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)
# Disable emmeans computation limits for large models
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)Group CoM Analysis 2
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")# 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"
)# ---- Plot Mean RMS per Axis ----
plot_rms_axis <- function(data, axis, y_label, title_prefix) {
axis_mean <- paste0("mean_rms_", axis)
axis_se <- paste0("se_rms_", axis)
ggplot(data, aes(x = TrialInBlock, y = .data[[axis_mean]], color = factor(Block))) +
geom_line(size = 1) +
geom_ribbon(aes(
ymin = .data[[axis_mean]] - .data[[axis_se]],
ymax = .data[[axis_mean]] + .data[[axis_se]],
fill = factor(Block)
), alpha = 0.2, color = NA) +
facet_wrap(~ phase, nrow = 1) +
ylim(0, 2) +
labs(
title = paste(title_prefix, "-", toupper(axis), "Axis"),
x = "Trial Number",
y = y_label,
color = "Block",
fill = "Block"
) +
theme_minimal() +
theme(text = element_text(size = 12))
}
# ---- Plot for Mixed Dataset Only ----
plot_rms_axis(group_rms_summary, "x", "RMS Acceleration", "Mean RMS of CoM Acceleration")
plot_rms_axis(group_rms_summary, "y", "RMS Acceleration", "Mean RMS of CoM Acceleration")
plot_rms_axis(group_rms_summary, "z", "RMS Acceleration", "Mean RMS of CoM Acceleration")
# -------- Acceleration Trends over Trials (Execution & Preparation) --------
plot_acc_trends <- function(df, phase_filter, y_limit, title_text) {
colors <- c("blue", "green", "red", "purple", "orange")
plot_list <- list()
for (block in 1:5) {
block_data <- df %>% filter(phase == phase_filter, Block == block)
if (nrow(block_data) > 0) {
block_long <- block_data %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(Axis = sub("rms_", "", Axis))
p <- ggplot(block_long, aes(x = trial, y = RMS)) +
geom_point(alpha = 0.6) +
geom_smooth(method = "lm", se = TRUE, color = colors[block]) +
facet_wrap(~ Axis, nrow = 1) +
ylim(0, y_limit) +
labs(
title = paste("Block", block),
x = "Trial",
y = "RMS Acceleration (m/s²)"
) +
theme_minimal()
plot_list[[paste0("Block", block)]] <- p
}
}
if (length(plot_list) > 0) {
wrap_plots(plot_list, nrow = 1) +
plot_annotation(
title = title_text,
theme = theme(plot.title = element_text(hjust = 0.5, size = 16))
)
} else {
message("No plots to display. Check that data exists for the requested phase and blocks.")
}
}
# ---- Generate Plots for Execution and Preparation ----
print(plot_acc_trends(rms_data, "Execution", 2.5, "CoM RMS Acceleration Trends Across Trials - Execution Phase"))`geom_smooth()` using formula = 'y ~ x'Warning: Removed 65 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 65 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 56 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 56 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 17 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 17 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 39 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 39 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 17 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 17 rows containing missing values or values outside the scale range
(`geom_point()`).
print(plot_acc_trends(rms_data, "Preparation", 1.0, "CoM RMS Acceleration Trends Across Trials - Preparation Phase"))`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'Warning: Removed 45 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 45 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 69 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 69 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 61 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 61 rows containing missing values or values outside the scale range
(`geom_point()`).`geom_smooth()` using formula = 'y ~ x'Warning: Removed 44 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 44 rows containing missing values or values outside the scale range
(`geom_point()`).
1 Acceleration in Blocks and phases
#1.1.1 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: CoM Acceleration RMS -", toupper(axis), "Axis"),
x = "Block",
y = "RMS Acceleration"
) +
theme_minimal() +
theme(text = element_text(size = 12), 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()`).
#1.1.2 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: CoM RMS -", toupper(axis), "Axis"),
x = "Block",
y = "RMS Acceleration"
) +
theme_minimal()
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()`).
#1.2.1 LMM to assess whether block and phase significantly influence rms (per axis)
# --- Function: Run Random Intercept LMMs and Extract ANOVA P-Values ---
extract_rms_interceptonly_pvalues <- function(data, label) {
# Assume data is already tagged
rms_data <- compute_rms(data) %>%
mutate(Block = factor(Block), subject = factor(subject))
axes <- c("x", "y", "z")
results <- map_dfr(axes, function(axis) {
formula <- as.formula(paste0("rms_", axis, " ~ Block * phase + (1 | subject) + (1 | TrialInBlock)"))
model <- lmer(formula, data = rms_data, REML = FALSE)
anova_tbl <- anova(model)
tibble(
Dataset = label,
Axis = toupper(axis),
`Block p-value` = anova_tbl["Block", "Pr(>F)"],
`Phase p-value` = anova_tbl["phase", "Pr(>F)"],
`Interaction p-value` = anova_tbl["Block:phase", "Pr(>F)"]
)
})
return(results)
}
# --- Run Model on Mixed Data (Tagged Once) ---
interceptonly_pvals <- extract_rms_interceptonly_pvalues(tagged_data, "Mixed")boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')# --- Display Results ---
print(interceptonly_pvals)# A tibble: 3 × 5
Dataset Axis `Block p-value` `Phase p-value` `Interaction p-value`
<chr> <chr> <dbl> <dbl> <dbl>
1 Mixed X 2.09e-33 0 8.06e-76
2 Mixed Y 5.37e-32 0 6.63e-61
3 Mixed Z 2.30e-25 0 1.28e-43#results:
#block p-value <0.05 :This suggests learning or adaptation effects across blocks
#phase p-value 0 because it is either execution or preparation
#interaction <0.05 :this suggest the effect of block is different depending on phase
#clean vs unclean dataset: unclean p-values< clean p-values: probably because of more variability# --- Extended Function: Run Random Intercept LMMs and Extract All Outputs ---
extract_rms_intercept_model_diagnostics <- function(data, label) {
rms_data <- compute_rms(data) %>%
mutate(Block = factor(Block), subject = factor(subject))
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
formula <- as.formula(paste0("rms_", axis, " ~ Block * phase + (1 | subject) + (1 | TrialInBlock)"))
model <- lmer(formula, data = rms_data, REML = FALSE)
# Store everything
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
anova = anova(model),
emmeans = emmeans(model, ~ Block * phase),
fixed_effects = fixef(model),
random_effects = ranef(model),
scaled_residuals = resid(model, scaled = TRUE),
model = model # include model object in case you want to inspect further
)
}
return(results)
}
# --- Run and Store Full Diagnostics ---
intercept_diagnostics <- extract_rms_intercept_model_diagnostics(tagged_data, "Mixed")boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')cat("\n=== Axis X ===\n")
=== Axis X ===print(intercept_diagnostics$Mixed_X$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 10.49 2.62 4 6521.7 40.303 < 2.2e-16 ***
phase 573.66 573.66 1 6521.0 8815.596 < 2.2e-16 ***
Block:phase 23.82 5.95 4 6521.0 91.511 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(intercept_diagnostics$Mixed_X$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.8548 0.0338 22.8 0.78477 0.925
