20.41 -1.058524e-03
22.41 -3.136854e-03
23.41 -3.020288e-01
2.42 6.973404e-03
3.42 4.507341e-01
4.42 1.228680e-01
5.42 3.360594e-01
7.42 -2.097632e-01
8.42 7.954175e-01
10.42 -8.615449e-01
11.42 -8.575679e-01
13.42 -1.108396e+00
14.42 2.958513e-01
15.42 -4.213407e-01
16.42 7.289382e-02
17.42 -2.466091e-01
18.42 -5.147511e-02
19.42 9.222583e-02
20.42 -7.466975e-02
22.42 1.173063e-01
23.42 -7.341554e-01
2.43 1.303708e-02
3.43 -4.978391e-01
4.43 -3.135135e-01
5.43 1.282683e-01
7.43 -4.339483e-01
8.43 -6.331264e-01
10.43 -1.019275e+00
11.43 -9.206275e-02
13.43 -1.042176e+00
14.43 3.921767e-02
15.43 2.886497e-01
16.43 -1.589483e-02
17.43 -2.078898e-01
18.43 -1.682711e-01
19.43 -1.183684e-01
20.43 5.110050e-01
22.43 -2.618663e-01
23.43 -3.493532e-01
2.44 -7.027992e-01
3.44 2.531621e-01
4.44 4.285720e-01
5.44 5.955837e-02
7.44 -5.931051e-01
8.44 -6.394728e-01
10.44 -1.017606e+00
11.44 2.806301e-01
13.44 -1.936346e-01
14.44 -4.359391e-01
15.44 -3.621063e-01
16.44 -2.158879e-01
17.44 3.161099e-03
18.44 3.448711e-01
19.44 7.574989e-02
20.44 -2.284181e-01
22.44 -2.692724e-01
23.44 -1.649336e-01
2.45 6.291565e-02
3.45 2.849142e-01
4.45 7.938436e-02
5.45 3.389282e-02
7.45 -3.782864e-01
8.45 -1.067031e+00
10.45 -1.396054e+00
11.45 -7.341349e-01
13.45 -4.776445e-01
14.45 -2.821107e-01
15.45 -4.804285e-02
16.45 -2.745234e-02
17.45 1.602162e-01
18.45 -5.019158e-02
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#3.2 12 steps Block 2,4 & 5
# --- 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
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18.40 -1.483313e-02
19.40 3.291512e-02
20.40 -7.599283e-02
22.40 1.949805e-01
23.40 -3.425731e-01
2.41 2.724224e-01
3.41 -1.753693e-01
4.41 2.602195e-02
5.41 1.600585e-01
7.41 1.523877e-02
8.41 -2.302760e-01
10.41 -1.193203e+00
11.41 -1.380318e-01
13.41 -1.810715e-01
14.41 -6.070735e-02
15.41 1.340019e-02
16.41 -5.173318e-02
17.41 6.615731e-02
18.41 1.975066e-01
19.41 1.728263e-01
20.41 -7.818691e-02
22.41 -6.345192e-03
23.41 1.916161e-01
2.42 2.043420e-01
3.42 -8.225178e-02
4.42 -8.918268e-02
5.42 9.751589e-02
7.42 6.882531e-02
8.42 -8.471967e-02
10.42 -9.386470e-01
11.42 -4.561624e-01
13.42 -3.384406e-01
14.42 4.819912e-01
15.42 -2.914724e-01
16.42 8.238830e-02
17.42 -8.102148e-02
18.42 2.800659e-01
19.42 6.973439e-02
20.42 7.539102e-02
22.42 9.491278e-03
23.42 -2.185760e-01
2.43 -3.353268e-01
3.43 1.549182e-01
4.43 -1.391707e-01
5.43 6.352833e-02
7.43 -8.798918e-02
8.43 -6.139329e-01
10.43 -3.319159e-01
11.43 -1.134726e-01
13.43 -3.702428e-01
14.43 -2.819937e-02
15.43 -1.487703e-01
16.43 -9.283657e-02
17.43 -2.785466e-01
18.43 3.652876e-02
19.43 3.326068e-02
20.43 2.764662e-02
22.43 -3.294515e-01
23.43 -2.081508e-01
2.44 -3.949549e-01
3.44 -1.104208e-01
4.44 -5.911769e-02
5.44 8.357683e-03
7.44 8.678449e-02
8.44 -6.618380e-02
10.44 -2.741549e-01
11.44 -1.567536e-01
13.44 -2.794608e-01
14.44 -1.926346e-01
15.44 -9.570308e-02
16.44 -5.824601e-02
17.44 4.640851e-02
18.44 6.146800e-01
19.44 2.228497e-02
20.44 8.448140e-03
22.44 -2.735694e-01
23.44 -1.671452e-01
2.45 -1.619930e-01
3.45 -1.835070e-02
4.45 -3.118473e-01
5.45 -7.427762e-02
7.45 -3.400812e-01
8.45 3.615117e-01
10.45 -8.598205e-01
11.45 -5.752664e-01
13.45 -5.761135e-02
14.45 -2.726633e-01
15.45 3.788120e-03
16.45 -2.405106e-01
17.45 -2.247451e-01
18.45 2.600418e-01
19.45 2.545691e-02
20.45 2.092703e-02
22.45 -3.928135e-01
23.45 -3.995642e-01
2.46 -1.066826e-01
3.46 -1.968958e-01
4.46 1.612042e-01
5.46 -1.407436e-01
7.46 -2.863495e-01
8.46 -5.789390e-01
10.46 -7.718879e-01
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
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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#3.3 18 steps Block 3,4 & 5
# --- 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
4.4 -0.0445124809
5.4 -0.0696108386
7.4 0.0655377774
8.4 -0.0679583229
10.4 -0.5528066937
11.4 0.4065030907
13.4 -0.0585275635
14.4 0.0049387956
15.4 -0.0996057731
16.4 -0.0980298405
17.4 -0.0157438445
18.4 0.0629668981
19.4 0.0362435524
20.4 -0.0318853389
22.4 0.0533008415
23.4 0.0135581937
2.5 0.1775734801
3.5 0.1026554590
4.5 0.0303931514
5.5 -0.0960711059
7.5 0.0320622511
8.5 -0.0987490195
10.5 0.2625748870
11.5 -0.0736469376
13.5 0.0030869089
14.5 0.1510275829
15.5 0.0788968232
16.5 -0.0381116625
17.5 0.0247488300
18.5 0.1181053285
19.5 -0.1119334609
20.5 -0.0503565415
22.5 0.0801567265
23.5 0.0615228083
2.6 -0.0988054049
3.6 -0.1478938183
4.6 -0.0062006137
5.6 0.0045113970
7.6 0.0904424549
8.6 0.3754190817
10.6 0.2733997314
11.6 0.1888009990
13.6 0.0642362413
14.6 -0.0153983719
15.6 -0.0347718444
16.6 -0.0370876013
17.6 0.0190558941
18.6 0.1930571318
19.6 -0.0359876542
20.6 -0.0554865633
22.6 0.0496147255
23.6 0.2206752902
2.7 -0.1066229759
3.7 0.1222971990
4.7 0.0391776538
5.7 0.0288402600
7.7 0.0556613829
8.7 0.0951052000
10.7 0.4334661309
11.7 0.1203734532
13.7 0.0727584533
14.7 0.1257940664
15.7 0.0082939903
16.7 0.0355076429
17.7 -0.0054677591
18.7 0.1452634143
19.7 -0.0062423151
20.7 -0.0083351181
22.7 -0.0294852470
23.7 0.0896790507
2.8 -0.0457373212
3.8 0.1198355995
4.8 0.0358688902
5.8 -0.0360747809
7.8 0.0151517825
8.8 0.0659593797
10.8 0.0228868849
11.8 -0.2306445510
13.8 0.0935361060
14.8 -0.1616986122
15.8 -0.1578188304
16.8 -0.0367554227
17.8 0.0401319978
18.8 -0.1465350496
19.8 0.0857492268
20.8 -0.0440761713
22.8 0.0325499060
23.8 0.0505129369
2.9 -0.1787202682
3.9 0.0227875616
4.9 0.0264346304
5.9 -0.0551095236
7.9 0.0424150401
8.9 -0.0743711928
10.9 0.4961496128
11.9 -0.0366106026
13.9 -0.0798629303
14.9 -0.1054741770
15.9 0.0092968179
16.9 -0.0774317677
17.9 -0.0268693953
18.9 -0.2628901321
19.9 0.0203443419
20.9 -0.0358903365
22.9 0.0431289626
23.9 0.0252293967
2.10 -0.1567536328
3.10 -0.0752308156
4.10 0.0781817020
5.10 -0.0511137430
7.10 -0.0655559641
8.10 -0.0334378201
10.10 0.1324004259
11.10 0.0994136676
13.10 -0.0357894239
14.10 0.0336775513
15.10 -0.0426576282
16.10 -0.0583246880
17.10 -0.0437114137
18.10 0.0279850879
19.10 0.0631842977
20.10 0.0827982245
22.10 0.0780199498
23.10 -0.1340493119
2.11 0.0057821815
3.11 0.0209844017
4.11 -0.0191059039
5.11 0.0702343549
7.11 -0.0952531731
8.11 0.0343376996
10.11 0.2379147358
11.11 -0.1610510959
13.11 -0.0620528758
14.11 -0.1552191606
15.11 -0.0921602318
16.11 0.0027125196
17.11 -0.0347118337
18.11 0.0347029667
19.11 -0.0050665431
20.11 -0.0114874628
22.11 0.0774560088
23.11 -0.0890245343
2.12 0.0402539028
3.12 0.0937993927
4.12 0.1012174521
5.12 0.0004101190
7.12 -0.0209477803
8.12 0.3287995373
10.12 0.0341428452
11.12 -0.1480413095
13.12 0.1512877013
14.12 0.0166312154
15.12 0.0119443534
16.12 -0.1818310859
17.12 -0.0328942624
18.12 -0.1456310142
19.12 0.0770394790
20.12 -0.0248439211
22.12 0.0042608475
23.12 -0.0458354744
2.13 -0.0673909755
3.13 0.1337820990
4.13 -0.0103304635
5.13 0.0004586019
7.13 -0.0283205652
8.13 0.0507144819
10.13 0.2481621542
11.13 -0.0457868000
13.13 -0.0336627815
14.13 0.0904777108
15.13 -0.1113613665
16.13 -0.0980781574
17.13 -0.0229732667
18.13 0.1150960506
19.13 0.0211864715
20.13 0.1093987693
22.13 0.0468152756
23.13 0.0179611522
2.14 0.0481260010
3.14 0.1416294632
4.14 -0.0376397587
5.14 -0.0350755561
7.14 0.0503115827
8.14 0.4279091370
10.14 0.4344549996
11.14 0.0632995442
13.14 -0.0783386395
14.14 -0.0808186481
15.14 -0.0500230986
16.14 -0.0647729426
17.14 0.0901778856
18.14 -0.1351119229
19.14 0.0271360887
20.14 0.0510954426
22.14 0.0135845256
23.14 -0.0534339355
2.15 0.0556293489
3.15 0.0562929750
4.15 -0.0353064049
5.15 -0.0066327895
7.15 -0.0340612531
8.15 -0.0659393605
10.15 0.5978540418
11.15 -0.0578125935
13.15 0.1057722120
14.15 -0.0963149713
15.15 -0.0758408364
16.15 -0.0913184245
17.15 0.0758743366
18.15 0.2014106907
19.15 -0.0951635615
20.15 0.0699253436
22.15 0.0984044828
23.15 0.0003736060
2.16 -0.1055172606
3.16 0.0745826742
4.16 -0.1360810011
5.16 -0.0283439999
7.16 0.0196851267
8.16 -0.0571042662
10.16 0.1709448453
11.16 0.0588134514
13.16 0.1042807730
14.16 -0.0056992534
15.16 0.0093881387
16.16 -0.0975128660
17.16 -0.0370843935
18.16 0.0344717102
19.16 -0.0396792302
20.16 -0.0118981841
22.16 0.0213328664
23.16 -0.0654956641
2.17 -0.0287406740
3.17 -0.1009769659
4.17 0.1016929734
5.17 0.0451185172
7.17 -0.0806213001
8.17 0.4764924250
10.17 0.6642988868
11.17 -0.0260388562
13.17 0.0510942881
14.17 0.1316991562
15.17 0.0401113838
16.17 -0.1773481314
17.17 -0.0178374390
18.17 -0.0243519092
19.17 -0.0036452292
20.17 -0.0149546725
22.17 0.0653844702
23.17 -0.0816930322
2.18 0.3235274186
3.18 -0.1007058699
4.18 0.0193038143
5.18 0.0777759803
7.18 0.0225049211
8.18 0.1544417940
10.18 0.6983667269
11.18 -0.1184862525
13.18 0.0019690570
14.18 -0.2006014522
15.18 0.0090217665
16.18 -0.0867586035
17.18 0.1129099001
18.18 0.0955011262
19.18 -0.0025974868
20.18 -0.0045064669
22.18 0.0591448069
23.18 -0.2106539508
2.19 -0.1620705479
3.19 0.1796557497
4.19 -0.0223008136
5.19 -0.0100444157
7.19 0.2690921274
8.19 -0.1601049158
10.19 0.5101868473
11.19 0.5610625339
13.19 0.1709263343
14.19 0.0738375690
15.19 -0.0004553561
16.19 -0.0122317959
17.19 -0.0884163789
18.19 0.0888683437
19.19 -0.0963521105
20.19 -0.0129101492
22.19 -0.0314669166
23.19 0.0303067527
2.20 -0.2731002402
3.20 0.1190463912
4.20 0.0387500951
5.20 -0.0307158689
7.20 -0.0770472348
8.20 -0.1418717071
10.20 0.3583477315
11.20 -0.1590512195
13.20 0.0914703912
14.20 0.0350202898
15.20 -0.1574020582
16.20 -0.0563938248
17.20 0.0038863205
18.20 0.0646677932
19.20 0.0519489056
20.20 0.0624562737
22.20 0.0069426583
23.20 -0.1312614895
2.21 0.3161488915
3.21 -0.0089799440
4.21 0.0679352199
5.21 -0.0426661423
7.21 0.2919168059
8.21 0.3596067650
10.21 0.4656768137
11.21 -0.1698370421
13.21 0.2109996908
14.21 -0.0009395571
15.21 -0.0004883510
16.21 0.0879895457
17.21 0.0289618865
18.21 -0.0420235694
19.21 0.0047429358
20.21 0.0016144418
22.21 0.2084769086
23.21 -0.1750550861
2.22 -0.0292113648
3.22 -0.1352183675
4.22 0.0160208410
5.22 0.0668762275
7.22 0.0922931255
8.22 0.2103000570
10.22 0.3460389188
11.22 0.3649366142
13.22 0.0871112992
14.22 0.0593789697
15.22 -0.0221205306
16.22 0.1545185639
17.22 0.1020683966
18.22 0.1871278265
19.22 0.0004311631
20.22 -0.0184123129
22.22 -0.0079950330
23.22 -0.0273171925
2.23 0.0067472108
3.23 0.0270251398
4.23 0.0942545031
5.23 0.0142091696
7.23 -0.0026310965
8.23 0.3599791805
10.23 0.4873705152
11.23 -0.1335071595
13.23 -0.0284439659
14.23 -0.0411318636
15.23 -0.0072515205
16.23 0.2501425985
17.23 0.1266619245
18.23 -0.1943343627
19.23 -0.0385741431
20.23 -0.0127725113
22.23 -0.0539004547
23.23 -0.0386140474
2.24 -0.0975918631
3.24 0.1921792759
4.24 0.0146794941
5.24 0.0219450842
7.24 -0.0348018817
8.24 0.0696692655
10.24 0.2899205047
11.24 -0.2045172834
13.24 0.1022621000
14.24 0.0579313181
15.24 -0.0361632922
16.24 0.2420902794
17.24 0.1283004172
18.24 0.0282218958
19.24 0.0295397660
20.24 0.0865854341
22.24 -0.0162227360
23.24 0.0619940250
2.25 0.2100035354
3.25 0.0435826362
4.25 -0.0686192778
5.25 -0.0216648846
7.25 -0.0512532479
8.25 0.0734951264
10.25 0.0632768994
11.25 0.2591095233
13.25 0.1262403466
14.25 -0.0249431319
15.25 -0.1285910992
16.25 0.1602732192
17.25 0.0501386833
18.25 0.0732009191
19.25 -0.0091115152
20.25 -0.0429402682
22.25 0.0832377231
23.25 0.2660924103
2.26 0.1983983559
3.26 -0.0057389268
4.26 -0.0585141646
5.26 0.2140005765
7.26 -0.0872965284
8.26 0.4756923230
10.26 0.4814401717
11.26 0.1262495544
13.26 0.1656336507
14.26 0.1783808641
15.26 0.0732811982
16.26 -0.0023343948
17.26 0.0954484675
18.26 0.2461895254
19.26 -0.0183823254
20.26 0.0416108133
22.26 0.0924194121
23.26 0.0868006964
2.27 0.2624029449
3.27 -0.0621919372
4.27 -0.0474558185
5.27 0.1576004991
7.27 0.1724222165
8.27 0.5701035891
10.27 0.1164023993
11.27 -0.0195224473