2 Execution 0.7951 0.0341 23.4 0.72470 0.866
3 Execution 0.6665 0.0345 24.7 0.59539 0.738
4 Execution 0.7384 0.0335 21.9 0.66885 0.808
5 Execution 0.5848 0.0335 21.9 0.51530 0.654
1 Preparation 0.0653 0.0338 22.6 -0.00462 0.135
2 Preparation 0.1178 0.0340 23.4 0.04746 0.188
3 Preparation 0.1670 0.0345 24.6 0.09596 0.238
4 Preparation 0.1246 0.0335 21.9 0.05505 0.194
5 Preparation 0.1266 0.0335 21.8 0.05716 0.196
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(intercept_diagnostics$Mixed_X$fixed_effects) (Intercept) Block2 Block3
0.85480165 -0.05969952 -0.18831819
Block4 Block5 phasePreparation
-0.11640071 -0.26998999 -0.78950868
Block2:phasePreparation Block3:phasePreparation Block4:phasePreparation
0.11223106 0.29001003 0.17566536
Block5:phasePreparation
0.33133074 print(intercept_diagnostics$Mixed_X$random_effects)$TrialInBlock
(Intercept)
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
38 0
39 0
40 0
41 0
42 0
43 0
44 0
45 0
46 0
47 0
$subject
(Intercept)
2 0.084959638
3 0.009364058
4 -0.080528746
5 -0.168694714
7 -0.048952044
8 0.054209259
10 0.363123135
11 0.234222092
13 -0.064380022
14 0.068621634
15 -0.055710537
16 -0.013565294
17 -0.107231929
18 -0.022325251
19 -0.152035277
20 -0.114690560
22 -0.094722921
23 0.108337479
with conditional variances for "TrialInBlock" "subject" print(head(intercept_diagnostics$Mixed_X$scaled_residuals)) 1 2 3 4 5 6
-0.6855627 -0.7206152 0.9381860 -0.8704046 -0.4171842 -0.7726668 cat("\n=== Axis Y ===\n")
=== Axis Y ===print(intercept_diagnostics$Mixed_Y$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 14.13 3.53 4 6521.7 38.620 < 2.2e-16 ***
phase 640.85 640.85 1 6521.0 7007.730 < 2.2e-16 ***
Block:phase 26.84 6.71 4 6521.0 73.362 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(intercept_diagnostics$Mixed_Y$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.902 0.0385 23.1 0.8225 0.982
2 Execution 0.844 0.0388 23.9 0.7636 0.924
3 Execution 0.696 0.0393 25.3 0.6154 0.777
4 Execution 0.769 0.0381 22.2 0.6902 0.848
5 Execution 0.608 0.0381 22.1 0.5293 0.687
1 Preparation 0.064 0.0384 22.9 -0.0155 0.144
2 Preparation 0.129 0.0388 23.8 0.0493 0.209
3 Preparation 0.173 0.0393 25.1 0.0924 0.254
4 Preparation 0.121 0.0381 22.1 0.0422 0.200
5 Preparation 0.121 0.0381 22.1 0.0417 0.200
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(intercept_diagnostics$Mixed_Y$fixed_effects) (Intercept) Block2 Block3
0.90214276 -0.05842377 -0.20575453
Block4 Block5 phasePreparation
-0.13285794 -0.29386277 -0.83811781
Block2:phasePreparation Block3:phasePreparation Block4:phasePreparation
0.12373927 0.31502104 0.19003310
Block5:phasePreparation
0.35047549 print(intercept_diagnostics$Mixed_Y$random_effects)$TrialInBlock
(Intercept)
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
38 0
39 0
40 0
41 0
42 0
43 0
44 0
45 0
46 0
47 0
$subject
(Intercept)
2 0.07607719
3 0.06014675
4 -0.12497919
5 -0.19130128
7 -0.05470047
8 0.12826081
10 0.38400762
11 0.24920485
13 -0.04855387
14 0.03922394
15 -0.07320697
16 -0.01721857
17 -0.09868179
18 -0.03594357
19 -0.18125383
20 -0.13068631
22 -0.13748388
23 0.15708857
with conditional variances for "TrialInBlock" "subject" print(head(intercept_diagnostics$Mixed_Y$scaled_residuals)) 1 2 3 4 5 6
-0.5318674 -0.5359392 0.3359262 -0.3116383 -0.4810701 -0.5891674 cat("\n=== Axis Z ===\n")
=== Axis Z ===print(intercept_diagnostics$Mixed_Z$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 29.25 7.31 4 6521.7 30.709 < 2.2e-16 ***
phase 1874.32 1874.32 1 6521.0 7871.441 < 2.2e-16 ***
Block:phase 50.03 12.51 4 6521.0 52.528 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(intercept_diagnostics$Mixed_Z$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 1.4005 0.0637 22.9 1.2686 1.532
2 Execution 1.3897 0.0642 23.6 1.2572 1.522
3 Execution 1.1908 0.0650 24.9 1.0569 1.325
4 Execution 1.2873 0.0631 22.0 1.1564 1.418
5 Execution 1.0224 0.0631 22.0 0.8916 1.153
1 Preparation 0.0654 0.0636 22.7 -0.0662 0.197
2 Preparation 0.1707 0.0641 23.5 0.0382 0.303
3 Preparation 0.2442 0.0649 24.8 0.1104 0.378
4 Preparation 0.1603 0.0631 21.9 0.0295 0.291
5 Preparation 0.1581 0.0630 21.9 0.0274 0.289
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(intercept_diagnostics$Mixed_Z$fixed_effects) (Intercept) Block2 Block3
1.40045721 -0.01071856 -0.20969227
Block4 Block5 phasePreparation
-0.11316313 -0.37806730 -1.33509017
Block2:phasePreparation Block3:phasePreparation Block4:phasePreparation
0.11606228 0.38849177 0.20809330
Block5:phasePreparation
0.47083282 print(intercept_diagnostics$Mixed_Z$random_effects)$TrialInBlock
(Intercept)
1 -4.672739e-18
2 -3.785541e-18
3 -2.639675e-18
4 -3.196648e-18
5 -2.018497e-18
6 -1.254622e-18
7 -1.531263e-18
8 -1.534912e-18
9 -9.670340e-19
10 -8.655370e-19
11 -1.800131e-18
12 -1.742469e-18
13 -1.414453e-18
14 7.297968e-19
15 -1.288192e-18
16 1.223828e-19
17 -8.045113e-20
18 1.364653e-18
19 8.512410e-19
20 7.695664e-19
21 7.388552e-19
22 6.277646e-19
23 2.888206e-18
24 1.126255e-18
25 8.512645e-19
26 1.405709e-18
27 4.969577e-19
28 4.371513e-19
29 1.793159e-18
30 7.012849e-19
31 2.616306e-18
32 1.360328e-18
33 5.462224e-19
34 2.275377e-18
35 1.018464e-18
36 -3.964937e-19
37 6.194290e-19
38 1.006329e-19
39 3.669487e-19
40 -1.097710e-18
41 2.495015e-19
42 7.556181e-19
43 4.742588e-20
44 1.341924e-18
45 1.992059e-18
46 2.020313e-18
47 7.156944e-20
$subject
(Intercept)
2 -0.06278903
3 0.11146166
4 -0.16036249
5 -0.33042021
7 0.03383043
8 0.25270668
10 0.57795953
11 0.40688787
13 -0.01408191
14 -0.01304987
15 -0.09268749
16 0.10293051
17 -0.25400560
18 0.05092086
19 -0.30976159
20 -0.22418418
22 -0.32333051
23 0.24797532
with conditional variances for "TrialInBlock" "subject" print(head(intercept_diagnostics$Mixed_Z$scaled_residuals)) 1 2 3 4 5 6
-0.009895962 -0.166656384 0.182396834 -0.682980337 -0.517337694 -0.905689179 #1.2.2 Random slope model to assess whether block and phase significantly influence rms (per axis)
# --- Function to Run Random Slope LMMs and Extract ANOVA P-Values ---
extract_rms_randomslope_pvalues <- function(tagged_df, label) {
# Compute RMS and prepare data
rms_data <- compute_rms(tagged_df) %>%
mutate(Block = factor(Block), subject = factor(subject))
# Axes to iterate over
axes <- c("x", "y", "z")
# Fit models and extract p-values in loop
map_dfr(axes, function(axis) {
formula <- as.formula(paste0("rms_", axis, " ~ Block * phase + (1 + Block | subject) + (1 | TrialInBlock)"))
model <- lmer(formula, data = rms_data, REML = FALSE)
aov_tbl <- anova(model)
tibble(
Dataset = label,
Axis = toupper(axis),
`Block p-value` = aov_tbl["Block", "Pr(>F)"],
`Phase p-value` = aov_tbl["phase", "Pr(>F)"],
`Interaction p-value` = aov_tbl["Block:phase", "Pr(>F)"]
)
})
}
# Run Random Slope LMMs for tagged and cleaned "Mixed" dataset
randomslope_pvals_mixed <- extract_rms_randomslope_pvalues(tagged_data, "Mixed")boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')# View results
print(randomslope_pvals_mixed)# A tibble: 3 × 5
Dataset Axis `Block p-value` `Phase p-value` `Interaction p-value`
<chr> <chr> <dbl> <dbl> <dbl>
1 Mixed X 0.0291 0 1.72e-81
2 Mixed Y 0.0497 0 1.54e-66
3 Mixed Z 0.0799 0 5.21e-47#compared to the first model this also includes a random slope for Block within subjects
#results:
#block p-value >0.05 (z - axis) :This suggests no learning or adaptation effects across blocks after accounting for between subject
#block p-value <0.05 (x & y axis) :This suggests learning or adaptation effects across blocks after accounting for between subject variation
#phase p-value 0 :because it is either execution or preparation
#interaction <0.05 :this suggest the effect of block is different depending on phase
#clean vs unclean dataset: unclean p-values< clean p-values: probably because of more variability# --- Extended: Run Random Slope LMMs + Extract Diagnostics per Axis ---
extract_rms_randomslope_model_diagnostics <- function(tagged_df, label) {
# Compute RMS and prepare data
rms_data <- compute_rms(tagged_df) %>%
mutate(Block = factor(Block), subject = factor(subject))
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
formula <- as.formula(paste0("rms_", axis, " ~ Block * phase + (1 + Block | subject) + (1 | TrialInBlock)"))
model <- lmer(formula, data = rms_data, REML = FALSE)
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
anova = anova(model),
emmeans = emmeans(model, ~ Block * phase),
fixed_effects = fixef(model),
random_effects = ranef(model),
scaled_residuals = resid(model, scaled = TRUE),
model = model
)
}
return(results)
}
# --- Run Full Diagnostic Extraction ---
randomslope_diagnostics <- extract_rms_randomslope_model_diagnostics(tagged_data, "Mixed")boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')Warning: Model failed to converge with 1 negative eigenvalue: -2.8e+02boundary (singular) fit: see help('isSingular')
boundary (singular) fit: see help('isSingular')# --- Example: Output for Axis X ---
cat("\n=== RANDOM SLOPE MODEL: Axis X ===\n")
=== RANDOM SLOPE MODEL: Axis X ===print(randomslope_diagnostics$Mixed_X$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 0.84 0.21 4 18.2 3.4446 0.0291 *
phase 573.74 573.74 1 6449.7 9439.2430 <2e-16 ***
Block:phase 23.95 5.99 4 6449.6 98.4879 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(randomslope_diagnostics$Mixed_X$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.8581 0.0462 20.1 0.7617 0.954
2 Execution 0.7961 0.0458 20.2 0.7006 0.892
3 Execution 0.6647 0.0337 21.7 0.5948 0.735
4 Execution 0.7388 0.0372 20.3 0.6612 0.816
5 Execution 0.5846 0.0233 22.2 0.5363 0.633
1 Preparation 0.0679 0.0462 20.0 -0.0284 0.164
2 Preparation 0.1189 0.0458 20.2 0.0235 0.214
3 Preparation 0.1654 0.0336 21.6 0.0956 0.235
4 Preparation 0.1246 0.0372 20.2 0.0471 0.202
5 Preparation 0.1268 0.0233 22.1 0.0785 0.175
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(randomslope_diagnostics$Mixed_X$fixed_effects) (Intercept) Block2 Block3
0.85807572 -0.06199209 -0.19338294
Block4 Block5 phasePreparation
-0.11932482 -0.27343346 -0.79017599
Block2:phasePreparation Block3:phasePreparation Block4:phasePreparation
0.11300841 0.29089739 0.17599842
Block5:phasePreparation
0.33233393 print(randomslope_diagnostics$Mixed_X$random_effects)$TrialInBlock
(Intercept)
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
38 0
39 0
40 0
41 0
42 0
43 0
44 0
45 0
46 0
47 0
$subject
(Intercept) Block2 Block3 Block4 Block5
2 -0.002130586 0.14017493 0.148701112 0.08993780 0.060847144
3 0.210340137 -0.19493023 -0.262292535 -0.27672991 -0.248451306
4 -0.085446616 -0.05020446 -0.016821648 -0.01101010 0.060940174
5 -0.114092690 -0.06979523 -0.052808530 -0.09701340 -0.035909232
7 -0.082545142 0.03209474 0.069011823 0.06584268 0.008289092
8 0.024054267 0.03420203 0.004816552 0.05241983 0.044426694
10 0.320462541 0.17465061 0.053780616 0.09681161 -0.085178938
11 0.419658078 -0.04906292 -0.228674348 -0.17200762 -0.340715848
13 -0.104908274 -0.01293570 0.032276596 0.08150349 0.073389640
14 0.121877414 -0.04187897 -0.085279110 -0.08689654 -0.062858733
15 -0.119542720 0.01146563 0.051490105 0.01877142 0.183808910
16 -0.102998188 0.06985160 0.128249919 0.16846852 0.071799365
17 -0.191048839 0.04562005 0.120572790 0.08978650 0.150921427
18 -0.098169526 0.06185725 0.127720268 0.13486697 0.066073017
19 -0.198929688 0.01751672 0.078972777 0.05765067 0.087451508
20 -0.125914157 -0.01192369 0.014789375 -0.02058285 0.060390331
22 -0.155593412 0.02648825 0.076921180 0.05137631 0.128263021
23 0.284927402 -0.18319063 -0.261426942 -0.24319536 -0.223486265
with conditional variances for "TrialInBlock" "subject" print(head(randomslope_diagnostics$Mixed_X$scaled_residuals)) 1 2 3 4 5 6
-0.7209621 -0.6398466 0.1449765 -0.5947548 -0.1244542 -0.6062213 cat("\n=== RANDOM SLOPE MODEL: Axis Y ===\n")
=== RANDOM SLOPE MODEL: Axis Y ===print(randomslope_diagnostics$Mixed_Y$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 0.99 0.25 4 17.9 2.9365 0.04966 *
phase 641.04 641.04 1 6451.0 7581.0440 < 2e-16 ***
Block:phase 27.13 6.78 4 6451.0 80.2193 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(randomslope_diagnostics$Mixed_Y$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.9082 0.0583 19.9 0.7866 1.030
2 Execution 0.8494 0.0544 20.2 0.7359 0.963
3 Execution 0.6935 0.0349 22.0 0.6211 0.766
4 Execution 0.7690 0.0421 20.2 0.6813 0.857
5 Execution 0.6079 0.0242 23.3 0.5579 0.658
1 Preparation 0.0681 0.0582 19.8 -0.0534 0.190
2 Preparation 0.1356 0.0544 20.2 0.0221 0.249
3 Preparation 0.1709 0.0349 21.8 0.0985 0.243
4 Preparation 0.1209 0.0421 20.1 0.0332 0.209
5 Preparation 0.1207 0.0242 23.1 0.0707 0.171
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(randomslope_diagnostics$Mixed_Y$fixed_effects) (Intercept) Block2 Block3
0.90817438 -0.05879782 -0.21466453
Block4 Block5 phasePreparation
-0.13912680 -0.30022914 -0.84004818
Block2:phasePreparation Block3:phasePreparation Block4:phasePreparation
0.12622211 0.31739871 0.19188449
Block5:phasePreparation
0.35280793 print(randomslope_diagnostics$Mixed_Y$random_effects)$TrialInBlock
(Intercept)
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
38 0
39 0
40 0
41 0
42 0
43 0
44 0
45 0
46 0
47 0
$subject
(Intercept) Block2 Block3 Block4 Block5
2 -0.08078052 0.181935400 0.21041561 0.18173095 0.17466746
3 0.04556358 0.030170428 0.03304694 0.02365688 -0.01363942
4 -0.18623694 -0.016290519 0.08655674 0.04621311 0.15558167
5 -0.22381098 -0.006486568 0.06116852 0.01923111 0.08840549
7 -0.10910846 0.025773837 0.06166384 0.03566723 0.11834885
8 0.14429595 0.083351323 -0.04796118 0.01425454 -0.09529695
10 0.44806386 0.019942566 -0.08193563 -0.01763671 -0.22373269
11 0.49539636 0.049356876 -0.36602737 -0.19090847 -0.52891486
13 0.08060563 -0.171227191 -0.19367681 -0.17094475 -0.11370305
14 0.13504171 -0.098395040 -0.14268455 -0.12321746 -0.13346534
15 -0.12719732 -0.045048083 0.07748791 0.03302485 0.16035012
16 -0.12430409 0.075884559 0.14903445 0.12545229 0.16456399
17 -0.24725183 0.127249131 0.20977745 0.16258130 0.22582123
18 -0.08917553 0.020109577 0.12522703 0.07813967 0.06961063
19 -0.21076853 0.022316268 0.04029086 0.01720718 0.06758009
20 -0.15632996 0.044182478 0.04304839 0.02083403 0.03819070
22 -0.20436428 0.004752615 0.08691285 0.04679237 0.15696899
23 0.41036134 -0.347577658 -0.35234508 -0.30207813 -0.31133692
with conditional variances for "TrialInBlock" "subject" print(head(randomslope_diagnostics$Mixed_Y$scaled_residuals)) 1 2 3 4 5 6
-0.6375648 -0.6188274 0.3853927 -0.3544758 -0.5304047 -0.5144974 cat("\n=== RANDOM SLOPE MODEL: Axis Z ===\n")
=== RANDOM SLOPE MODEL: Axis Z ===print(randomslope_diagnostics$Mixed_Z$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Block 2.22 0.55 4 18.1 2.4874 0.07987 .