13.27 0.2265717209
14.27 0.0631369122
15.27 -0.0531785280
16.27 0.2130666842
17.27 0.1058844064
18.27 0.0832070535
19.27 -0.0467721994
20.27 -0.0211086100
22.27 -0.0113488325
23.27 0.1725869803
2.28 0.0090445071
3.28 -0.0579692865
4.28 -0.0681010653
5.28 0.1471827996
7.28 -0.0482124765
8.28 0.6254185648
10.28 -0.2287497242
11.28 -0.1206582865
13.28 0.3343245047
14.28 -0.1717922474
15.28 0.0174422999
16.28 0.2440172675
17.28 0.4115202572
18.28 0.0471696596
19.28 0.0204467330
20.28 -0.0028410238
22.28 -0.0824351594
23.28 0.1465168020
2.29 0.3375838611
3.29 0.1673468233
4.29 0.0682899860
5.29 0.0149884623
7.29 0.1047624835
8.29 -0.0330028365
10.29 0.1191704644
11.29 0.2920364194
13.29 0.2466777170
14.29 0.0348677634
15.29 -0.0483899168
16.29 0.2718402730
17.29 0.0970637175
18.29 -0.2231944347
19.29 0.0874054180
20.29 0.0324491051
22.29 0.1123340647
23.29 -0.2365015759
2.30 0.0951179816
3.30 0.2313829129
4.30 -0.0078200382
5.30 0.0252556684
7.30 0.0618838281
8.30 -0.1329220028
10.30 -0.2775101271
11.30 0.3891087327
13.30 0.0335408123
14.30 0.0581993597
15.30 0.1069220946
16.30 0.2722765701
17.30 0.0143269421
18.30 0.2064470760
19.30 -0.0907345019
20.30 0.0079127238
22.30 0.0071805353
23.30 -0.1878005194
2.31 -0.0921969727
3.31 0.0740279917
4.31 0.1068834438
5.31 -0.0257839716
7.31 0.0303541327
8.31 -0.0681065773
10.31 0.1033106858
11.31 0.1057975062
13.31 -0.1379420093
14.31 0.1892519581
15.31 0.1432552942
16.31 0.3214722367
17.31 0.0092582626
18.31 -0.0079828269
19.31 0.0859829063
20.31 0.0866804471
22.31 0.0186371165
23.31 0.1540572965
2.32 -0.1494820328
3.32 0.0095283161
4.32 0.1484783881
5.32 0.0075408002
7.32 -0.0991811690
8.32 0.0793405997
10.32 -0.2930947811
11.32 0.3783350101
13.32 0.0338898024
14.32 -0.0273183890
15.32 0.4892518821
16.32 -0.0464599365
17.32 -0.0793060112
18.32 -0.0121037865
19.32 -0.1039548768
20.32 0.0759088932
22.32 0.0187673805
23.32 0.2251932988
2.33 -0.1442749572
3.33 0.2067874975
4.33 0.0247419605
5.33 0.0063963810
7.33 0.0664786101
8.33 -0.0854867205
10.33 0.2060181891
11.33 0.1229615853
13.33 0.0460991141
14.33 -0.1062012527
15.33 0.0376599166
16.33 -0.0318511892
17.33 -0.0588925458
18.33 0.0444288860
19.33 -0.0050706063
20.33 0.0934410688
22.33 0.2264362458
23.33 0.0864952683
2.34 0.1669979034
3.34 -0.0043249529
4.34 0.1065773789
5.34 0.0041518505
7.34 0.0279297435
8.34 -0.1701284197
10.34 -0.4406093728
11.34 0.1110796548
13.34 0.1188643088
14.34 0.0294664234
15.34 0.0683768829
16.34 0.1873302425
17.34 0.0093344533
18.34 -0.1181498276
19.34 -0.0060878970
20.34 0.1903918741
22.34 0.2182102546
23.34 0.0787028516
2.35 0.0024307743
3.35 -0.1153687075
4.35 -0.0548759578
5.35 0.0336741825
7.35 0.0376302164
8.35 -0.2726925018
10.35 -0.2142788168
11.35 0.4314328742
13.35 0.0607919265
14.35 0.2187921546
15.35 -0.0875162588
16.35 0.2316661171
17.35 0.0988049007
18.35 -0.1554546796
19.35 0.0497005382
20.35 -0.0159516281
22.35 0.0584384047
23.35 0.0030529146
2.36 0.1977341538
3.36 0.1475931113
4.36 -0.0457494391
5.36 -0.1168109210
7.36 0.0974947300
8.36 -0.4499669515
10.36 -0.3651318535
11.36 0.1623447435
13.36 0.1590107245
14.36 0.1717211334
15.36 0.1714775733
16.36 0.0718551682
17.36 -0.0073534983
18.36 -0.1912639678
19.36 0.0219189686
20.36 0.0570716667
22.36 -0.1051490775
23.36 0.0792240608
2.37 -0.1605378752
3.37 0.0433560684
4.37 -0.0932766125
5.37 -0.0737452769
7.37 0.0495017616
8.37 0.0498295877
10.37 -0.4190117120
11.37 0.1063019267
13.37 -0.1357318301
14.37 0.1458671261
15.37 -0.0028806045
16.37 0.1002136283
17.37 0.0960206609
18.37 0.0247997813
19.37 -0.0079286610
20.37 -0.0482874798
22.37 0.1495456125
23.37 -0.0577587250
2.38 0.1399259888
3.38 -0.1404943786
4.38 -0.0513711621
5.38 -0.0777490506
7.38 -0.1561826451
8.38 0.1313355521
10.38 -0.6315448777
11.38 -0.1209498308
13.38 -0.1554899117
14.38 0.1717733006
15.38 0.0554838144
16.38 -0.1406618341
17.38 0.0204368264
18.38 -0.0942937538
19.38 0.1029607109
20.38 -0.0917562184
22.38 -0.1153201650
23.38 -0.1231371343
2.39 0.9729802655
3.39 0.0492591436
4.39 -0.1400775109
5.39 0.0019867120
7.39 0.0095032003
8.39 -0.4574586701
10.39 -0.7131568583
11.39 -0.1205129127
13.39 -0.1606233333
14.39 -0.0419548162
15.39 0.1466686503
16.39 -0.0303004038
17.39 -0.0440914243
18.39 0.0296733569
19.39 -0.0734579520
20.39 0.0151999231
22.39 -0.0733048372
23.39 -0.1201363722
2.40 0.2023889342
3.40 -0.1325280961
4.40 0.0307007095
5.40 -0.0309122398
7.40 0.0506570512
8.40 -0.2562768492
10.40 -0.3276841291
11.40 -0.3848566010
13.40 -0.2197268984
14.40 -0.0172743067
15.40 -0.0482096974
16.40 0.0668973263
17.40 -0.1175919280
18.40 -0.2260540680
19.40 0.0683568651
20.40 -0.1322305613
22.40 0.0549368480
23.40 -0.1813650696
2.41 0.0207234718
3.41 -0.1662130518
4.41 0.0933831181
5.41 0.0606344009
7.41 -0.1763646687
8.41 -0.3857443445
10.41 -0.8172767529
11.41 -0.1776920386
13.41 -0.3150237302
14.41 -0.0564217828
15.41 -0.1623422348
16.41 0.0146084224
17.41 -0.0536674899
18.41 -0.0117274598
19.41 0.0342049423
20.41 -0.1506204851
22.41 0.0104210684
23.41 0.1747251138
2.42 -0.1719603155
3.42 -0.1383075246
4.42 -0.1314993091
5.42 -0.0254807070
7.42 0.1147241473
8.42 -0.2940631103
10.42 -0.4314043112
11.42 -0.3386642948
13.42 -0.3223787037
14.42 0.4024015849
15.42 -0.1514637395
16.42 -0.0925942790
17.42 -0.2081903342
18.42 0.0226225561
19.42 -0.0069150021
20.42 0.0207256450
22.42 -0.1208774936
23.42 -0.0684979599
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
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23.41 -0.1313221288
2.42 -0.2565653361
3.42 -0.6605432949
4.42 -0.0951136708
5.42 -0.0316816057
7.42 -0.1655708305
8.42 -0.3041269167
10.42 -1.3095892929
11.42 -0.7638230856
13.42 -1.0369257332
14.42 0.2560907272
15.42 -0.6198887870
16.42 -0.3486854916
17.42 -0.4149474722
18.42 -0.8569143669
19.42 0.0084081842
20.42 -0.0880982611
22.42 -0.2563668972
23.42 -0.3874747915
2.43 -0.3493516772
3.43 -0.3774218892
4.43 -0.3133990094
5.43 -0.1718736800
7.43 -0.7274013337
8.43 -1.4282102173
10.43 -1.3114232237
11.43 -0.7182961933
13.43 -1.0174776228
14.43 -0.3867885398
15.43 -0.3173512479
16.43 -0.3828153596
17.43 -0.4880622414
18.43 -0.2354846081
19.43 -0.1778048064
20.43 0.1135604938
22.43 -0.5606285260
23.43 -0.1762823988
2.44 -0.8787853678
3.44 -0.4520368028
4.44 0.0904967055
5.44 -0.1706423680
7.44 -0.8491629590
8.44 -0.9070271296
10.44 -2.0133459213
11.44 -0.6208545667
13.44 -0.6793768560
14.44 -0.5195491627
15.44 -0.7269738812
16.44 -0.7984730329
17.44 -0.3469311275
18.44 -0.1732531295
19.44 -0.2033053632
20.44 -0.4245571523
22.44 -0.6207773159
23.44 -0.4054651824
2.45 -0.5474976820
3.45 -0.7308245870
4.45 -0.1555532343
5.45 -0.0937585830
7.45 -1.0632944335
8.45 -0.1176632978
10.45 -1.8401427881
11.45 -1.2487970912
13.45 -0.8847972711
14.45 -0.7432382991
15.45 -0.8131545274
16.45 -0.7808563690
17.45 0.0027832956
18.45 -0.6537006289
19.45 0.3645543401
20.45 -0.1930169594
22.45 -0.7774388833
23.45 -0.9751351355
2.46 -0.5302218764
3.46 -0.9232579792
4.46 -0.1662054231
5.46 -0.2033658549
7.46 -1.0583368441
8.46 -0.9749895283
10.46 -2.0665269476
11.46 0.0600916078
13.46 -0.9053615896
14.46 -0.8703050062
15.46 -0.4191632926
16.46 -1.1377871115
17.46 -0.3022809867
18.46 -1.3128903943
19.46 -0.4030513441
20.46 -0.2607044325
22.46 -0.5226335654
23.46 -1.1561902177
2.47 -0.6137646724
3.47 -0.8398764988
4.47 -0.1705593455
5.47 -0.3590183783
7.47 -0.6972024622
8.47 -0.9321482416
10.47 -2.2393606019
11.47 -0.9455765376
13.47 -0.6822245648
14.47 -0.8187467578
15.47 -0.7601773486
16.47 -1.2042271575
17.47 -0.5976658286
18.47 -0.9720001357
19.47 -0.3694330857
20.47 -0.3132193255
22.47 -0.5633458196
2.48 -0.9226659263
$subject
(Intercept)
2 -0.02898547
3 0.18026470
4 -0.51925966
5 -0.65750137
7 0.18599708
8 0.37715748
10 1.68351789
11 0.22509990
13 -0.18066826
14 -0.15034864
15 0.09038732
16 0.19134839
17 -0.39320912
18 0.33325712
19 -0.61380972
20 -0.39736447
22 -0.47922581
23 0.15334265
with conditional variances for "trial_id" "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.9727586 0.6818716 0.4764641 0.4835448 0.3609605 0.2563628
=============================================================# -------- Identify Stepwise EMM Outliers vs. Overall Mean (per Axis × Block) --------
# Bind all EMMs into one dataframe
all_emm <- bind_rows(lapply(rms_lmm_results_18step, function(res) res$EmmeansStepBlock), .id = "AxisLabel")
# Extract axis from label (e.g., "RMS_X" -> "X")
all_emm <- all_emm %>%
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 <- all_emm %>%
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 <- left_join(all_emm, overall_stats, by = c("Block", "Axis")) %>%
mutate(
is_outlier = emmean < lower_bound | emmean > upper_bound
) %>%
filter(is_outlier)
# View flagged outlier steps
print(emm_outliers) AxisLabel Step Block emmean SE df lower.CL upper.CL Axis
1 RMS_X 1 3 0.5346131 0.05108435 17.93901 0.4272627 0.6419635 X
2 RMS_X 2 3 0.5439213 0.05125504 18.17996 0.4363148 0.6515278 X
3 RMS_X 3 3 0.5673217 0.05162074 18.70438 0.4591625 0.6754808 X
4 RMS_X 4 3 0.5465394 0.05108435 17.93901 0.4391890 0.6538898 X
5 RMS_X 5 3 0.5484741 0.05125542 18.18050 0.4408670 0.6560811 X
6 RMS_X 6 3 0.5469790 0.05161978 18.70298 0.4388214 0.6551367 X
7 RMS_X 7 3 0.5410507 0.05125542 18.18050 0.4334436 0.6486577 X
8 RMS_X 8 3 0.5331025 0.05125922 18.18590 0.4254897 0.6407153 X
9 RMS_X 14 3 0.4940204 0.05125542 18.18050 0.3864134 0.6016275 X
10 RMS_X 15 3 0.4860231 0.05108435 17.93901 0.3786727 0.5933735 X
11 RMS_X 16 3 0.4678642 0.05162074 18.70438 0.3597050 0.5760233 X
12 RMS_X 17 3 0.4630512 0.05125504 18.17996 0.3554447 0.5706577 X
13 RMS_X 18 3 0.4521806 0.05108435 17.93901 0.3448302 0.5595310 X
14 RMS_X 1 4 0.6847193 0.05098365 17.79804 0.5775195 0.7919192 X
15 RMS_X 2 4 0.6940274 0.05119400 18.09357 0.5865127 0.8015422 X
16 RMS_X 3 4 0.7174279 0.05163059 18.71871 0.6092538 0.8256019 X
17 RMS_X 4 4 0.6966455 0.05098365 17.79804 0.5894457 0.8038454 X
18 RMS_X 5 4 0.6985802 0.05119462 18.09445 0.5910645 0.8060959 X
19 RMS_X 6 4 0.6970852 0.05162918 18.71666 0.5889133 0.8052571 X
20 RMS_X 7 4 0.6911568 0.05119462 18.09445 0.5836412 0.7986725 X
21 RMS_X 8 4 0.6832087 0.05119070 18.08892 0.5756989 0.7907185 X
22 RMS_X 14 4 0.6441266 0.05119462 18.09445 0.5366109 0.7516423 X
23 RMS_X 15 4 0.6361292 0.05098365 17.79804 0.5289294 0.7433291 X
24 RMS_X 16 4 0.6179703 0.05163059 18.71871 0.5097963 0.7261444 X
25 RMS_X 17 4 0.6131574 0.05119400 18.09357 0.5056426 0.7206721 X
26 RMS_X 18 4 0.6022867 0.05098365 17.79804 0.4950869 0.7094866 X
27 RMS_X 1 5 0.5960427 0.05098029 17.79336 0.4888479 0.7032376 X
28 RMS_X 2 5 0.6053509 0.05119334 18.09265 0.4978371 0.7128646 X
29 RMS_X 3 5 0.6287513 0.05163219 18.72103 0.5205748 0.7369278 X
30 RMS_X 4 5 0.6079690 0.05098029 17.79336 0.5007741 0.7151638 X
31 RMS_X 5 5 0.6099037 0.05119382 18.09332 0.5023892 0.7174181 X
32 RMS_X 6 5 0.6084087 0.05163100 18.71931 0.5002339 0.7165834 X
33 RMS_X 7 5 0.6024803 0.05119382 18.09332 0.4949658 0.7099947 X
34 RMS_X 8 5 0.5945321 0.05118803 18.08515 0.4870263 0.7020379 X
35 RMS_X 14 5 0.5554500 0.05119382 18.09332 0.4479356 0.6629645 X
36 RMS_X 15 5 0.5474527 0.05098029 17.79336 0.4402578 0.6546475 X
37 RMS_X 16 5 0.5292938 0.05163219 18.72103 0.4211173 0.6374703 X
38 RMS_X 17 5 0.5244808 0.05119334 18.09265 0.4169670 0.6319946 X
39 RMS_X 18 5 0.5136102 0.05098029 17.79336 0.4064153 0.6208050 X
40 RMS_Y 1 3 0.5646985 0.05484619 18.14257 0.4495358 0.6798612 Y
41 RMS_Y 2 3 0.5732991 0.05506723 18.43678 0.4578033 0.6887949 Y
42 RMS_Y 3 3 0.5722059 0.05553973 19.07773 0.4559919 0.6884198 Y
43 RMS_Y 4 3 0.5593917 0.05484619 18.14257 0.4442290 0.6745544 Y
44 RMS_Y 5 3 0.5628699 0.05506771 18.43743 0.4473733 0.6783664 Y
45 RMS_Y 6 3 0.5387681 0.05553848 19.07603 0.4225561 0.6549801 Y
46 RMS_Y 7 3 0.5422974 0.05506771 18.43743 0.4268008 0.6577939 Y
47 RMS_Y 14 3 0.4672712 0.05506771 18.43743 0.3517746 0.5827677 Y
48 RMS_Y 15 3 0.4644374 0.05484619 18.14257 0.3492747 0.5796001 Y
49 RMS_Y 16 3 0.4359598 0.05553973 19.07773 0.3197459 0.5521738 Y
50 RMS_Y 17 3 0.4260496 0.05506723 18.43678 0.3105538 0.5415454 Y
51 RMS_Y 18 3 0.4274787 0.05484619 18.14257 0.3123160 0.5426414 Y
52 RMS_Y 1 4 0.7704391 0.05471469 17.96928 0.6554737 0.8854045 Y
53 RMS_Y 2 4 0.7790397 0.05498725 18.32999 0.6636647 0.8944148 Y
54 RMS_Y 3 4 0.7779465 0.05555148 19.09396 0.6617146 0.8941784 Y
55 RMS_Y 4 4 0.7651323 0.05471469 17.96928 0.6501669 0.8800977 Y
56 RMS_Y 5 4 0.7686105 0.05498806 18.33106 0.6532343 0.8839868 Y
57 RMS_Y 6 4 0.7445087 0.05554966 19.09146 0.6282796 0.8607378 Y
58 RMS_Y 7 4 0.7480380 0.05498806 18.33106 0.6326618 0.8634142 Y
59 RMS_Y 14 4 0.6730118 0.05498806 18.33106 0.5576356 0.7883881 Y
60 RMS_Y 15 4 0.6701781 0.05471469 17.96928 0.5552127 0.7851435 Y
61 RMS_Y 16 4 0.6417005 0.05555148 19.09396 0.5254686 0.7579323 Y
62 RMS_Y 17 4 0.6317902 0.05498725 18.32999 0.5164152 0.7471653 Y
63 RMS_Y 18 4 0.6332194 0.05471469 17.96928 0.5182540 0.7481847 Y
64 RMS_Y 1 5 0.6692260 0.05471026 17.96345 0.5542672 0.7841847 Y
65 RMS_Y 2 5 0.6778266 0.05498631 18.32873 0.5624530 0.7932002 Y
66 RMS_Y 3 5 0.6767333 0.05555345 19.09667 0.5604984 0.7929682 Y
67 RMS_Y 4 5 0.6639192 0.05471026 17.96345 0.5489604 0.7788779 Y
68 RMS_Y 5 5 0.6673974 0.05498692 18.32955 0.5520228 0.7827719 Y
69 RMS_Y 6 5 0.6432956 0.05555192 19.09456 0.5270630 0.7595281 Y
70 RMS_Y 7 5 0.6468248 0.05498692 18.32955 0.5314503 0.7621994 Y
71 RMS_Y 14 5 0.5717986 0.05498692 18.32955 0.4564241 0.6871732 Y
72 RMS_Y 15 5 0.5689649 0.05471026 17.96345 0.4540062 0.6839237 Y
73 RMS_Y 16 5 0.5404873 0.05555345 19.09667 0.4242524 0.6567222 Y
74 RMS_Y 17 5 0.5305771 0.05498631 18.32873 0.4152035 0.6459507 Y
75 RMS_Y 18 5 0.5320062 0.05471026 17.96345 0.4170474 0.6469649 Y
76 RMS_Z 1 3 1.2199468 0.13070908 17.55450 0.9448369 1.4950568 Z
77 RMS_Z 2 3 1.2380736 0.13097145 17.69587 0.9625734 1.5135737 Z
78 RMS_Z 3 3 1.2434480 0.13153318 18.00141 0.9671086 1.5197874 Z
79 RMS_Z 4 3 1.2137223 0.13070908 17.55450 0.9386124 1.4888323 Z
80 RMS_Z 5 3 1.2280307 0.13097202 17.69618 0.9525297 1.5035317 Z
81 RMS_Z 6 3 1.1791638 0.13153171 18.00060 0.9028266 1.4555010 Z
82 RMS_Z 7 3 1.1876054 0.13097202 17.69618 0.9121044 1.4631065 Z
83 RMS_Z 14 3 1.0581993 0.13097202 17.69618 0.7826983 1.3337004 Z
84 RMS_Z 15 3 1.0436269 0.13070908 17.55450 0.7685169 1.3187368 Z
85 RMS_Z 16 3 1.0167149 0.13153318 18.00141 0.7403755 1.2930543 Z
86 RMS_Z 17 3 0.9713299 0.13097145 17.69587 0.6958298 1.2468301 Z
87 RMS_Z 18 3 0.9564141 0.13070908 17.55450 0.6813042 1.2315241 Z
88 RMS_Z 1 4 1.5772932 0.13055173 17.47015 1.3024168 1.8521697 Z
89 RMS_Z 2 4 1.5954199 0.13087504 17.64385 1.3200633 1.8707766 Z
90 RMS_Z 3 4 1.6007944 0.13154573 18.00830 1.3244362 1.8771526 Z
91 RMS_Z 4 4 1.5710687 0.13055173 17.47015 1.2961923 1.8459452 Z
92 RMS_Z 5 4 1.5853771 0.13087600 17.64436 1.3100190 1.8607351 Z
93 RMS_Z 6 4 1.5365102 0.13154356 18.00711 1.2601553 1.8128652 Z
94 RMS_Z 7 4 1.5449518 0.13087600 17.64436 1.2695938 1.8203099 Z
95 RMS_Z 14 4 1.4155457 0.13087600 17.64436 1.1401877 1.6909038 Z
96 RMS_Z 15 4 1.4009733 0.13055173 17.47015 1.1260968 1.6758497 Z
97 RMS_Z 16 4 1.3740613 0.13154573 18.00830 1.0977031 1.6504195 Z
98 RMS_Z 17 4 1.3286763 0.13087504 17.64385 1.0533197 1.6040330 Z
99 RMS_Z 18 4 1.3137605 0.13055173 17.47015 1.0388840 1.5886370 Z
100 RMS_Z 1 5 1.3662774 0.13054633 17.46726 1.0914089 1.6411459 Z
101 RMS_Z 2 5 1.3844041 0.13087376 17.64316 1.1090493 1.6597588 Z
102 RMS_Z 3 5 1.3897785 0.13154792 18.00950 1.1134170 1.6661400 Z
103 RMS_Z 4 5 1.3600529 0.13054633 17.46726 1.0851844 1.6349214 Z
104 RMS_Z 5 5 1.3743612 0.13087449 17.64355 1.0990054 1.6497170 Z
105 RMS_Z 6 5 1.3254944 0.13154609 18.00850 1.0491356 1.6018531 Z
106 RMS_Z 7 5 1.3339360 0.13087449 17.64355 1.0585801 1.6092918 Z
107 RMS_Z 14 5 1.2045298 0.13087449 17.64355 0.9291740 1.4798857 Z
108 RMS_Z 15 5 1.1899574 0.13054633 17.46726 0.9150889 1.4648259 Z
109 RMS_Z 16 5 1.1630454 0.13154792 18.00950 0.8866839 1.4394069 Z
110 RMS_Z 17 5 1.1176604 0.13087376 17.64316 0.8423057 1.3930152 Z
111 RMS_Z 18 5 1.1027447 0.13054633 17.46726 0.8278762 1.3776131 Z
overall_mean overall_se lower_bound upper_bound is_outlier
1 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
2 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
3 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
4 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
5 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
6 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
7 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
8 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
9 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
10 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
11 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
12 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
13 0.5173480 0.007770598 0.5021177 0.5325784 TRUE
14 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
15 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
16 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
17 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
18 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
19 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
20 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
21 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
22 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
23 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
24 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
25 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
26 0.6674542 0.007770598 0.6522238 0.6826846 TRUE
27 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
28 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
29 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
30 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
31 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
32 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
33 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
34 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
35 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
36 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
37 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
38 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
39 0.5787777 0.007770598 0.5635473 0.5940080 TRUE
40 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
41 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
42 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
43 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
44 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
45 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
46 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
47 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
48 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
49 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
50 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
51 0.5113313 0.011773107 0.4882560 0.5344065 TRUE
52 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
53 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
54 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
55 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
56 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
57 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
58 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
59 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
60 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
61 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
62 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
63 0.7170719 0.011773107 0.6939966 0.7401472 TRUE
64 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
65 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
66 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
67 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
68 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
69 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
70 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
71 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
72 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
73 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
74 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
75 0.6158587 0.011773107 0.5927834 0.6389340 TRUE
76 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
77 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
78 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
79 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
80 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
81 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
82 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
83 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
84 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
85 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
86 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
87 1.1287163 0.021160686 1.0872413 1.1701912 TRUE
88 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
89 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
90 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
91 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
92 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
93 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
94 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
95 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
96 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
97 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
98 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
99 1.4860627 0.021160686 1.4445877 1.5275376 TRUE
100 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
101 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
102 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
103 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
104 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
105 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
106 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
107 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
108 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
109 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
110 1.2750468 0.021160686 1.2335718 1.3165217 TRUE
111 1.2750468 0.021160686 1.2335718 1.3165217 TRUE#4 Reaction Times #4.1 RT stepwise per block
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)) %>%
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)# Subset by block (sessions 1 to 5)
df_B1 <- df_acc %>% filter(session == 1)
df_B2 <- df_acc %>% filter(session == 2)
df_B3 <- df_acc %>% filter(session == 3)
df_B4 <- df_acc %>% filter(session == 4)
df_B5 <- df_acc %>% filter(session == 5)
### BLOCK 1 ANALYSIS
M_B1 <- lmer(feedback.RT ~ 0 + sub.trial.number +
(1 | subject) + (1 | trial),
data = df_B1)
Anova(M_B1)Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 602.58 6 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ae.m.M_B1 <- allEffects(M_B1)
ae.m.M_B1.df <- as.data.frame(ae.m.M_B1[1])
plot(ae.m.M_B1)
summary(M_B1)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ 0 + sub.trial.number + (1 | subject) + (1 | trial)
Data: df_B1
REML criterion at convergence: 63545
Scaled residuals:
Min 1Q Median 3Q Max
-4.2607 -0.3704 -0.0988 0.2392 29.5066
Random effects:
Groups Name Variance Std.Dev.