phase 1874.02 1874.02 1 6450.9 8416.9276 < 2e-16 ***
Block:phase 50.41 12.60 4 6450.9 56.6080 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(randomslope_diagnostics$Mixed_Z$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 1.4106 0.0868 20.0 1.22941 1.592
2 Execution 1.3960 0.0880 20.2 1.21265 1.579
3 Execution 1.1816 0.0663 21.6 1.04381 1.319
4 Execution 1.2868 0.0665 20.4 1.14826 1.425
5 Execution 1.0219 0.0506 21.4 0.91673 1.127
1 Preparation 0.0737 0.0867 19.9 -0.10723 0.255
2 Preparation 0.1777 0.0879 20.1 -0.00565 0.361
3 Preparation 0.2358 0.0663 21.5 0.09815 0.373
4 Preparation 0.1597 0.0665 20.4 0.02121 0.298
5 Preparation 0.1582 0.0506 21.4 0.05313 0.263
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(randomslope_diagnostics$Mixed_Z$fixed_effects) (Intercept) Block2 Block3
1.41055951 -0.01451272 -0.22900373
Block4 Block5 phasePreparation
-0.12374563 -0.38869059 -1.33681079
Block2:phasePreparation Block3:phasePreparation Block4:phasePreparation
0.11844394 0.39103417 0.20968663
Block5:phasePreparation
0.47312389 print(randomslope_diagnostics$Mixed_Z$random_effects)$TrialInBlock
(Intercept)
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 0
18 0
19 0
20 0
21 0
22 0
23 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
38 0
39 0
40 0
41 0
42 0
43 0
44 0
45 0
46 0
47 0
$subject
(Intercept) Block2 Block3 Block4 Block5
2 -0.304860092 0.232026688 0.34789249 0.26744037 0.32438026
3 0.335394305 -0.215269615 -0.27735356 -0.26123632 -0.33676956
4 -0.163414581 -0.112151047 -0.04214627 -0.03622428 0.12262390
5 -0.318903056 -0.028105370 0.00237320 -0.01340532 -0.01312176
7 -0.008331758 0.024204490 0.10292948 0.09537122 -0.01174119
8 0.236457901 0.161103937 -0.03235719 0.04204253 -0.04791900
10 0.480200692 0.202724692 0.16116345 0.10935513 0.03266552
11 0.843843879 0.008190312 -0.60477913 -0.43901462 -0.82331915
13 0.116667046 -0.237355164 -0.27024477 -0.21975774 0.01838803
14 -0.027545810 -0.007698254 0.07932719 0.04880952 -0.03417139
15 -0.139398643 -0.100411511 -0.04265057 -0.05971883 0.31589393
16 -0.080901993 0.246104730 0.25249949 0.22399302 0.18511139
17 -0.445123398 0.102517498 0.29627519 0.23720892 0.30187712
18 -0.076939097 0.093506386 0.33161479 0.24947682 0.04223143
19 -0.310712178 -0.034224562 -0.01156170 -0.01691626 0.03859358
20 -0.253668742 -0.009628290 0.02563412 0.01478410 0.08087746
22 -0.391165577 -0.021001007 0.05325682 0.03750079 0.18759053
23 0.508401103 -0.304533911 -0.37187302 -0.27970905 -0.38319112
with conditional variances for "TrialInBlock" "subject" print(head(randomslope_diagnostics$Mixed_Z$scaled_residuals)) 1 2 3 4 5 6
-0.06271144 -0.34689028 -0.30371480 -0.62623216 -0.45466235 -0.69638425 #1.2.3 Model: CoM RMS Acceleration changes over time
# --- Optimized: Extract p-values from RMS learning LMMs (TrialInBlock * Block * Phase) ---
extract_learning_pvalues <- function(df, label) {
rms_df <- compute_rms(df) %>%
mutate(
Block = factor(Block),
subject = factor(subject),
phase = factor(phase)
)
fit_model_and_anova <- function(axis) {
model <- lmer(as.formula(paste0("rms_", axis, " ~ TrialInBlock * Block * phase + (1 + TrialInBlock | subject)")),
data = rms_df)
anova(model)
}
an_x <- fit_model_and_anova("x")
an_y <- fit_model_and_anova("y")
an_z <- fit_model_and_anova("z")
tibble(
Dataset = label,
Axis = c("X", "Y", "Z"),
`TrialInBlock p-value` = c(an_x["TrialInBlock", "Pr(>F)"], an_y["TrialInBlock", "Pr(>F)"], an_z["TrialInBlock", "Pr(>F)"]),
`Block p-value` = c(an_x["Block", "Pr(>F)"], an_y["Block", "Pr(>F)"], an_z["Block", "Pr(>F)"]),
`Phase p-value` = c(an_x["phase", "Pr(>F)"], an_y["phase", "Pr(>F)"], an_z["phase", "Pr(>F)"]),
`TrialInBlock:Block p` = c(an_x["TrialInBlock:Block", "Pr(>F)"], an_y["TrialInBlock:Block", "Pr(>F)"], an_z["TrialInBlock:Block", "Pr(>F)"]),
`TrialInBlock:Phase p` = c(an_x["TrialInBlock:phase", "Pr(>F)"], an_y["TrialInBlock:phase", "Pr(>F)"], an_z["TrialInBlock:phase", "Pr(>F)"]),
`Block:Phase p` = c(an_x["Block:phase", "Pr(>F)"], an_y["Block:phase", "Pr(>F)"], an_z["Block:phase", "Pr(>F)"]),
`3-way p-value` = c(an_x["TrialInBlock:Block:phase", "Pr(>F)"],
an_y["TrialInBlock:Block:phase", "Pr(>F)"],
an_z["TrialInBlock:Block:phase", "Pr(>F)"])
)
}
# Use pre-tagged data (tagged_data) instead of tagging again
learning_pvals_mixed <- extract_learning_pvalues(tagged_data, "Mixed")Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
unable to evaluate scaled gradientWarning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge: degenerate Hessian with 1 negative eigenvaluesWarning: Model failed to converge with 1 negative eigenvalue: -3.1e+00Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.886971 (tol = 0.002, component 1)Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.345604 (tol = 0.002, component 1)Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?# Show result
print(learning_pvals_mixed)# A tibble: 3 × 9
Dataset Axis `TrialInBlock p-value` `Block p-value` `Phase p-value`
<chr> <chr> <dbl> <dbl> <dbl>
1 Mixed X 0.537 2.48e-25 0
2 Mixed Y 0.504 2.30e-15 0
3 Mixed Z 0.0791 1.87e-14 0
# ℹ 4 more variables: `TrialInBlock:Block p` <dbl>,
# `TrialInBlock:Phase p` <dbl>, `Block:Phase p` <dbl>, `3-way p-value` <dbl>#results:
#trial in block p-value >0.05 : Participants do not change rms within block
#block p-value <0.05 : RMS differs significantly between blocks
#phase p-value : 0 because it is either execution or preparation
#Trial in block x Block <0.05 : significant changes across blocks (except y )
#Trial in block x phase <0.05 : as before different phases differ
#Block x phase <0.05 : changes in blocks differ across phases
#trial in block x block x phase <0.05 : trial in block changes across both blocks and phases
#clean vs unclean dataset: unclean p-values< clean p-values: probably because of more variability# --- Global Options to Suppress Emmeans Warnings ---
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# --- Extended: Extract Full Diagnostics from Learning LMM (TrialInBlock * Block * Phase) ---
extract_learning_model_diagnostics <- function(df, label) {
rms_df <- compute_rms(df) %>%
mutate(
Block = factor(Block),
subject = factor(subject),
phase = factor(phase)
)
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
formula <- as.formula(paste0("rms_", axis, " ~ TrialInBlock * Block * phase + (1 + TrialInBlock | subject)"))
model <- lmer(formula, data = rms_df)
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
anova = anova(model),
emmeans = emmeans(model, ~ Block * phase),
fixed_effects = fixef(model),
random_effects = ranef(model),
scaled_residuals = resid(model, scaled = TRUE),
model = model
)
}
return(results)
}
# --- Run Diagnostics on Mixed Data ---
learning_diagnostics <- extract_learning_model_diagnostics(tagged_data, "Mixed")Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
unable to evaluate scaled gradientWarning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge: degenerate Hessian with 1 negative eigenvaluesWarning: Model failed to converge with 1 negative eigenvalue: -3.1e+00NOTE: Results may be misleading due to involvement in interactionsWarning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.886971 (tol = 0.002, component 1)Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?NOTE: Results may be misleading due to involvement in interactionsWarning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model failed to converge with max|grad| = 0.345604 (tol = 0.002, component 1)
Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : Model is nearly unidentifiable: very large eigenvalue
- Rescale variables?NOTE: Results may be misleading due to involvement in interactions# --- Display Example for Axis X ---
cat("\n=== LEARNING MODEL: Axis X ===\n")
=== LEARNING MODEL: Axis X ===print(learning_diagnostics$Mixed_X$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
TrialInBlock 0.024 0.024 1 14.9 0.4001 0.5366
Block 7.478 1.869 4 6510.9 30.6708 < 2.2e-16 ***
phase 247.417 247.417 1 6502.0 4059.3063 < 2.2e-16 ***
TrialInBlock:Block 1.579 0.395 4 6486.8 6.4766 3.379e-05 ***
TrialInBlock:phase 17.990 17.990 1 6502.5 295.1528 < 2.2e-16 ***
Block:phase 6.830 1.707 4 6502.1 28.0133 < 2.2e-16 ***
TrialInBlock:Block:phase 7.787 1.947 4 6503.0 31.9385 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(learning_diagnostics$Mixed_X$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.8534 0.0604 17.9 0.7264 0.980
2 Execution 0.7689 0.0606 18.1 0.6416 0.896
3 Execution 0.6016 0.0612 18.9 0.4734 0.730
4 Execution 0.7505 0.0602 17.7 0.6238 0.877
5 Execution 0.5829 0.0602 17.7 0.4562 0.710
1 Preparation 0.0652 0.0603 17.8 -0.0616 0.192
2 Preparation 0.1409 0.0606 18.1 0.0137 0.268
3 Preparation 0.2242 0.0611 18.8 0.0962 0.352
4 Preparation 0.1080 0.0602 17.7 -0.0187 0.235
5 Preparation 0.1090 0.0602 17.7 -0.0177 0.236
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(learning_diagnostics$Mixed_X$fixed_effects) (Intercept) TrialInBlock
0.869554190 -0.000815170
Block2 Block3
0.056231080 -0.046320814
Block4 Block5
-0.030141574 -0.298745743
phasePreparation TrialInBlock:Block2
-0.802993291 -0.007086100
TrialInBlock:Block3 TrialInBlock:Block4
-0.010345664 -0.003661642
TrialInBlock:Block5 TrialInBlock:phasePreparation
0.001422747 0.000747590
Block2:phasePreparation Block3:phasePreparation
-0.131199560 -0.005336387
Block4:phasePreparation Block5:phasePreparation
-0.033760839 0.241061209
TrialInBlock:Block2:phasePreparation TrialInBlock:Block3:phasePreparation
0.014672477 0.020955325
TrialInBlock:Block4:phasePreparation TrialInBlock:Block5:phasePreparation
0.009034563 0.003688619 print(learning_diagnostics$Mixed_X$random_effects)$subject
(Intercept) TrialInBlock
2 0.07302469 5.308416e-04
3 0.01624823 -3.243428e-04
4 -0.08363521 1.630923e-04
5 -0.18109175 6.672144e-04
7 -0.04714231 -9.913308e-05
8 0.03653227 8.672690e-04
10 0.47350198 -5.353684e-03
11 0.24204458 -4.588085e-04
13 -0.06004387 -1.949274e-04
14 0.10671382 -1.819133e-03
15 -0.08623060 1.476287e-03
16 -0.02883266 7.445906e-04
17 -0.11511557 4.420390e-04
18 -0.03941152 8.196021e-04
19 -0.16774728 6.936795e-04
20 -0.13467107 9.835804e-04
22 -0.12154706 1.325688e-03
23 0.11740332 -4.638557e-04
with conditional variances for "subject" print(head(learning_diagnostics$Mixed_X$scaled_residuals)) 1 2 3 4 5 6
-0.18990813 -0.24184350 0.93796009 -1.31694436 0.01463411 -0.77067947 # --- Display Example for Axis Y ---
cat("\n=== LEARNING MODEL: Axis Y ===\n")
=== LEARNING MODEL: Axis Y ===print(learning_diagnostics$Mixed_Y$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
TrialInBlock 0.041 0.041 1 13.1 0.4724 0.5038
Block 6.540 1.635 4 6496.5 18.7812 2.300e-15 ***
phase 277.980 277.980 1 6486.7 3193.3384 < 2.2e-16 ***
TrialInBlock:Block 0.674 0.168 4 6450.8 1.9345 0.1018
TrialInBlock:phase 20.516 20.516 1 6487.4 235.6777 < 2.2e-16 ***
Block:phase 5.954 1.488 4 6486.9 17.0991 5.858e-14 ***
TrialInBlock:Block:phase 8.840 2.210 4 6488.0 25.3869 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(learning_diagnostics$Mixed_Y$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.9023 0.0466 19.2 0.80476 1.000
2 Execution 0.8161 0.0470 19.8 0.71804 0.914
3 Execution 0.6231 0.0482 21.9 0.52317 0.723
4 Execution 0.7800 0.0463 18.7 0.68293 0.877
5 Execution 0.6116 0.0463 18.7 0.51455 0.709
1 Preparation 0.0639 0.0465 19.0 -0.03346 0.161
2 Preparation 0.1544 0.0469 19.7 0.05643 0.252
3 Preparation 0.2321 0.0480 21.5 0.13244 0.332
4 Preparation 0.1034 0.0463 18.7 0.00637 0.200
5 Preparation 0.1030 0.0463 18.7 0.00598 0.200
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(learning_diagnostics$Mixed_Y$fixed_effects) (Intercept) TrialInBlock
0.8965891748 0.0002860064
Block2 Block3
0.0834540742 -0.0231160443
Block4 Block5
-0.0366819627 -0.2625843564
phasePreparation TrialInBlock:Block2
-0.8353361241 -0.0085408622
TrialInBlock:Block3 TrialInBlock:Block4
-0.0128963730 -0.0043103349
TrialInBlock:Block5 TrialInBlock:phasePreparation
-0.0014139899 -0.0001539001
Block2:phasePreparation Block3:phasePreparation
-0.1539901171 -0.0211594939
Block4:phasePreparation Block5:phasePreparation
-0.0335017769 0.2046221909
TrialInBlock:Block2:phasePreparation TrialInBlock:Block3:phasePreparation
0.0166549728 0.0235975593
TrialInBlock:Block4:phasePreparation TrialInBlock:Block5:phasePreparation
0.0098371767 0.0063052323 print(learning_diagnostics$Mixed_Y$random_effects)$subject
(Intercept) TrialInBlock
2 0.06495950 4.992502e-04
3 0.06287877 -1.311103e-04
4 -0.15039502 1.250827e-03
5 -0.21147593 1.057579e-03
7 -0.05367103 -3.655988e-05
8 0.12560239 1.045282e-04
10 0.48398030 -4.861964e-03
11 0.25602323 -4.358573e-04
13 -0.03175058 -7.612633e-04
14 0.05977602 -9.739708e-04
15 -0.09637827 1.127104e-03
16 -0.03957080 1.076302e-03
17 -0.11636312 8.997991e-04
18 -0.05116744 7.111814e-04
19 -0.19782374 7.779060e-04
20 -0.14111958 5.308198e-04
22 -0.16429801 1.335118e-03
23 0.20079332 -2.169688e-03
with conditional variances for "subject" print(head(learning_diagnostics$Mixed_Y$scaled_residuals)) 1 2 3 4 5 6
-0.08727244 -0.13262099 0.34444084 -0.62174085 -0.08001239 -0.69605215 # --- Display Example for Axis Z ---
cat("\n=== LEARNING MODEL: Axis Z ===\n")
=== LEARNING MODEL: Axis Z ===print(learning_diagnostics$Mixed_Z$anova)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
TrialInBlock 0.77 0.77 1 21.2 3.4021 0.07910 .