trial (Intercept) 13795 117.5
subject (Intercept) 68992 262.7
Residual 102211 319.7
Number of obs: 4410, groups: trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
sub.trial.number1 760.52 65.27 20.68 11.652 1.52e-10 ***
sub.trial.number2 464.27 65.27 20.68 7.113 5.62e-07 ***
sub.trial.number3 442.12 65.27 20.68 6.774 1.15e-06 ***
sub.trial.number4 453.28 65.27 20.68 6.945 8.02e-07 ***
sub.trial.number5 472.08 65.27 20.68 7.233 4.38e-07 ***
sub.trial.number6 479.82 65.27 20.68 7.351 3.42e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
sb.t.1 sb.t.2 sb.t.3 sb.t.4 sb.t.5
sb.trl.nmb2 0.967
sb.trl.nmb3 0.967 0.967
sb.trl.nmb4 0.967 0.967 0.967
sb.trl.nmb5 0.967 0.967 0.967 0.967
sb.trl.nmb6 0.967 0.967 0.967 0.967 0.967 posthocM_B1 <- emmeans(M_B1, ~ factor(sub.trial.number))
pairwise_comparisonsM_B1 <- pairs(posthocM_B1)
summary(pairwise_comparisonsM_B1) contrast estimate SE df t.ratio p.value
sub.trial.number1 - sub.trial.number2 296.25 16.7 4340 17.764 <.0001
sub.trial.number1 - sub.trial.number3 318.39 16.7 4340 19.092 <.0001
sub.trial.number1 - sub.trial.number4 307.24 16.7 4340 18.423 <.0001
sub.trial.number1 - sub.trial.number5 288.44 16.7 4340 17.296 <.0001
sub.trial.number1 - sub.trial.number6 280.70 16.7 4340 16.832 <.0001
sub.trial.number2 - sub.trial.number3 22.14 16.7 4340 1.328 0.7696
sub.trial.number2 - sub.trial.number4 10.99 16.7 4340 0.659 0.9863
sub.trial.number2 - sub.trial.number5 -7.81 16.7 4340 -0.468 0.9972
sub.trial.number2 - sub.trial.number6 -15.55 16.7 4340 -0.932 0.9382
sub.trial.number3 - sub.trial.number4 -11.15 16.7 4340 -0.669 0.9853
sub.trial.number3 - sub.trial.number5 -29.95 16.7 4340 -1.796 0.4684
sub.trial.number3 - sub.trial.number6 -37.69 16.7 4340 -2.260 0.2109
sub.trial.number4 - sub.trial.number5 -18.80 16.7 4340 -1.127 0.8701
sub.trial.number4 - sub.trial.number6 -26.54 16.7 4340 -1.591 0.6043
sub.trial.number5 - sub.trial.number6 -7.74 16.7 4340 -0.464 0.9973
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates ### BLOCK 2 ANALYSIS
M_B2 <- lmer(feedback.RT ~ 0 + sub.trial.number +
(1 | subject) + (1 | trial),
data = df_B2)
Anova(M_B2)Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 726.83 12 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ae.m.M_B2 <- allEffects(M_B2)
ae.m.M_B2.df <- as.data.frame(ae.m.M_B2[1])
plot(ae.m.M_B2)
summary(M_B2)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ 0 + sub.trial.number + (1 | subject) + (1 | trial)
Data: df_B2
REML criterion at convergence: 107563.7
Scaled residuals:
Min 1Q Median 3Q Max
-3.4650 -0.4593 -0.1806 0.1814 12.4992
Random effects:
Groups Name Variance Std.Dev.
trial (Intercept) 3901 62.46
subject (Intercept) 60187 245.33
Residual 81544 285.56
Number of obs: 7596, groups: trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
sub.trial.number1 766.95 59.62 19.02 12.863 7.82e-11 ***
sub.trial.number2 478.14 59.62 19.02 8.019 1.60e-07 ***
sub.trial.number3 448.41 59.62 19.02 7.521 4.11e-07 ***
sub.trial.number4 417.93 59.62 19.02 7.010 1.12e-06 ***
sub.trial.number5 528.07 59.62 19.02 8.857 3.55e-08 ***
sub.trial.number6 490.32 59.62 19.02 8.224 1.10e-07 ***
sub.trial.number7 536.07 59.62 19.02 8.991 2.81e-08 ***
sub.trial.number8 504.41 59.62 19.02 8.460 7.17e-08 ***
sub.trial.number9 528.69 59.62 19.02 8.867 3.48e-08 ***
sub.trial.number10 501.77 59.62 19.02 8.416 7.76e-08 ***
sub.trial.number11 464.25 59.62 19.02 7.786 2.48e-07 ***
sub.trial.number12 485.15 59.62 19.02 8.137 1.29e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
sb.t.1 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 0.964
sb.trl.nmb3 0.964 0.964
sb.trl.nmb4 0.964 0.964 0.964
sb.trl.nmb5 0.964 0.964 0.964 0.964
sb.trl.nmb6 0.964 0.964 0.964 0.964 0.964
sb.trl.nmb7 0.964 0.964 0.964 0.964 0.964 0.964
sb.trl.nmb8 0.964 0.964 0.964 0.964 0.964 0.964 0.964
sb.trl.nmb9 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964
sb.trl.nm10 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964
sb.trl.nm11 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964
sb.trl.nm12 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964 0.964
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 0.964
sb.trl.nm12 0.964 0.964 posthocM_B2 <- emmeans(M_B2, ~ factor(sub.trial.number))
pairwise_comparisonsM_B2 <- pairs(posthocM_B2)
summary(pairwise_comparisonsM_B2) contrast estimate SE df t.ratio p.value
sub.trial.number1 - sub.trial.number2 288.807 16.1 7520 17.993 <.0001
sub.trial.number1 - sub.trial.number3 318.537 16.1 7520 19.845 <.0001
sub.trial.number1 - sub.trial.number4 349.021 16.1 7520 21.744 <.0001
sub.trial.number1 - sub.trial.number5 238.880 16.1 7520 14.882 <.0001
sub.trial.number1 - sub.trial.number6 276.632 16.1 7520 17.234 <.0001
sub.trial.number1 - sub.trial.number7 230.885 16.1 7520 14.384 <.0001
sub.trial.number1 - sub.trial.number8 262.545 16.1 7520 16.357 <.0001
sub.trial.number1 - sub.trial.number9 238.256 16.1 7520 14.843 <.0001
sub.trial.number1 - sub.trial.number10 265.180 16.1 7520 16.521 <.0001
sub.trial.number1 - sub.trial.number11 302.703 16.1 7520 18.859 <.0001
sub.trial.number1 - sub.trial.number12 281.799 16.1 7520 17.556 <.0001
sub.trial.number2 - sub.trial.number3 29.730 16.1 7520 1.852 0.7887
sub.trial.number2 - sub.trial.number4 60.213 16.1 7520 3.751 0.0097
sub.trial.number2 - sub.trial.number5 -49.927 16.1 7520 -3.110 0.0800
sub.trial.number2 - sub.trial.number6 -12.175 16.1 7520 -0.759 0.9998
sub.trial.number2 - sub.trial.number7 -57.923 16.1 7520 -3.609 0.0162
sub.trial.number2 - sub.trial.number8 -26.262 16.1 7520 -1.636 0.8958
sub.trial.number2 - sub.trial.number9 -50.551 16.1 7520 -3.149 0.0715
sub.trial.number2 - sub.trial.number10 -23.627 16.1 7520 -1.472 0.9482
sub.trial.number2 - sub.trial.number11 13.896 16.1 7520 0.866 0.9994
sub.trial.number2 - sub.trial.number12 -7.008 16.1 7520 -0.437 1.0000
sub.trial.number3 - sub.trial.number4 30.483 16.1 7520 1.899 0.7601
sub.trial.number3 - sub.trial.number5 -79.657 16.1 7520 -4.963 <.0001
sub.trial.number3 - sub.trial.number6 -41.905 16.1 7520 -2.611 0.2736
sub.trial.number3 - sub.trial.number7 -87.652 16.1 7520 -5.461 <.0001
sub.trial.number3 - sub.trial.number8 -55.992 16.1 7520 -3.488 0.0246
sub.trial.number3 - sub.trial.number9 -80.281 16.1 7520 -5.002 <.0001
sub.trial.number3 - sub.trial.number10 -53.357 16.1 7520 -3.324 0.0421
sub.trial.number3 - sub.trial.number11 -15.834 16.1 7520 -0.986 0.9980
sub.trial.number3 - sub.trial.number12 -36.738 16.1 7520 -2.289 0.4847
sub.trial.number4 - sub.trial.number5 -110.141 16.1 7520 -6.862 <.0001
sub.trial.number4 - sub.trial.number6 -72.389 16.1 7520 -4.510 0.0004
sub.trial.number4 - sub.trial.number7 -118.136 16.1 7520 -7.360 <.0001
sub.trial.number4 - sub.trial.number8 -86.475 16.1 7520 -5.387 <.0001
sub.trial.number4 - sub.trial.number9 -110.765 16.1 7520 -6.901 <.0001
sub.trial.number4 - sub.trial.number10 -83.840 16.1 7520 -5.223 <.0001
sub.trial.number4 - sub.trial.number11 -46.318 16.1 7520 -2.886 0.1461
sub.trial.number4 - sub.trial.number12 -67.221 16.1 7520 -4.188 0.0017
sub.trial.number5 - sub.trial.number6 37.752 16.1 7520 2.352 0.4394
sub.trial.number5 - sub.trial.number7 -7.995 16.1 7520 -0.498 1.0000
sub.trial.number5 - sub.trial.number8 23.665 16.1 7520 1.474 0.9476
sub.trial.number5 - sub.trial.number9 -0.624 16.1 7520 -0.039 1.0000
sub.trial.number5 - sub.trial.number10 26.300 16.1 7520 1.639 0.8949
sub.trial.number5 - sub.trial.number11 63.823 16.1 7520 3.976 0.0041
sub.trial.number5 - sub.trial.number12 42.919 16.1 7520 2.674 0.2395
sub.trial.number6 - sub.trial.number7 -45.747 16.1 7520 -2.850 0.1595
sub.trial.number6 - sub.trial.number8 -14.087 16.1 7520 -0.878 0.9993
sub.trial.number6 - sub.trial.number9 -38.376 16.1 7520 -2.391 0.4123
sub.trial.number6 - sub.trial.number10 -11.452 16.1 7520 -0.713 0.9999
sub.trial.number6 - sub.trial.number11 26.071 16.1 7520 1.624 0.9005
sub.trial.number6 - sub.trial.number12 5.168 16.1 7520 0.322 1.0000
sub.trial.number7 - sub.trial.number8 31.660 16.1 7520 1.972 0.7124
sub.trial.number7 - sub.trial.number9 7.371 16.1 7520 0.459 1.0000
sub.trial.number7 - sub.trial.number10 34.295 16.1 7520 2.137 0.5962
sub.trial.number7 - sub.trial.number11 71.818 16.1 7520 4.474 0.0005
sub.trial.number7 - sub.trial.number12 50.915 16.1 7520 3.172 0.0670
sub.trial.number8 - sub.trial.number9 -24.289 16.1 7520 -1.513 0.9373
sub.trial.number8 - sub.trial.number10 2.635 16.1 7520 0.164 1.0000
sub.trial.number8 - sub.trial.number11 40.158 16.1 7520 2.502 0.3387
sub.trial.number8 - sub.trial.number12 19.254 16.1 7520 1.200 0.9891
sub.trial.number9 - sub.trial.number10 26.924 16.1 7520 1.677 0.8787
sub.trial.number9 - sub.trial.number11 64.447 16.1 7520 4.015 0.0035
sub.trial.number9 - sub.trial.number12 43.543 16.1 7520 2.713 0.2199
sub.trial.number10 - sub.trial.number11 37.523 16.1 7520 2.338 0.4496
sub.trial.number10 - sub.trial.number12 16.619 16.1 7520 1.035 0.9969
sub.trial.number11 - sub.trial.number12 -20.904 16.1 7520 -1.302 0.9790
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates ### BLOCK 3 ANALYSIS
M_B3 <- lmer(feedback.RT ~ 0 + sub.trial.number +
(1 | subject) + (1 | trial),
data = df_B3)
Anova(M_B3)Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 816.07 18 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ae.m.M_B3 <- allEffects(M_B3)
ae.m.M_B3.df <- as.data.frame(ae.m.M_B3[1])
plot(ae.m.M_B3)
summary(M_B3)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ 0 + sub.trial.number + (1 | subject) + (1 | trial)
Data: df_B3
REML criterion at convergence: 148465.6
Scaled residuals:
Min 1Q Median 3Q Max
-2.5209 -0.4299 -0.1722 0.1637 29.6780
Random effects:
Groups Name Variance Std.Dev.
trial (Intercept) 1366 36.96
subject (Intercept) 42285 205.63
Residual 115584 339.98
Number of obs: 10242, groups: trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
sub.trial.number1 821.31 50.82 20.28 16.160 4.75e-13 ***
sub.trial.number2 495.98 50.82 20.28 9.759 4.17e-09 ***
sub.trial.number3 468.55 50.82 20.28 9.219 1.08e-08 ***
sub.trial.number4 449.90 50.82 20.28 8.852 2.10e-08 ***
sub.trial.number5 555.18 50.82 20.28 10.924 6.02e-10 ***
sub.trial.number6 533.84 50.82 20.28 10.504 1.19e-09 ***
sub.trial.number7 528.27 50.82 20.28 10.394 1.42e-09 ***
sub.trial.number8 513.04 50.82 20.28 10.095 2.35e-09 ***
sub.trial.number9 561.74 50.82 20.28 11.053 4.90e-10 ***
sub.trial.number10 574.64 50.82 20.28 11.307 3.29e-10 ***
sub.trial.number11 542.80 50.82 20.28 10.680 8.91e-10 ***
sub.trial.number12 481.91 50.82 20.28 9.482 6.76e-09 ***
sub.trial.number13 728.99 50.82 20.28 14.344 4.42e-12 ***
sub.trial.number14 586.87 50.82 20.28 11.547 2.27e-10 ***
sub.trial.number15 536.93 50.82 20.28 10.565 1.08e-09 ***
sub.trial.number16 481.77 50.82 20.28 9.479 6.80e-09 ***
sub.trial.number17 521.32 50.82 20.28 10.258 1.79e-09 ***
sub.trial.number18 535.39 50.82 20.28 10.534 1.13e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation matrix not shown by default, as p = 18 > 12.