Block 15.99 4.00 4 6494.4 17.6929 1.869e-14 ***
phase 780.96 780.96 1 6485.6 3456.6273 < 2.2e-16 ***
TrialInBlock:Block 2.44 0.61 4 6473.9 2.7037 0.02881 *
TrialInBlock:phase 50.18 50.18 1 6486.1 222.1007 < 2.2e-16 ***
Block:phase 16.82 4.21 4 6485.7 18.6161 3.162e-15 ***
TrialInBlock:Block:phase 25.85 6.46 4 6486.6 28.6040 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(learning_diagnostics$Mixed_Z$emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 1.4038 0.0644 20.1 1.26954 1.538
2 Execution 1.3592 0.0651 21.0 1.22387 1.495
3 Execution 1.0714 0.0673 23.9 0.93260 1.210
4 Execution 1.3077 0.0638 19.4 1.17430 1.441
5 Execution 1.0219 0.0638 19.4 0.88852 1.155
1 Preparation 0.0652 0.0642 19.8 -0.06868 0.199
2 Preparation 0.2134 0.0650 20.9 0.07819 0.349
3 Preparation 0.3485 0.0669 23.5 0.21023 0.487
4 Preparation 0.1298 0.0638 19.4 -0.00360 0.263
5 Preparation 0.1270 0.0638 19.4 -0.00635 0.260
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(learning_diagnostics$Mixed_Z$fixed_effects) (Intercept) TrialInBlock
1.353577419 0.002528096
Block2 Block3
0.187019467 0.126105269
Block4 Block5
0.105883854 -0.334139230
phasePreparation TrialInBlock:Block2
-1.299114412 -0.011662011
TrialInBlock:Block3 TrialInBlock:Block4
-0.023089554 -0.010171168
TrialInBlock:Block5 TrialInBlock:phasePreparation
-0.002404067 -0.001985429
Block2:phasePreparation Block3:phasePreparation
-0.305102557 -0.213476645
Block4:phasePreparation Block5:phasePreparation
-0.223802256 0.230539774
TrialInBlock:Block2:phasePreparation TrialInBlock:Block3:phasePreparation
0.025071416 0.041757496
TrialInBlock:Block4:phasePreparation TrialInBlock:Block5:phasePreparation
0.019360686 0.010732750 print(learning_diagnostics$Mixed_Z$random_effects)$subject
(Intercept) TrialInBlock
2 -0.12659865 0.0029943843
3 0.07188886 0.0019215453
4 -0.18003179 0.0010373833
5 -0.34805899 0.0010072593
7 0.05044426 -0.0008655676
8 0.24469200 0.0004400951
10 0.73778702 -0.0079000916
11 0.47466205 -0.0034692325
13 0.03063876 -0.0021687529
14 0.04276772 -0.0026600999
15 -0.12972566 0.0018099850
16 0.04714354 0.0025942608
17 -0.27112242 0.0008305766
18 0.04492925 0.0001822943
19 -0.33312577 0.0011472055
20 -0.25977048 0.0019207945
22 -0.37044512 0.0025131660
23 0.27392543 -0.0013352055
with conditional variances for "subject" print(head(learning_diagnostics$Mixed_Z$scaled_residuals)) 1 2 3 4 5 6
0.56805124 0.37425066 0.28826247 -0.96807903 -0.00162998 -0.84463387 2 Movement Variability
#2.1 SD of RMS Plots
# -------- Standard Deviation Summary & Plot (Movement Variability) --------
# Convert to long format
rms_data_long <- rms_data %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(Axis = sub("rms_", "", Axis))
# Compute SD per trial per phase
rms_sd_summary <- rms_data_long %>%
group_by(Block, phase, trial, Axis) %>%
summarise(
sd_RMS = sd(RMS, na.rm = TRUE),
.groups = "drop"
)
# Compute mean SD per block-phase-axis
mean_sd_per_block_phase <- rms_sd_summary %>%
group_by(Block, phase, Axis) %>%
summarise(mean_sd = mean(sd_RMS, na.rm = TRUE), .groups = "drop")
# ---- Plot Movement Variability (SD) ----
ggplot(mean_sd_per_block_phase, aes(x = factor(Block), y = mean_sd, fill = phase)) +
geom_bar(stat = "identity", position = "dodge", width = 0.7) +
geom_vline(xintercept = 3.5, linetype = "dashed", color = "black") +
facet_wrap(~ Axis, nrow = 1) +
ylim(0, 1) +
labs(
title = "Mean Standard Deviation of CoM RMS Acceleration",
x = "Block",
y = "Mean SD of RMS Acceleration (m/s²)",
fill = "Phase"
) +
theme_minimal() +
theme(
text = element_text(size = 14),
strip.text = element_text(face = "bold"),
legend.position = "top"
)
#2.2 CV of RMS Plots
# -------- CV, Skewness, Kurtosis Summary (Long Format) --------
cv_long_summary <- rms_data %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(Axis = sub("rms_", "", Axis)) %>%
group_by(subject, Block, phase, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
sd_rms = sd(RMS, na.rm = TRUE),
cv = sd_rms / mean_rms,
skew = skewness(RMS, na.rm = TRUE),
kurt = kurtosis(RMS, na.rm = TRUE),
.groups = "drop"
)
# -------- CV Boxplot by Axis & Phase --------
ggplot(cv_long_summary, aes(x = factor(Block), y = cv, color = phase)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(width = 0.2, alpha = 0.4, size = 0.7) +
facet_wrap(~ Axis, nrow = 1) +
ylim(0, 3.5) +
labs(
title = "Coefficient of Variation (CV) of CoM RMS Acceleration",
x = "Block",
y = "CV",
color = "Phase"
) +
theme_minimal() +
theme(text = element_text(size = 12))Warning: Removed 1 row containing non-finite outside the scale range
(`stat_boxplot()`).Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_point()`).
3 Step-Analysis
#3.1 Plots for RMS ± SD: Separate Plot per Block
# -------- Step-Wise RMS ± SD: Separate Plot per Block --------
plot_stepwise_rms_by_block_split <- function(tagged_data) {
step_markers <- c(14, 15, 16, 17)
buffer <- 5
# Assign step numbers and buffer rows
step_data <- tagged_data %>%
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)
})
# Compute RMS
step_summary <- window_data %>%
group_by(subject, Block, 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 = as.numeric(Step),
Block = factor(Block)
)
# Summary for plotting
plot_data <- step_summary %>%
group_by(Block, Step, Axis) %>%
summarise(
mean_rms = mean(RMS, na.rm = TRUE),
sd_rms = sd(RMS, na.rm = TRUE),
.groups = "drop"
)
# Generate separate plots per block
blocks <- unique(plot_data$Block)
plots <- map(blocks, function(b) {
block_data <- filter(plot_data, Block == b)
ggplot(block_data, aes(x = Step, y = mean_rms)) +
geom_point(color = "steelblue", size = 2) +
geom_errorbar(aes(ymin = mean_rms - sd_rms, ymax = mean_rms + sd_rms), width = 0.3) +
facet_wrap(~ Axis, scales = "free_y") +
ylim(0, 3.25) +
labs(
title = paste("Block", b, "- Step-Wise CoM RMS Acceleration ± SD"),
x = "Step Number",
y = "RMS Acceleration (m/s²)"
) +
theme_minimal() +
theme(
text = element_text(size = 12),
strip.text = element_text(face = "bold")
)
})
names(plots) <- paste0("Block_", blocks)
return(plots)
}
# ---- Generate and Print Separate Plots per Block ----
stepwise_block_plots <- plot_stepwise_rms_by_block_split(tagged_data)
# Display them one by one
for (plot_name in names(stepwise_block_plots)) {
cat("\n\n=====", plot_name, "=====\n\n")
print(stepwise_block_plots[[plot_name]])
}
===== Block_1 =====
===== Block_2 =====
===== Block_3 =====
===== Block_4 =====
===== Block_5 =====
#3.2 Step Pairwise Model RMS
# -------- Global Settings to Suppress Emmeans Warnings --------
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# -------- Step-Wise LMM + Full Diagnostics --------
run_stepwise_lmm_full_diagnostics <- function(tagged_data, dataset_name = "Mixed") {
step_markers <- c(14, 15, 16, 17)
buffer <- 5
step_data <- tagged_data %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_block() %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup()
step_indices <- step_data %>%
select(subject, Block, trial, row_id, Step)
window_data <- map_dfr(1:nrow(step_indices), function(i) {
step <- step_indices[i, ]
rows <- (step$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$Step)
})
step_summary <- window_data %>%
group_by(subject, Block, Step) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = toupper(gsub("rms_", "", Axis)),
Step = factor(Step),
Block = factor(Block),
subject = factor(subject)
)
axis_labels <- c("X", "Y", "Z")
blocks <- unique(step_summary$Block)
results <- list()
for (blk in blocks) {
for (axis in axis_labels) {
data_sub <- step_summary %>%
filter(Block == blk, Axis == axis)
model <- lmer(RMS ~ Step + (1 | subject), data = data_sub)
aov_tbl <- anova(model)
emmeans_out <- emmeans(model, pairwise ~ Step)
key <- glue::glue("{dataset_name} - Block {blk} - Axis {axis}")
results[[key]] <- list(
ANOVA = aov_tbl,
Pairwise = summary(emmeans_out$contrasts),
Emmeans = summary(emmeans_out$emmeans),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
}
return(results)
}
# -------- Run Full Diagnostic LMMs --------
stepwise_lmm_diag_results <- run_stepwise_lmm_full_diagnostics(tagged_data)Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
unable to evaluate scaled gradientWarning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge: degenerate Hessian with 1 negative eigenvalues# -------- Print Function --------
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]]$ANOVA)
cat("\nPairwise Comparisons:\n")
print(results_list[[key]]$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")
}
}
# -------- Output Diagnostics --------
print_stepwise_lmm_diagnostics(stepwise_lmm_diag_results)=========== STEPWISE LMM DIAGNOSTICS: Mixed ===========
--- Mixed - Block 1 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 3.6349e-05 7.2698e-06 5 85 0.5483 0.7392
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000000 0.00121 85 0.000 1.0000
Step1 - Step3 -0.000237 0.00121 85 -0.195 1.0000
Step1 - Step4 0.001436 0.00121 85 1.183 0.8438
Step1 - Step5 -0.000237 0.00121 85 -0.195 1.0000
Step1 - Step6 0.000000 0.00121 85 0.000 1.0000
Step2 - Step3 -0.000237 0.00121 85 -0.195 1.0000
Step2 - Step4 0.001436 0.00121 85 1.183 0.8438
Step2 - Step5 -0.000237 0.00121 85 -0.195 1.0000
Step2 - Step6 0.000000 0.00121 85 0.000 1.0000
Step3 - Step4 0.001673 0.00121 85 1.378 0.7399
Step3 - Step5 0.000000 0.00121 85 0.000 1.0000
Step3 - Step6 0.000237 0.00121 85 0.195 1.0000
Step4 - Step5 -0.001673 0.00121 85 -1.378 0.7399
Step4 - Step6 -0.001436 0.00121 85 -1.183 0.8438
Step5 - Step6 0.000237 0.00121 85 0.195 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
9.033510e-01 -1.343375e-15 2.369465e-04 -1.435722e-03 2.369465e-04
Step6
-1.343278e-15
Random Effects:
$subject
(Intercept)
2 -0.31304681
3 0.46726960
4 -0.35153031
5 -0.35685471
7 -0.25416428
8 0.43417162
10 0.79640301
11 1.18636141
13 -0.27453277
14 0.27470644
15 -0.03594521
16 -0.29490285
17 -0.53490624
18 -0.36116900
19 -0.59237201
20 -0.35929688
22 -0.36247753
23 0.93228652
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.04467009 -0.04467009 -0.10974188 0.34961708 -0.10974188 -0.04467009
=============================================================
--- Mixed - Block 1 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 6.5888e-05 1.3178e-05 5 85 1.0991 0.367
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000000 0.00115 85 0.000 1.0000
Step1 - Step3 -0.000478 0.00115 85 -0.414 0.9984
Step1 - Step4 -0.002207 0.00115 85 -1.912 0.4020
Step1 - Step5 -0.000478 0.00115 85 -0.414 0.9984
Step1 - Step6 0.000000 0.00115 85 0.000 1.0000
Step2 - Step3 -0.000478 0.00115 85 -0.414 0.9984
Step2 - Step4 -0.002207 0.00115 85 -1.912 0.4020
Step2 - Step5 -0.000478 0.00115 85 -0.414 0.9984
Step2 - Step6 0.000000 0.00115 85 0.000 1.0000
Step3 - Step4 -0.001729 0.00115 85 -1.498 0.6665
Step3 - Step5 0.000000 0.00115 85 0.000 1.0000
Step3 - Step6 0.000478 0.00115 85 0.414 0.9984
Step4 - Step5 0.001729 0.00115 85 1.498 0.6665
Step4 - Step6 0.002207 0.00115 85 1.912 0.4020
Step5 - Step6 0.000478 0.00115 85 0.414 0.9984
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
9.193385e-01 3.718384e-15 4.780119e-04 2.207022e-03 4.780119e-04 3.718139e-15
Random Effects:
$subject
(Intercept)
2 -0.34149126
3 -0.01557639
4 -0.51582035
5 -0.46789552
7 -0.35147498
8 0.51884042
10 1.46390217
11 1.54996497
13 -0.02793612
14 0.33124128
15 -0.37957661
16 -0.42647561
17 -0.52143573
18 -0.32044305
19 -0.50343505
20 -0.34561824
22 -0.53641670
23 0.88964677
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.15181965 0.15181965 0.01376883 -0.48557269 0.01376883 0.15181965
=============================================================
--- Mixed - Block 1 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.0001275 2.5499e-05 5 85 1.4231 0.2242
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00000 0.00141 85 0.000 1.0000
Step1 - Step3 0.00030 0.00141 85 0.213 0.9999
Step1 - Step4 -0.00277 0.00141 85 -1.965 0.3708
Step1 - Step5 0.00030 0.00141 85 0.213 0.9999
Step1 - Step6 0.00000 0.00141 85 0.000 1.0000
Step2 - Step3 0.00030 0.00141 85 0.213 0.9999
Step2 - Step4 -0.00277 0.00141 85 -1.965 0.3708
Step2 - Step5 0.00030 0.00141 85 0.213 0.9999
Step2 - Step6 0.00000 0.00141 85 0.000 1.0000
Step3 - Step4 -0.00307 0.00141 85 -2.178 0.2588
Step3 - Step5 0.00000 0.00141 85 0.000 1.0000
Step3 - Step6 -0.00030 0.00141 85 -0.213 0.9999
Step4 - Step5 0.00307 0.00141 85 2.178 0.2588
Step4 - Step6 0.00277 0.00141 85 1.965 0.3708
Step5 - Step6 -0.00030 0.00141 85 -0.213 0.9999
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
1.911159e+00 9.972743e-15 -3.002440e-04 2.772995e-03 -3.002440e-04
Step6
9.972708e-15
Random Effects:
$subject
(Intercept)
2 -0.89159251
3 0.99106197
4 -0.73766169
5 -1.02403754
7 0.13388536
8 0.94843933
10 1.28591024
11 2.54731932
13 0.37298319
14 -0.92657390
15 -0.00723227
16 -0.55180433
17 -1.37027671
18 0.13952567
19 -0.98476620
20 -0.93961104
22 -0.83624691
23 1.85067803
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.0850446 0.0850446 0.1559748 -0.5700529 0.1559748 0.0850446
=============================================================
--- Mixed - Block 2 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.34496 0.03136 11 187 6.5814 3.014e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.01821 0.023 187 0.791 0.9997