Use print(x, correlation=TRUE) or
vcov(x) if you need itposthocM_B3 <- emmeans(M_B3, ~ factor(sub.trial.number))
pairwise_comparisonsM_B3 <- pairs(posthocM_B3)
summary(pairwise_comparisonsM_B3) contrast estimate SE df t.ratio p.value
sub.trial.number1 - sub.trial.number2 325.330 20.2 10160 16.141 <.0001
sub.trial.number1 - sub.trial.number3 352.761 20.2 10160 17.501 <.0001
sub.trial.number1 - sub.trial.number4 371.413 20.2 10160 18.427 <.0001
sub.trial.number1 - sub.trial.number5 266.135 20.2 10160 13.204 <.0001
sub.trial.number1 - sub.trial.number6 287.473 20.2 10160 14.262 <.0001
sub.trial.number1 - sub.trial.number7 293.037 20.2 10160 14.538 <.0001
sub.trial.number1 - sub.trial.number8 308.276 20.2 10160 15.294 <.0001
sub.trial.number1 - sub.trial.number9 259.576 20.2 10160 12.878 <.0001
sub.trial.number1 - sub.trial.number10 246.677 20.2 10160 12.238 <.0001
sub.trial.number1 - sub.trial.number11 278.510 20.2 10160 13.818 <.0001
sub.trial.number1 - sub.trial.number12 339.397 20.2 10160 16.838 <.0001
sub.trial.number1 - sub.trial.number13 92.325 20.2 10160 4.580 0.0007
sub.trial.number1 - sub.trial.number14 234.438 20.2 10160 11.631 <.0001
sub.trial.number1 - sub.trial.number15 284.378 20.2 10160 14.109 <.0001
sub.trial.number1 - sub.trial.number16 339.539 20.2 10160 16.845 <.0001
sub.trial.number1 - sub.trial.number17 299.988 20.2 10160 14.883 <.0001
sub.trial.number1 - sub.trial.number18 285.919 20.2 10160 14.185 <.0001
sub.trial.number2 - sub.trial.number3 27.431 20.2 10160 1.361 0.9969
sub.trial.number2 - sub.trial.number4 46.083 20.2 10160 2.286 0.6936
sub.trial.number2 - sub.trial.number5 -59.195 20.2 10160 -2.937 0.2322
sub.trial.number2 - sub.trial.number6 -37.858 20.2 10160 -1.878 0.9201
sub.trial.number2 - sub.trial.number7 -32.294 20.2 10160 -1.602 0.9815
sub.trial.number2 - sub.trial.number8 -17.055 20.2 10160 -0.846 1.0000
sub.trial.number2 - sub.trial.number9 -65.754 20.2 10160 -3.262 0.1000
sub.trial.number2 - sub.trial.number10 -78.654 20.2 10160 -3.902 0.0117
sub.trial.number2 - sub.trial.number11 -46.821 20.2 10160 -2.323 0.6666
sub.trial.number2 - sub.trial.number12 14.067 20.2 10160 0.698 1.0000
sub.trial.number2 - sub.trial.number13 -233.005 20.2 10160 -11.560 <.0001
sub.trial.number2 - sub.trial.number14 -90.893 20.2 10160 -4.509 0.0009
sub.trial.number2 - sub.trial.number15 -40.953 20.2 10160 -2.032 0.8540
sub.trial.number2 - sub.trial.number16 14.209 20.2 10160 0.705 1.0000
sub.trial.number2 - sub.trial.number17 -25.343 20.2 10160 -1.257 0.9988
sub.trial.number2 - sub.trial.number18 -39.411 20.2 10160 -1.955 0.8901
sub.trial.number3 - sub.trial.number4 18.652 20.2 10160 0.925 1.0000
sub.trial.number3 - sub.trial.number5 -86.626 20.2 10160 -4.298 0.0023
sub.trial.number3 - sub.trial.number6 -65.288 20.2 10160 -3.239 0.1068
sub.trial.number3 - sub.trial.number7 -59.724 20.2 10160 -2.963 0.2185
sub.trial.number3 - sub.trial.number8 -44.485 20.2 10160 -2.207 0.7492
sub.trial.number3 - sub.trial.number9 -93.184 20.2 10160 -4.623 0.0005
sub.trial.number3 - sub.trial.number10 -106.084 20.2 10160 -5.263 <.0001
sub.trial.number3 - sub.trial.number11 -74.251 20.2 10160 -3.684 0.0260
sub.trial.number3 - sub.trial.number12 -13.364 20.2 10160 -0.663 1.0000
sub.trial.number3 - sub.trial.number13 -260.436 20.2 10160 -12.921 <.0001
sub.trial.number3 - sub.trial.number14 -118.323 20.2 10160 -5.870 <.0001
sub.trial.number3 - sub.trial.number15 -68.383 20.2 10160 -3.393 0.0679
sub.trial.number3 - sub.trial.number16 -13.221 20.2 10160 -0.656 1.0000
sub.trial.number3 - sub.trial.number17 -52.773 20.2 10160 -2.618 0.4398
sub.trial.number3 - sub.trial.number18 -66.842 20.2 10160 -3.316 0.0854
sub.trial.number4 - sub.trial.number5 -105.278 20.2 10160 -5.223 <.0001
sub.trial.number4 - sub.trial.number6 -83.940 20.2 10160 -4.164 0.0041
sub.trial.number4 - sub.trial.number7 -78.376 20.2 10160 -3.888 0.0123
sub.trial.number4 - sub.trial.number8 -63.137 20.2 10160 -3.132 0.1430
sub.trial.number4 - sub.trial.number9 -111.837 20.2 10160 -5.549 <.0001
sub.trial.number4 - sub.trial.number10 -124.736 20.2 10160 -6.189 <.0001
sub.trial.number4 - sub.trial.number11 -92.903 20.2 10160 -4.609 0.0006
sub.trial.number4 - sub.trial.number12 -32.016 20.2 10160 -1.588 0.9831
sub.trial.number4 - sub.trial.number13 -279.088 20.2 10160 -13.846 <.0001
sub.trial.number4 - sub.trial.number14 -136.975 20.2 10160 -6.796 <.0001
sub.trial.number4 - sub.trial.number15 -87.035 20.2 10160 -4.318 0.0021
sub.trial.number4 - sub.trial.number16 -31.873 20.2 10160 -1.581 0.9838
sub.trial.number4 - sub.trial.number17 -71.425 20.2 10160 -3.544 0.0419
sub.trial.number4 - sub.trial.number18 -85.494 20.2 10160 -4.242 0.0030
sub.trial.number5 - sub.trial.number6 21.337 20.2 10160 1.059 0.9999
sub.trial.number5 - sub.trial.number7 26.902 20.2 10160 1.335 0.9976
sub.trial.number5 - sub.trial.number8 42.141 20.2 10160 2.091 0.8220
sub.trial.number5 - sub.trial.number9 -6.559 20.2 10160 -0.325 1.0000
sub.trial.number5 - sub.trial.number10 -19.459 20.2 10160 -0.965 1.0000
sub.trial.number5 - sub.trial.number11 12.374 20.2 10160 0.614 1.0000
sub.trial.number5 - sub.trial.number12 73.262 20.2 10160 3.635 0.0308
sub.trial.number5 - sub.trial.number13 -173.810 20.2 10160 -8.623 <.0001
sub.trial.number5 - sub.trial.number14 -31.698 20.2 10160 -1.573 0.9847
sub.trial.number5 - sub.trial.number15 18.242 20.2 10160 0.905 1.0000
sub.trial.number5 - sub.trial.number16 73.404 20.2 10160 3.642 0.0301
sub.trial.number5 - sub.trial.number17 33.852 20.2 10160 1.680 0.9706
sub.trial.number5 - sub.trial.number18 19.784 20.2 10160 0.982 1.0000
sub.trial.number6 - sub.trial.number7 5.564 20.2 10160 0.276 1.0000
sub.trial.number6 - sub.trial.number8 20.803 20.2 10160 1.032 0.9999
sub.trial.number6 - sub.trial.number9 -27.896 20.2 10160 -1.384 0.9963
sub.trial.number6 - sub.trial.number10 -40.796 20.2 10160 -2.024 0.8580
sub.trial.number6 - sub.trial.number11 -8.963 20.2 10160 -0.445 1.0000
sub.trial.number6 - sub.trial.number12 51.924 20.2 10160 2.576 0.4716
sub.trial.number6 - sub.trial.number13 -195.148 20.2 10160 -9.682 <.0001
sub.trial.number6 - sub.trial.number14 -53.035 20.2 10160 -2.631 0.4302
sub.trial.number6 - sub.trial.number15 -3.095 20.2 10160 -0.154 1.0000
sub.trial.number6 - sub.trial.number16 52.067 20.2 10160 2.583 0.4662
sub.trial.number6 - sub.trial.number17 12.515 20.2 10160 0.621 1.0000
sub.trial.number6 - sub.trial.number18 -1.554 20.2 10160 -0.077 1.0000
sub.trial.number7 - sub.trial.number8 15.239 20.2 10160 0.756 1.0000
sub.trial.number7 - sub.trial.number9 -33.461 20.2 10160 -1.660 0.9737
sub.trial.number7 - sub.trial.number10 -46.360 20.2 10160 -2.300 0.6835
sub.trial.number7 - sub.trial.number11 -14.527 20.2 10160 -0.721 1.0000
sub.trial.number7 - sub.trial.number12 46.360 20.2 10160 2.300 0.6835
sub.trial.number7 - sub.trial.number13 -200.712 20.2 10160 -9.958 <.0001
sub.trial.number7 - sub.trial.number14 -58.599 20.2 10160 -2.907 0.2484
sub.trial.number7 - sub.trial.number15 -8.659 20.2 10160 -0.430 1.0000
sub.trial.number7 - sub.trial.number16 46.503 20.2 10160 2.307 0.6783
sub.trial.number7 - sub.trial.number17 6.951 20.2 10160 0.345 1.0000
sub.trial.number7 - sub.trial.number18 -7.118 20.2 10160 -0.353 1.0000
sub.trial.number8 - sub.trial.number9 -48.700 20.2 10160 -2.416 0.5955
sub.trial.number8 - sub.trial.number10 -61.599 20.2 10160 -3.056 0.1742
sub.trial.number8 - sub.trial.number11 -29.766 20.2 10160 -1.477 0.9922
sub.trial.number8 - sub.trial.number12 31.121 20.2 10160 1.544 0.9874
sub.trial.number8 - sub.trial.number13 -215.951 20.2 10160 -10.714 <.0001
sub.trial.number8 - sub.trial.number14 -73.838 20.2 10160 -3.663 0.0279
sub.trial.number8 - sub.trial.number15 -23.898 20.2 10160 -1.186 0.9994
sub.trial.number8 - sub.trial.number16 31.264 20.2 10160 1.551 0.9868
sub.trial.number8 - sub.trial.number17 -8.288 20.2 10160 -0.411 1.0000
sub.trial.number8 - sub.trial.number18 -22.357 20.2 10160 -1.109 0.9998
sub.trial.number9 - sub.trial.number10 -12.900 20.2 10160 -0.640 1.0000
sub.trial.number9 - sub.trial.number11 18.933 20.2 10160 0.939 1.0000
sub.trial.number9 - sub.trial.number12 79.821 20.2 10160 3.960 0.0094
sub.trial.number9 - sub.trial.number13 -167.251 20.2 10160 -8.298 <.0001
sub.trial.number9 - sub.trial.number14 -25.139 20.2 10160 -1.247 0.9989
sub.trial.number9 - sub.trial.number15 24.801 20.2 10160 1.230 0.9991
sub.trial.number9 - sub.trial.number16 79.963 20.2 10160 3.967 0.0091
sub.trial.number9 - sub.trial.number17 40.411 20.2 10160 2.005 0.8674
sub.trial.number9 - sub.trial.number18 26.343 20.2 10160 1.307 0.9981
sub.trial.number10 - sub.trial.number11 31.833 20.2 10160 1.579 0.9841
sub.trial.number10 - sub.trial.number12 92.721 20.2 10160 4.600 0.0006
sub.trial.number10 - sub.trial.number13 -154.351 20.2 10160 -7.658 <.0001
sub.trial.number10 - sub.trial.number14 -12.239 20.2 10160 -0.607 1.0000
sub.trial.number10 - sub.trial.number15 37.701 20.2 10160 1.870 0.9228
sub.trial.number10 - sub.trial.number16 92.863 20.2 10160 4.607 0.0006
sub.trial.number10 - sub.trial.number17 53.311 20.2 10160 2.645 0.4201
sub.trial.number10 - sub.trial.number18 39.242 20.2 10160 1.947 0.8936
sub.trial.number11 - sub.trial.number12 60.888 20.2 10160 3.021 0.1902
sub.trial.number11 - sub.trial.number13 -186.185 20.2 10160 -9.237 <.0001
sub.trial.number11 - sub.trial.number14 -44.072 20.2 10160 -2.187 0.7629
sub.trial.number11 - sub.trial.number15 5.868 20.2 10160 0.291 1.0000
sub.trial.number11 - sub.trial.number16 61.030 20.2 10160 3.028 0.1869
sub.trial.number11 - sub.trial.number17 21.478 20.2 10160 1.066 0.9999
sub.trial.number11 - sub.trial.number18 7.410 20.2 10160 0.368 1.0000
sub.trial.number12 - sub.trial.number13 -247.072 20.2 10160 -12.258 <.0001
sub.trial.number12 - sub.trial.number14 -104.960 20.2 10160 -5.207 <.0001
sub.trial.number12 - sub.trial.number15 -55.019 20.2 10160 -2.730 0.3596
sub.trial.number12 - sub.trial.number16 0.142 20.2 10160 0.007 1.0000
sub.trial.number12 - sub.trial.number17 -39.410 20.2 10160 -1.955 0.8901
sub.trial.number12 - sub.trial.number18 -53.478 20.2 10160 -2.653 0.4140
sub.trial.number13 - sub.trial.number14 142.113 20.2 10160 7.051 <.0001
sub.trial.number13 - sub.trial.number15 192.053 20.2 10160 9.528 <.0001
sub.trial.number13 - sub.trial.number16 247.214 20.2 10160 12.265 <.0001
sub.trial.number13 - sub.trial.number17 207.663 20.2 10160 10.303 <.0001
sub.trial.number13 - sub.trial.number18 193.594 20.2 10160 9.605 <.0001
sub.trial.number14 - sub.trial.number15 49.940 20.2 10160 2.478 0.5477
sub.trial.number14 - sub.trial.number16 105.102 20.2 10160 5.214 <.0001
sub.trial.number14 - sub.trial.number17 65.550 20.2 10160 3.252 0.1029
sub.trial.number14 - sub.trial.number18 51.481 20.2 10160 2.554 0.4884
sub.trial.number15 - sub.trial.number16 55.162 20.2 10160 2.737 0.3548
sub.trial.number15 - sub.trial.number17 15.610 20.2 10160 0.774 1.0000
sub.trial.number15 - sub.trial.number18 1.541 20.2 10160 0.076 1.0000
sub.trial.number16 - sub.trial.number17 -39.552 20.2 10160 -1.962 0.8870
sub.trial.number16 - sub.trial.number18 -53.620 20.2 10160 -2.660 0.4088
sub.trial.number17 - sub.trial.number18 -14.069 20.2 10160 -0.698 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates ### BLOCK 4 ANALYSIS
M_B4 <- lmer(feedback.RT ~ 0 + sub.trial.number +
(1 | subject) + (1 | trial),
data = df_B4)
Anova(M_B4)Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 572.2 18 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ae.m.M_B4 <- allEffects(M_B4)
ae.m.M_B4.df <- as.data.frame(ae.m.M_B4[1])
plot(ae.m.M_B4)
summary(M_B4)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ 0 + sub.trial.number + (1 | subject) + (1 | trial)
Data: df_B4
REML criterion at convergence: 156256.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.848 -0.351 -0.144 0.100 51.954
Random effects:
Groups Name Variance Std.Dev.
trial (Intercept) 1328 36.44
subject (Intercept) 44522 211.00
Residual 206208 454.10
Number of obs: 10368, groups: trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
sub.trial.number1 763.47 52.34 20.52 14.586 2.67e-12 ***
sub.trial.number2 435.49 52.34 20.52 8.320 5.20e-08 ***
sub.trial.number3 405.84 52.34 20.52 7.754 1.58e-07 ***
sub.trial.number4 404.66 52.34 20.52 7.731 1.66e-07 ***
sub.trial.number5 448.41 52.34 20.52 8.567 3.25e-08 ***
sub.trial.number6 479.41 52.34 20.52 9.159 1.08e-08 ***
sub.trial.number7 576.61 53.48 22.36 10.783 2.51e-10 ***
sub.trial.number8 498.84 53.48 22.36 9.328 3.63e-09 ***
sub.trial.number9 551.88 53.48 22.36 10.320 5.71e-10 ***
sub.trial.number10 495.03 53.48 22.36 9.257 4.17e-09 ***
sub.trial.number11 496.18 53.48 22.36 9.279 4.00e-09 ***
sub.trial.number12 483.05 53.48 22.36 9.033 6.45e-09 ***
sub.trial.number13 575.96 56.73 28.32 10.152 6.09e-11 ***
sub.trial.number14 549.78 56.73 28.32 9.691 1.71e-10 ***
sub.trial.number15 456.74 56.73 28.32 8.051 8.39e-09 ***
sub.trial.number16 470.68 56.73 28.32 8.297 4.58e-09 ***
sub.trial.number17 487.84 56.73 28.32 8.599 2.20e-09 ***
sub.trial.number18 660.11 56.73 28.32 11.636 2.64e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation matrix not shown by default, as p = 18 > 12.
Use print(x, correlation=TRUE) or
vcov(x) if you need itposthocM_B4 <- emmeans(M_B4, ~ factor(sub.trial.number))
pairwise_comparisonsM_B4 <- pairs(posthocM_B4)
summary(pairwise_comparisonsM_B4) contrast estimate SE df t.ratio p.value
sub.trial.number1 - sub.trial.number2 327.98 21.8 10286 15.012 <.0001
sub.trial.number1 - sub.trial.number3 357.62 21.8 10286 16.369 <.0001
sub.trial.number1 - sub.trial.number4 358.81 21.8 10286 16.423 <.0001
sub.trial.number1 - sub.trial.number5 315.06 21.8 10286 14.421 <.0001
sub.trial.number1 - sub.trial.number6 284.06 21.8 10286 13.001 <.0001
sub.trial.number1 - sub.trial.number7 186.86 24.4 10298 7.647 <.0001
sub.trial.number1 - sub.trial.number8 264.63 24.4 10298 10.829 <.0001
sub.trial.number1 - sub.trial.number9 211.59 24.4 10298 8.659 <.0001
sub.trial.number1 - sub.trial.number10 268.43 24.4 10298 10.985 <.0001
sub.trial.number1 - sub.trial.number11 267.28 24.4 10298 10.938 <.0001
sub.trial.number1 - sub.trial.number12 280.42 24.4 10298 11.475 <.0001
sub.trial.number1 - sub.trial.number13 187.51 30.9 10304 6.064 <.0001
sub.trial.number1 - sub.trial.number14 213.69 30.9 10304 6.911 <.0001
sub.trial.number1 - sub.trial.number15 306.72 30.9 10304 9.920 <.0001
sub.trial.number1 - sub.trial.number16 292.79 30.9 10304 9.469 <.0001
sub.trial.number1 - sub.trial.number17 275.63 30.9 10304 8.914 <.0001
sub.trial.number1 - sub.trial.number18 103.36 30.9 10304 3.343 0.0790
sub.trial.number2 - sub.trial.number3 29.65 21.8 10286 1.357 0.9970
sub.trial.number2 - sub.trial.number4 30.84 21.8 10286 1.411 0.9953
sub.trial.number2 - sub.trial.number5 -12.92 21.8 10286 -0.591 1.0000
sub.trial.number2 - sub.trial.number6 -43.92 21.8 10286 -2.010 0.8648
sub.trial.number2 - sub.trial.number7 -141.12 24.4 10298 -5.775 <.0001
sub.trial.number2 - sub.trial.number8 -63.35 24.4 10298 -2.592 0.4594
sub.trial.number2 - sub.trial.number9 -116.39 24.4 10298 -4.763 0.0003
sub.trial.number2 - sub.trial.number10 -59.54 24.4 10298 -2.437 0.5796
sub.trial.number2 - sub.trial.number11 -60.69 24.4 10298 -2.484 0.5430
sub.trial.number2 - sub.trial.number12 -47.56 24.4 10298 -1.946 0.8940
sub.trial.number2 - sub.trial.number13 -140.47 30.9 10304 -4.543 0.0008
sub.trial.number2 - sub.trial.number14 -114.29 30.9 10304 -3.696 0.0249
sub.trial.number2 - sub.trial.number15 -21.25 30.9 10304 -0.687 1.0000
sub.trial.number2 - sub.trial.number16 -35.19 30.9 10304 -1.138 0.9997
sub.trial.number2 - sub.trial.number17 -52.35 30.9 10304 -1.693 0.9682
sub.trial.number2 - sub.trial.number18 -224.62 30.9 10304 -7.265 <.0001
sub.trial.number3 - sub.trial.number4 1.19 21.8 10286 0.054 1.0000
sub.trial.number3 - sub.trial.number5 -42.57 21.8 10286 -1.948 0.8931
sub.trial.number3 - sub.trial.number6 -73.57 21.8 10286 -3.367 0.0733
sub.trial.number3 - sub.trial.number7 -170.77 24.4 10298 -6.988 <.0001
sub.trial.number3 - sub.trial.number8 -93.00 24.4 10298 -3.806 0.0168
sub.trial.number3 - sub.trial.number9 -146.04 24.4 10298 -5.976 <.0001
sub.trial.number3 - sub.trial.number10 -89.19 24.4 10298 -3.650 0.0293
sub.trial.number3 - sub.trial.number11 -90.34 24.4 10298 -3.697 0.0248
sub.trial.number3 - sub.trial.number12 -77.21 24.4 10298 -3.159 0.1331
sub.trial.number3 - sub.trial.number13 -170.12 30.9 10304 -5.502 <.0001
sub.trial.number3 - sub.trial.number14 -143.94 30.9 10304 -4.655 0.0005
sub.trial.number3 - sub.trial.number15 -50.90 30.9 10304 -1.646 0.9758
sub.trial.number3 - sub.trial.number16 -64.84 30.9 10304 -2.097 0.8184
sub.trial.number3 - sub.trial.number17 -81.99 30.9 10304 -2.652 0.4149
sub.trial.number3 - sub.trial.number18 -254.27 30.9 10304 -8.224 <.0001
sub.trial.number4 - sub.trial.number5 -43.75 21.8 10286 -2.003 0.8685
sub.trial.number4 - sub.trial.number6 -74.76 21.8 10286 -3.422 0.0620
sub.trial.number4 - sub.trial.number7 -171.95 24.4 10298 -7.037 <.0001
sub.trial.number4 - sub.trial.number8 -94.18 24.4 10298 -3.854 0.0140
sub.trial.number4 - sub.trial.number9 -147.22 24.4 10298 -6.025 <.0001
sub.trial.number4 - sub.trial.number10 -90.38 24.4 10298 -3.698 0.0247
sub.trial.number4 - sub.trial.number11 -91.53 24.4 10298 -3.745 0.0209
sub.trial.number4 - sub.trial.number12 -78.39 24.4 10298 -3.208 0.1165
sub.trial.number4 - sub.trial.number13 -171.30 30.9 10304 -5.540 <.0001
sub.trial.number4 - sub.trial.number14 -145.13 30.9 10304 -4.694 0.0004
sub.trial.number4 - sub.trial.number15 -52.09 30.9 10304 -1.685 0.9697
sub.trial.number4 - sub.trial.number16 -66.03 30.9 10304 -2.135 0.7955
sub.trial.number4 - sub.trial.number17 -83.18 30.9 10304 -2.690 0.3872
sub.trial.number4 - sub.trial.number18 -255.46 30.9 10304 -8.262 <.0001
sub.trial.number5 - sub.trial.number6 -31.00 21.8 10286 -1.419 0.9950
sub.trial.number5 - sub.trial.number7 -128.20 24.4 10298 -5.246 <.0001
sub.trial.number5 - sub.trial.number8 -50.43 24.4 10298 -2.064 0.8372
sub.trial.number5 - sub.trial.number9 -103.47 24.4 10298 -4.234 0.0031
sub.trial.number5 - sub.trial.number10 -46.63 24.4 10298 -1.908 0.9093
sub.trial.number5 - sub.trial.number11 -47.77 24.4 10298 -1.955 0.8902
sub.trial.number5 - sub.trial.number12 -34.64 24.4 10298 -1.418 0.9951
sub.trial.number5 - sub.trial.number13 -127.55 30.9 10304 -4.125 0.0048
sub.trial.number5 - sub.trial.number14 -101.37 30.9 10304 -3.279 0.0954
sub.trial.number5 - sub.trial.number15 -8.34 30.9 10304 -0.270 1.0000
sub.trial.number5 - sub.trial.number16 -22.27 30.9 10304 -0.720 1.0000
sub.trial.number5 - sub.trial.number17 -39.43 30.9 10304 -1.275 0.9986
sub.trial.number5 - sub.trial.number18 -211.70 30.9 10304 -6.847 <.0001
sub.trial.number6 - sub.trial.number7 -97.20 24.4 10298 -3.977 0.0087
sub.trial.number6 - sub.trial.number8 -19.43 24.4 10298 -0.795 1.0000
sub.trial.number6 - sub.trial.number9 -72.47 24.4 10298 -2.965 0.2172
sub.trial.number6 - sub.trial.number10 -15.62 24.4 10298 -0.639 1.0000
sub.trial.number6 - sub.trial.number11 -16.77 24.4 10298 -0.686 1.0000
sub.trial.number6 - sub.trial.number12 -3.64 24.4 10298 -0.149 1.0000
sub.trial.number6 - sub.trial.number13 -96.55 30.9 10304 -3.123 0.1468
sub.trial.number6 - sub.trial.number14 -70.37 30.9 10304 -2.276 0.7011
sub.trial.number6 - sub.trial.number15 22.67 30.9 10304 0.733 1.0000
sub.trial.number6 - sub.trial.number16 8.73 30.9 10304 0.282 1.0000
sub.trial.number6 - sub.trial.number17 -8.43 30.9 10304 -0.272 1.0000
sub.trial.number6 - sub.trial.number18 -180.70 30.9 10304 -5.844 <.0001
sub.trial.number7 - sub.trial.number8 77.77 26.8 10286 2.906 0.2489
sub.trial.number7 - sub.trial.number9 24.73 26.8 10286 0.924 1.0000
sub.trial.number7 - sub.trial.number10 81.57 26.8 10286 3.049 0.1775
sub.trial.number7 - sub.trial.number11 80.43 26.8 10286 3.006 0.1973
sub.trial.number7 - sub.trial.number12 93.56 26.8 10286 3.496 0.0489
sub.trial.number7 - sub.trial.number13 0.65 32.8 10299 0.020 1.0000
sub.trial.number7 - sub.trial.number14 26.83 32.8 10299 0.818 1.0000
sub.trial.number7 - sub.trial.number15 119.87 32.8 10299 3.656 0.0287
sub.trial.number7 - sub.trial.number16 105.93 32.8 10299 3.231 0.1093
sub.trial.number7 - sub.trial.number17 88.77 32.8 10299 2.707 0.3751
sub.trial.number7 - sub.trial.number18 -83.50 32.8 10299 -2.547 0.4941
sub.trial.number8 - sub.trial.number9 -53.04 26.8 10286 -1.982 0.8781
sub.trial.number8 - sub.trial.number10 3.80 26.8 10286 0.142 1.0000
sub.trial.number8 - sub.trial.number11 2.65 26.8 10286 0.099 1.0000
sub.trial.number8 - sub.trial.number12 15.79 26.8 10286 0.590 1.0000
sub.trial.number8 - sub.trial.number13 -77.12 32.8 10299 -2.352 0.6446
sub.trial.number8 - sub.trial.number14 -50.94 32.8 10299 -1.554 0.9866
sub.trial.number8 - sub.trial.number15 42.09 32.8 10299 1.284 0.9985
sub.trial.number8 - sub.trial.number16 28.16 32.8 10299 0.859 1.0000
sub.trial.number8 - sub.trial.number17 11.00 32.8 10299 0.336 1.0000
sub.trial.number8 - sub.trial.number18 -161.27 32.8 10299 -4.919 0.0001
sub.trial.number9 - sub.trial.number10 56.85 26.8 10286 2.124 0.8022
sub.trial.number9 - sub.trial.number11 55.70 26.8 10286 2.081 0.8273
sub.trial.number9 - sub.trial.number12 68.83 26.8 10286 2.572 0.4745
sub.trial.number9 - sub.trial.number13 -24.08 32.8 10299 -0.734 1.0000
sub.trial.number9 - sub.trial.number14 2.10 32.8 10299 0.064 1.0000
sub.trial.number9 - sub.trial.number15 95.14 32.8 10299 2.902 0.2516
sub.trial.number9 - sub.trial.number16 81.20 32.8 10299 2.476 0.5486
sub.trial.number9 - sub.trial.number17 64.04 32.8 10299 1.953 0.8910
sub.trial.number9 - sub.trial.number18 -108.23 32.8 10299 -3.301 0.0894
sub.trial.number10 - sub.trial.number11 -1.15 26.8 10286 -0.043 1.0000
sub.trial.number10 - sub.trial.number12 11.98 26.8 10286 0.448 1.0000
sub.trial.number10 - sub.trial.number13 -80.92 32.8 10299 -2.468 0.5551
sub.trial.number10 - sub.trial.number14 -54.75 32.8 10299 -1.670 0.9722
sub.trial.number10 - sub.trial.number15 38.29 32.8 10299 1.168 0.9995
sub.trial.number10 - sub.trial.number16 24.35 32.8 10299 0.743 1.0000
sub.trial.number10 - sub.trial.number17 7.20 32.8 10299 0.219 1.0000
sub.trial.number10 - sub.trial.number18 -165.08 32.8 10299 -5.035 0.0001
sub.trial.number11 - sub.trial.number12 13.13 26.8 10286 0.491 1.0000
sub.trial.number11 - sub.trial.number13 -79.78 32.8 10299 -2.433 0.5824
sub.trial.number11 - sub.trial.number14 -53.60 32.8 10299 -1.635 0.9774
sub.trial.number11 - sub.trial.number15 39.44 32.8 10299 1.203 0.9993
sub.trial.number11 - sub.trial.number16 25.50 32.8 10299 0.778 1.0000
sub.trial.number11 - sub.trial.number17 8.35 32.8 10299 0.255 1.0000
sub.trial.number11 - sub.trial.number18 -163.93 32.8 10299 -5.000 0.0001
sub.trial.number12 - sub.trial.number13 -92.91 32.8 10299 -2.834 0.2917
sub.trial.number12 - sub.trial.number14 -66.73 32.8 10299 -2.035 0.8522
sub.trial.number12 - sub.trial.number15 26.31 32.8 10299 0.802 1.0000
sub.trial.number12 - sub.trial.number16 12.37 32.8 10299 0.377 1.0000
sub.trial.number12 - sub.trial.number17 -4.79 32.8 10299 -0.146 1.0000
sub.trial.number12 - sub.trial.number18 -177.06 32.8 10299 -5.400 <.0001
sub.trial.number13 - sub.trial.number14 26.18 37.8 10286 0.692 1.0000
sub.trial.number13 - sub.trial.number15 119.22 37.8 10286 3.150 0.1363
sub.trial.number13 - sub.trial.number16 105.28 37.8 10286 2.782 0.3244
sub.trial.number13 - sub.trial.number17 88.12 37.8 10286 2.329 0.6622
sub.trial.number13 - sub.trial.number18 -84.15 37.8 10286 -2.224 0.7378
sub.trial.number14 - sub.trial.number15 93.04 37.8 10286 2.459 0.5625
sub.trial.number14 - sub.trial.number16 79.10 37.8 10286 2.090 0.8223
sub.trial.number14 - sub.trial.number17 61.94 37.8 10286 1.637 0.9771
sub.trial.number14 - sub.trial.number18 -110.33 37.8 10286 -2.916 0.2438
sub.trial.number15 - sub.trial.number16 -13.94 37.8 10286 -0.368 1.0000
sub.trial.number15 - sub.trial.number17 -31.09 37.8 10286 -0.822 1.0000
sub.trial.number15 - sub.trial.number18 -203.37 37.8 10286 -5.374 <.0001
sub.trial.number16 - sub.trial.number17 -17.16 37.8 10286 -0.453 1.0000
sub.trial.number16 - sub.trial.number18 -189.43 37.8 10286 -5.006 0.0001
sub.trial.number17 - sub.trial.number18 -172.27 37.8 10286 -4.552 0.0008
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates ### BLOCK 5 ANALYSIS
M_B5 <- lmer(feedback.RT ~ 0 + sub.trial.number +
(1 | subject) + (1 | trial),
data = df_B5)
Anova(M_B5)Analysis of Deviance Table (Type II Wald chisquare tests)
Response: feedback.RT
Chisq Df Pr(>Chisq)
sub.trial.number 798.67 18 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ae.m.M_B5 <- allEffects(M_B5)
ae.m.M_B5.df <- as.data.frame(ae.m.M_B5[1])
plot(ae.m.M_B5)
summary(M_B5)Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: feedback.RT ~ 0 + sub.trial.number + (1 | subject) + (1 | trial)
Data: df_B5
REML criterion at convergence: 161038.9
Scaled residuals:
Min 1Q Median 3Q Max
-1.8748 -0.4251 -0.1891 0.1036 20.2648
Random effects:
Groups Name Variance Std.Dev.
trial (Intercept) 7455 86.34
subject (Intercept) 35794 189.19
Residual 326326 571.25
Number of obs: 10368, groups: trial, 48; subject, 18
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
sub.trial.number1 1035.27 50.22 26.40 20.62 < 2e-16 ***
sub.trial.number2 555.73 50.22 26.40 11.07 2.05e-11 ***
sub.trial.number3 550.34 50.22 26.40 10.96 2.53e-11 ***
sub.trial.number4 580.38 50.22 26.40 11.56 7.86e-12 ***
sub.trial.number5 636.34 50.22 26.40 12.67 9.91e-13 ***
sub.trial.number6 637.55 50.22 26.40 12.70 9.49e-13 ***
sub.trial.number7 770.84 52.07 30.51 14.80 1.80e-15 ***
sub.trial.number8 652.27 52.07 30.51 12.53 1.46e-13 ***
sub.trial.number9 845.19 52.07 30.51 16.23 < 2e-16 ***
sub.trial.number10 690.54 52.07 30.51 13.26 3.33e-14 ***
sub.trial.number11 601.79 52.07 30.51 11.56 1.13e-12 ***
sub.trial.number12 637.60 52.07 30.51 12.24 2.61e-13 ***
sub.trial.number13 869.38 57.26 44.61 15.18 < 2e-16 ***
sub.trial.number14 698.59 57.26 44.61 12.20 8.27e-16 ***
sub.trial.number15 586.12 57.26 44.61 10.24 2.76e-13 ***
sub.trial.number16 578.38 57.26 44.61 10.10 4.19e-13 ***
sub.trial.number17 610.81 57.26 44.61 10.67 7.38e-14 ***
sub.trial.number18 639.01 57.26 44.61 11.16 1.69e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation matrix not shown by default, as p = 18 > 12.
Use print(x, correlation=TRUE) or
vcov(x) if you need itposthocM_B5 <- emmeans(M_B5, ~ factor(sub.trial.number))
pairwise_comparisonsM_B5 <- pairs(posthocM_B5)
summary(pairwise_comparisonsM_B5) contrast estimate SE df t.ratio p.value
sub.trial.number1 - sub.trial.number2 479.5475 27.5 10286 17.448 <.0001
sub.trial.number1 - sub.trial.number3 484.9375 27.5 10286 17.644 <.0001
sub.trial.number1 - sub.trial.number4 454.8912 27.5 10286 16.551 <.0001
sub.trial.number1 - sub.trial.number5 398.9387 27.5 10286 14.515 <.0001
sub.trial.number1 - sub.trial.number6 397.7269 27.5 10286 14.471 <.0001
sub.trial.number1 - sub.trial.number7 264.4337 30.7 10289 8.602 <.0001
sub.trial.number1 - sub.trial.number8 383.0014 30.7 10289 12.459 <.0001
sub.trial.number1 - sub.trial.number9 190.0795 30.7 10289 6.183 <.0001
sub.trial.number1 - sub.trial.number10 344.7340 30.7 10289 11.214 <.0001
sub.trial.number1 - sub.trial.number11 433.4823 30.7 10289 14.101 <.0001
sub.trial.number1 - sub.trial.number12 397.6750 30.7 10289 12.936 <.0001
sub.trial.number1 - sub.trial.number13 165.8973 38.9 10291 4.266 0.0027
sub.trial.number1 - sub.trial.number14 336.6820 38.9 10291 8.657 <.0001
sub.trial.number1 - sub.trial.number15 449.1577 38.9 10291 11.549 <.0001
sub.trial.number1 - sub.trial.number16 456.8904 38.9 10291 11.748 <.0001
sub.trial.number1 - sub.trial.number17 424.4633 38.9 10291 10.914 <.0001
sub.trial.number1 - sub.trial.number18 396.2654 38.9 10291 10.189 <.0001
sub.trial.number2 - sub.trial.number3 5.3900 27.5 10286 0.196 1.0000
sub.trial.number2 - sub.trial.number4 -24.6562 27.5 10286 -0.897 1.0000
sub.trial.number2 - sub.trial.number5 -80.6088 27.5 10286 -2.933 0.2343
sub.trial.number2 - sub.trial.number6 -81.8206 27.5 10286 -2.977 0.2114
sub.trial.number2 - sub.trial.number7 -215.1138 30.7 10289 -6.998 <.0001
sub.trial.number2 - sub.trial.number8 -96.5461 30.7 10289 -3.141 0.1399
sub.trial.number2 - sub.trial.number9 -289.4679 30.7 10289 -9.416 <.0001
sub.trial.number2 - sub.trial.number10 -134.8134 30.7 10289 -4.385 0.0016
sub.trial.number2 - sub.trial.number11 -46.0651 30.7 10289 -1.498 0.9909
sub.trial.number2 - sub.trial.number12 -81.8724 30.7 10289 -2.663 0.4066
sub.trial.number2 - sub.trial.number13 -313.6502 38.9 10291 -8.065 <.0001
sub.trial.number2 - sub.trial.number14 -142.8654 38.9 10291 -3.673 0.0270
sub.trial.number2 - sub.trial.number15 -30.3897 38.9 10291 -0.781 1.0000
sub.trial.number2 - sub.trial.number16 -22.6571 38.9 10291 -0.583 1.0000
sub.trial.number2 - sub.trial.number17 -55.0842 38.9 10291 -1.416 0.9951
sub.trial.number2 - sub.trial.number18 -83.2821 38.9 10291 -2.141 0.7918
sub.trial.number3 - sub.trial.number4 -30.0463 27.5 10286 -1.093 0.9998
sub.trial.number3 - sub.trial.number5 -85.9988 27.5 10286 -3.129 0.1443
sub.trial.number3 - sub.trial.number6 -87.2106 27.5 10286 -3.173 0.1282
sub.trial.number3 - sub.trial.number7 -220.5038 30.7 10289 -7.173 <.0001
sub.trial.number3 - sub.trial.number8 -101.9361 30.7 10289 -3.316 0.0855
sub.trial.number3 - sub.trial.number9 -294.8580 30.7 10289 -9.592 <.0001
sub.trial.number3 - sub.trial.number10 -140.2035 30.7 10289 -4.561 0.0007
sub.trial.number3 - sub.trial.number11 -51.4552 30.7 10289 -1.674 0.9715
sub.trial.number3 - sub.trial.number12 -87.2625 30.7 10289 -2.839 0.2886
sub.trial.number3 - sub.trial.number13 -319.0402 38.9 10291 -8.203 <.0001
sub.trial.number3 - sub.trial.number14 -148.2555 38.9 10291 -3.812 0.0164
sub.trial.number3 - sub.trial.number15 -35.7798 38.9 10291 -0.920 1.0000
sub.trial.number3 - sub.trial.number16 -28.0471 38.9 10291 -0.721 1.0000
sub.trial.number3 - sub.trial.number17 -60.4742 38.9 10291 -1.555 0.9864
sub.trial.number3 - sub.trial.number18 -88.6721 38.9 10291 -2.280 0.6981
sub.trial.number4 - sub.trial.number5 -55.9525 27.5 10286 -2.036 0.8519
sub.trial.number4 - sub.trial.number6 -57.1644 27.5 10286 -2.080 0.8282
sub.trial.number4 - sub.trial.number7 -190.4575 30.7 10289 -6.196 <.0001
sub.trial.number4 - sub.trial.number8 -71.8898 30.7 10289 -2.339 0.6548
sub.trial.number4 - sub.trial.number9 -264.8117 30.7 10289 -8.614 <.0001
sub.trial.number4 - sub.trial.number10 -110.1572 30.7 10289 -3.583 0.0367
sub.trial.number4 - sub.trial.number11 -21.4089 30.7 10289 -0.696 1.0000
sub.trial.number4 - sub.trial.number12 -57.2162 30.7 10289 -1.861 0.9259
sub.trial.number4 - sub.trial.number13 -288.9939 38.9 10291 -7.431 <.0001
sub.trial.number4 - sub.trial.number14 -118.2092 38.9 10291 -3.039 0.1816
sub.trial.number4 - sub.trial.number15 -5.7335 38.9 10291 -0.147 1.0000
sub.trial.number4 - sub.trial.number16 1.9991 38.9 10291 0.051 1.0000
sub.trial.number4 - sub.trial.number17 -30.4279 38.9 10291 -0.782 1.0000
sub.trial.number4 - sub.trial.number18 -58.6259 38.9 10291 -1.507 0.9903
sub.trial.number5 - sub.trial.number6 -1.2118 27.5 10286 -0.044 1.0000
sub.trial.number5 - sub.trial.number7 -134.5050 30.7 10289 -4.375 0.0017
sub.trial.number5 - sub.trial.number8 -15.9373 30.7 10289 -0.518 1.0000
sub.trial.number5 - sub.trial.number9 -208.8591 30.7 10289 -6.794 <.0001
sub.trial.number5 - sub.trial.number10 -54.2046 30.7 10289 -1.763 0.9536
sub.trial.number5 - sub.trial.number11 34.5436 30.7 10289 1.124 0.9997
sub.trial.number5 - sub.trial.number12 -1.2636 30.7 10289 -0.041 1.0000
sub.trial.number5 - sub.trial.number13 -233.0414 38.9 10291 -5.992 <.0001
sub.trial.number5 - sub.trial.number14 -62.2566 38.9 10291 -1.601 0.9817
sub.trial.number5 - sub.trial.number15 50.2191 38.9 10291 1.291 0.9984
sub.trial.number5 - sub.trial.number16 57.9517 38.9 10291 1.490 0.9914
sub.trial.number5 - sub.trial.number17 25.5246 38.9 10291 0.656 1.0000
sub.trial.number5 - sub.trial.number18 -2.6733 38.9 10291 -0.069 1.0000
sub.trial.number6 - sub.trial.number7 -133.2932 30.7 10289 -4.336 0.0020
sub.trial.number6 - sub.trial.number8 -14.7254 30.7 10289 -0.479 1.0000
sub.trial.number6 - sub.trial.number9 -207.6473 30.7 10289 -6.755 <.0001
sub.trial.number6 - sub.trial.number10 -52.9928 30.7 10289 -1.724 0.9623
sub.trial.number6 - sub.trial.number11 35.7555 30.7 10289 1.163 0.9996
sub.trial.number6 - sub.trial.number12 -0.0518 30.7 10289 -0.002 1.0000
sub.trial.number6 - sub.trial.number13 -231.8296 38.9 10291 -5.961 <.0001
sub.trial.number6 - sub.trial.number14 -61.0448 38.9 10291 -1.570 0.9850
sub.trial.number6 - sub.trial.number15 51.4309 38.9 10291 1.322 0.9978
sub.trial.number6 - sub.trial.number16 59.1635 38.9 10291 1.521 0.9893
sub.trial.number6 - sub.trial.number17 26.7364 38.9 10291 0.687 1.0000
sub.trial.number6 - sub.trial.number18 -1.4615 38.9 10291 -0.038 1.0000
sub.trial.number7 - sub.trial.number8 118.5677 33.7 10286 3.522 0.0449
sub.trial.number7 - sub.trial.number9 -74.3542 33.7 10286 -2.209 0.7480
sub.trial.number7 - sub.trial.number10 80.3003 33.7 10286 2.386 0.6191
sub.trial.number7 - sub.trial.number11 169.0486 33.7 10286 5.022 0.0001
sub.trial.number7 - sub.trial.number12 133.2413 33.7 10286 3.958 0.0094
sub.trial.number7 - sub.trial.number13 -98.5364 41.2 10289 -2.389 0.6163
sub.trial.number7 - sub.trial.number14 72.2483 41.2 10289 1.752 0.9563
sub.trial.number7 - sub.trial.number15 184.7240 41.2 10289 4.479 0.0011
sub.trial.number7 - sub.trial.number16 192.4567 41.2 10289 4.666 0.0004
sub.trial.number7 - sub.trial.number17 160.0296 41.2 10289 3.880 0.0127
sub.trial.number7 - sub.trial.number18 131.8317 41.2 10289 3.196 0.1203
sub.trial.number8 - sub.trial.number9 -192.9219 33.7 10286 -5.731 <.0001
sub.trial.number8 - sub.trial.number10 -38.2674 33.7 10286 -1.137 0.9997
sub.trial.number8 - sub.trial.number11 50.4809 33.7 10286 1.500 0.9908
sub.trial.number8 - sub.trial.number12 14.6736 33.7 10286 0.436 1.0000
sub.trial.number8 - sub.trial.number13 -217.1041 41.2 10289 -5.264 <.0001
sub.trial.number8 - sub.trial.number14 -46.3194 41.2 10289 -1.123 0.9997
sub.trial.number8 - sub.trial.number15 66.1563 41.2 10289 1.604 0.9813
sub.trial.number8 - sub.trial.number16 73.8890 41.2 10289 1.792 0.9466
sub.trial.number8 - sub.trial.number17 41.4619 41.2 10289 1.005 0.9999
sub.trial.number8 - sub.trial.number18 13.2640 41.2 10289 0.322 1.0000
sub.trial.number9 - sub.trial.number10 154.6545 33.7 10286 4.594 0.0006
sub.trial.number9 - sub.trial.number11 243.4028 33.7 10286 7.231 <.0001
sub.trial.number9 - sub.trial.number12 207.5955 33.7 10286 6.167 <.0001
sub.trial.number9 - sub.trial.number13 -24.1822 41.2 10289 -0.586 1.0000
sub.trial.number9 - sub.trial.number14 146.6025 41.2 10289 3.555 0.0404
sub.trial.number9 - sub.trial.number15 259.0782 41.2 10289 6.282 <.0001
sub.trial.number9 - sub.trial.number16 266.8108 41.2 10289 6.469 <.0001
sub.trial.number9 - sub.trial.number17 234.3837 41.2 10289 5.683 <.0001
sub.trial.number9 - sub.trial.number18 206.1858 41.2 10289 4.999 0.0001
sub.trial.number10 - sub.trial.number11 88.7483 33.7 10286 2.637 0.4262
sub.trial.number10 - sub.trial.number12 52.9410 33.7 10286 1.573 0.9847
sub.trial.number10 - sub.trial.number13 -178.8367 41.2 10289 -4.336 0.0020
sub.trial.number10 - sub.trial.number14 -8.0520 41.2 10289 -0.195 1.0000
sub.trial.number10 - sub.trial.number15 104.4237 41.2 10289 2.532 0.5056
sub.trial.number10 - sub.trial.number16 112.1563 41.2 10289 2.719 0.3667
sub.trial.number10 - sub.trial.number17 79.7292 41.2 10289 1.933 0.8994
sub.trial.number10 - sub.trial.number18 51.5313 41.2 10289 1.249 0.9989
sub.trial.number11 - sub.trial.number12 -35.8073 33.7 10286 -1.064 0.9999
sub.trial.number11 - sub.trial.number13 -267.5850 41.2 10289 -6.488 <.0001
sub.trial.number11 - sub.trial.number14 -96.8003 41.2 10289 -2.347 0.6484
sub.trial.number11 - sub.trial.number15 15.6754 41.2 10289 0.380 1.0000
sub.trial.number11 - sub.trial.number16 23.4080 41.2 10289 0.568 1.0000
sub.trial.number11 - sub.trial.number17 -9.0190 41.2 10289 -0.219 1.0000
sub.trial.number11 - sub.trial.number18 -37.2170 41.2 10289 -0.902 1.0000
sub.trial.number12 - sub.trial.number13 -231.7777 41.2 10289 -5.620 <.0001
sub.trial.number12 - sub.trial.number14 -60.9930 41.2 10289 -1.479 0.9921
sub.trial.number12 - sub.trial.number15 51.4827 41.2 10289 1.248 0.9989
sub.trial.number12 - sub.trial.number16 59.2153 41.2 10289 1.436 0.9943
sub.trial.number12 - sub.trial.number17 26.7883 41.2 10289 0.650 1.0000
sub.trial.number12 - sub.trial.number18 -1.4097 41.2 10289 -0.034 1.0000
sub.trial.number13 - sub.trial.number14 170.7847 47.6 10286 3.588 0.0362
sub.trial.number13 - sub.trial.number15 283.2604 47.6 10286 5.950 <.0001
sub.trial.number13 - sub.trial.number16 290.9931 47.6 10286 6.113 <.0001
sub.trial.number13 - sub.trial.number17 258.5660 47.6 10286 5.432 <.0001
sub.trial.number13 - sub.trial.number18 230.3681 47.6 10286 4.839 0.0002
sub.trial.number14 - sub.trial.number15 112.4757 47.6 10286 2.363 0.6365
sub.trial.number14 - sub.trial.number16 120.2083 47.6 10286 2.525 0.5108
sub.trial.number14 - sub.trial.number17 87.7812 47.6 10286 1.844 0.9315
sub.trial.number14 - sub.trial.number18 59.5833 47.6 10286 1.252 0.9989
sub.trial.number15 - sub.trial.number16 7.7326 47.6 10286 0.162 1.0000
sub.trial.number15 - sub.trial.number17 -24.6944 47.6 10286 -0.519 1.0000
sub.trial.number15 - sub.trial.number18 -52.8924 47.6 10286 -1.111 0.9998
sub.trial.number16 - sub.trial.number17 -32.4271 47.6 10286 -0.681 1.0000
sub.trial.number16 - sub.trial.number18 -60.6250 47.6 10286 -1.274 0.9986
sub.trial.number17 - sub.trial.number18 -28.1979 47.6 10286 -0.592 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates # -------- Mean Reaction Time per Block (Session) --------
mean_rt_per_block <- df_acc %>%
group_by(session) %>%
summarise(
mean_RT = mean(feedback.RT, na.rm = TRUE),
sd_RT = sd(feedback.RT, na.rm = TRUE),
n = n(),
se_RT = sd_RT / sqrt(n)
) %>%
mutate(
session = factor(session, levels = 1:5, labels = paste("Block", 1:5))
)
print(mean_rt_per_block)# A tibble: 5 × 5
session mean_RT sd_RT n se_RT
<fct> <dbl> <dbl> <int> <dbl>
1 Block 1 504. 431. 4410 6.49
2 Block 2 485. 365. 7596 4.19
3 Block 3 509. 397. 10242 3.92
4 Block 4 505. 509. 10368 4.99
5 Block 5 677. 621. 10368 6.10# Optional: Plot mean RT ± SE for each block
ggplot(mean_rt_per_block, aes(x = session, y = mean_RT)) +
geom_col(fill = "steelblue", width = 0.6) +
geom_errorbar(aes(ymin = mean_RT - se_RT, ymax = mean_RT + se_RT), width = 0.2) +
labs(
title = "Mean Reaction Time per Block (± SE)",
x = "Block",
y = "Mean RT (ms)"
) +
theme_minimal(base_size = 12) +
theme(
panel.grid.major = element_blank(),
panel.grid.minor = element_blank())
# -------- Identify Steps with Significant RT Deviations per Block --------
# Use emmeans summary outputs if available, or generate anew:
get_significant_rt_deviations <- function(model, block_name) {
em <- emmeans::emmeans(model, ~ sub.trial.number)
em_df <- as.data.frame(em)
block_mean <- mean(em_df$emmean, na.rm = TRUE)
em_df %>%
mutate(
deviation = abs(emmean - block_mean),
threshold = 1.96 * SE,
is_significant = deviation > threshold,
Block = block_name
) %>%
filter(is_significant)
}
# Run for each block model
sig_B1 <- get_significant_rt_deviations(M_B1, "Block 1")
sig_B2 <- get_significant_rt_deviations(M_B2, "Block 2")
sig_B3 <- get_significant_rt_deviations(M_B3, "Block 3")
sig_B4 <- get_significant_rt_deviations(M_B4, "Block 4")
sig_B5 <- get_significant_rt_deviations(M_B5, "Block 5")
# Combine results
significant_steps_all_blocks <- bind_rows(sig_B1, sig_B2, sig_B3, sig_B4, sig_B5)
# View results
print(significant_steps_all_blocks) sub.trial.number emmean SE df lower.CL upper.CL deviation
1 1 760.5181 65.27089 20.69642 624.6586 896.3777 248.5048
2 1 766.9504 59.62335 19.07843 642.1920 891.7088 254.4371
3 1 821.3118 50.82339 20.31505 715.4014 927.2223 270.2873
4 4 449.8988 50.82339 20.31505 343.9884 555.8093 101.1257
5 13 728.9867 50.82339 20.31505 623.0763 834.8971 177.9622
6 1 763.4676 52.34304 20.52202 654.4597 872.4755 250.1350
7 3 405.8426 52.34304 20.52202 296.8347 514.8505 107.4900
8 4 404.6551 52.34304 20.52202 295.6472 513.6630 108.6775
9 18 660.1118 56.73170 28.31495 543.9603 776.2632 146.7792
10 1 1035.2743 50.21507 26.40020 932.1319 1138.4168 358.8224
11 2 555.7269 50.21507 26.40020 452.5844 658.8693 120.7250
12 3 550.3368 50.21507 26.40020 447.1944 653.4793 126.1151
13 9 845.1948 52.06903 30.51794 738.9313 951.4583 168.7429
14 13 869.3770 57.26016 44.61533 754.0217 984.7323 192.9251
threshold is_significant Block
1 127.93094 TRUE Block 1
2 116.86177 TRUE Block 2
3 99.61384 TRUE Block 3
4 99.61384 TRUE Block 3
5 99.61384 TRUE Block 3
6 102.59236 TRUE Block 4
7 102.59236 TRUE Block 4
8 102.59236 TRUE Block 4
9 111.19413 TRUE Block 4
10 98.42153 TRUE Block 5
11 98.42153 TRUE Block 5
12 98.42153 TRUE Block 5
13 102.05530 TRUE Block 5
14 112.22991 TRUE Block 5