Step1 - Step3 0.03153 0.023 187 1.370 0.9677
Step1 - Step4 0.03715 0.023 187 1.614 0.9018
Step1 - Step5 0.04117 0.023 187 1.789 0.8218
Step1 - Step6 0.04689 0.023 187 2.038 0.6669
Step1 - Step7 0.04862 0.023 187 2.113 0.6143
Step1 - Step8 0.06690 0.023 187 2.907 0.1469
Step1 - Step9 0.09947 0.023 187 4.323 0.0015
Step1 - Step10 0.10902 0.023 187 4.738 0.0003
Step1 - Step11 0.11852 0.023 187 5.151 <.0001
Step1 - Step12 0.12667 0.023 187 5.505 <.0001
Step2 - Step3 0.01332 0.023 187 0.579 1.0000
Step2 - Step4 0.01893 0.023 187 0.823 0.9996
Step2 - Step5 0.02296 0.023 187 0.998 0.9976
Step2 - Step6 0.02868 0.023 187 1.247 0.9843
Step2 - Step7 0.03041 0.023 187 1.321 0.9754
Step2 - Step8 0.04869 0.023 187 2.116 0.6121
Step2 - Step9 0.08126 0.023 187 3.531 0.0254
Step2 - Step10 0.09081 0.023 187 3.947 0.0061
Step2 - Step11 0.10031 0.023 187 4.360 0.0013
Step2 - Step12 0.10846 0.023 187 4.714 0.0003
Step3 - Step4 0.00561 0.023 187 0.244 1.0000
Step3 - Step5 0.00964 0.023 187 0.419 1.0000
Step3 - Step6 0.01536 0.023 187 0.668 0.9999
Step3 - Step7 0.01708 0.023 187 0.742 0.9999
Step3 - Step8 0.03536 0.023 187 1.537 0.9283
Step3 - Step9 0.06793 0.023 187 2.952 0.1316
Step3 - Step10 0.07749 0.023 187 3.368 0.0421
Step3 - Step11 0.08699 0.023 187 3.780 0.0111
Step3 - Step12 0.09514 0.023 187 4.135 0.0031
Step4 - Step5 0.00403 0.023 187 0.175 1.0000
Step4 - Step6 0.00975 0.023 187 0.424 1.0000
Step4 - Step7 0.01147 0.023 187 0.499 1.0000
Step4 - Step8 0.02975 0.023 187 1.293 0.9791
Step4 - Step9 0.06232 0.023 187 2.709 0.2304
Step4 - Step10 0.07188 0.023 187 3.124 0.0845
Step4 - Step11 0.08138 0.023 187 3.537 0.0249
Step4 - Step12 0.08953 0.023 187 3.891 0.0075
Step5 - Step6 0.00572 0.023 187 0.249 1.0000
Step5 - Step7 0.00744 0.023 187 0.323 1.0000
Step5 - Step8 0.02572 0.023 187 1.118 0.9936
Step5 - Step9 0.05829 0.023 187 2.533 0.3261
Step5 - Step10 0.06785 0.023 187 2.949 0.1329
Step5 - Step11 0.07735 0.023 187 3.362 0.0429
Step5 - Step12 0.08550 0.023 187 3.716 0.0138
Step6 - Step7 0.00172 0.023 187 0.075 1.0000
Step6 - Step8 0.02000 0.023 187 0.869 0.9993
Step6 - Step9 0.05257 0.023 187 2.285 0.4911
Step6 - Step10 0.06213 0.023 187 2.700 0.2346
Step6 - Step11 0.07163 0.023 187 3.113 0.0870
Step6 - Step12 0.07978 0.023 187 3.467 0.0311
Step7 - Step8 0.01828 0.023 187 0.794 0.9997
Step7 - Step9 0.05085 0.023 187 2.210 0.5446
Step7 - Step10 0.06040 0.023 187 2.625 0.2735
Step7 - Step11 0.06990 0.023 187 3.038 0.1060
Step7 - Step12 0.07806 0.023 187 3.392 0.0391
Step8 - Step9 0.03257 0.023 187 1.416 0.9592
Step8 - Step10 0.04213 0.023 187 1.831 0.7990
Step8 - Step11 0.05163 0.023 187 2.244 0.5204
Step8 - Step12 0.05978 0.023 187 2.598 0.2886
Step9 - Step10 0.00955 0.023 187 0.415 1.0000
Step9 - Step11 0.01905 0.023 187 0.828 0.9996
Step9 - Step12 0.02720 0.023 187 1.182 0.9897
Step10 - Step11 0.00950 0.023 187 0.413 1.0000
Step10 - Step12 0.01765 0.023 187 0.767 0.9998
Step11 - Step12 0.00815 0.023 187 0.354 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.87088941 -0.01821043 -0.03153397 -0.03714541 -0.04117452 -0.04689354
Step7 Step8 Step9 Step10 Step11 Step12
-0.04861641 -0.06689580 -0.09946748 -0.10902120 -0.11852127 -0.12667167
Random Effects:
$subject
(Intercept)
2 0.28233873
3 0.18937486
4 -0.34329097
5 -0.29571225
7 -0.18208210
8 0.17263703
10 0.84812261
11 0.98627106
13 -0.28153644
14 0.20444475
15 -0.16575175
16 -0.17554454
17 -0.31096263
18 -0.15518140
19 -0.34536283
20 -0.29928598
22 -0.15447203
23 0.02599387
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.5230097 -0.9884890 -1.4028116 -0.5991659 -0.3681573 0.3975858
=============================================================
--- Mixed - Block 2 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.15911 0.014465 11 187 2.1374 0.01966 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00221 0.0274 187 0.080 1.0000
Step1 - Step3 0.01473 0.0274 187 0.537 1.0000
Step1 - Step4 0.01980 0.0274 187 0.722 0.9999
Step1 - Step5 0.02304 0.0274 187 0.840 0.9995
Step1 - Step6 0.02620 0.0274 187 0.956 0.9984
Step1 - Step7 0.04122 0.0274 187 1.503 0.9381
Step1 - Step8 0.05133 0.0274 187 1.872 0.7749
Step1 - Step9 0.05716 0.0274 187 2.084 0.6344
Step1 - Step10 0.06187 0.0274 187 2.256 0.5115
Step1 - Step11 0.07664 0.0274 187 2.795 0.1909
Step1 - Step12 0.08556 0.0274 187 3.120 0.0854
Step2 - Step3 0.01252 0.0274 187 0.457 1.0000
Step2 - Step4 0.01759 0.0274 187 0.641 1.0000
Step2 - Step5 0.02083 0.0274 187 0.760 0.9998
Step2 - Step6 0.02400 0.0274 187 0.875 0.9993
Step2 - Step7 0.03902 0.0274 187 1.423 0.9576
Step2 - Step8 0.04913 0.0274 187 1.792 0.8207
Step2 - Step9 0.05495 0.0274 187 2.004 0.6902
Step2 - Step10 0.05966 0.0274 187 2.176 0.5693
Step2 - Step11 0.07443 0.0274 187 2.714 0.2276
Step2 - Step12 0.08335 0.0274 187 3.040 0.1056
Step3 - Step4 0.00507 0.0274 187 0.185 1.0000
Step3 - Step5 0.00831 0.0274 187 0.303 1.0000
Step3 - Step6 0.01148 0.0274 187 0.419 1.0000
Step3 - Step7 0.02650 0.0274 187 0.966 0.9982
Step3 - Step8 0.03661 0.0274 187 1.335 0.9734
Step3 - Step9 0.04243 0.0274 187 1.547 0.9250
Step3 - Step10 0.04714 0.0274 187 1.719 0.8573
Step3 - Step11 0.06191 0.0274 187 2.258 0.5103
Step3 - Step12 0.07083 0.0274 187 2.583 0.2970
Step4 - Step5 0.00324 0.0274 187 0.118 1.0000
Step4 - Step6 0.00641 0.0274 187 0.234 1.0000
Step4 - Step7 0.02143 0.0274 187 0.781 0.9998
Step4 - Step8 0.03154 0.0274 187 1.150 0.9918
Step4 - Step9 0.03736 0.0274 187 1.362 0.9691
Step4 - Step10 0.04207 0.0274 187 1.534 0.9291
Step4 - Step11 0.05684 0.0274 187 2.073 0.6426
Step4 - Step12 0.06576 0.0274 187 2.398 0.4126
Step5 - Step6 0.00317 0.0274 187 0.116 1.0000
Step5 - Step7 0.01819 0.0274 187 0.663 1.0000
Step5 - Step8 0.02830 0.0274 187 1.032 0.9968
Step5 - Step9 0.03412 0.0274 187 1.244 0.9845
Step5 - Step10 0.03883 0.0274 187 1.416 0.9591
Step5 - Step11 0.05360 0.0274 187 1.955 0.7229
Step5 - Step12 0.06252 0.0274 187 2.280 0.4945
Step6 - Step7 0.01502 0.0274 187 0.548 1.0000
Step6 - Step8 0.02513 0.0274 187 0.916 0.9989
Step6 - Step9 0.03096 0.0274 187 1.129 0.9930
Step6 - Step10 0.03566 0.0274 187 1.301 0.9782
Step6 - Step11 0.05044 0.0274 187 1.839 0.7941
Step6 - Step12 0.05935 0.0274 187 2.164 0.5773
Step7 - Step8 0.01011 0.0274 187 0.369 1.0000
Step7 - Step9 0.01593 0.0274 187 0.581 1.0000
Step7 - Step10 0.02064 0.0274 187 0.753 0.9998
Step7 - Step11 0.03541 0.0274 187 1.291 0.9793
Step7 - Step12 0.04433 0.0274 187 1.617 0.9010
Step8 - Step9 0.00583 0.0274 187 0.212 1.0000
Step8 - Step10 0.01053 0.0274 187 0.384 1.0000
Step8 - Step11 0.02531 0.0274 187 0.923 0.9988
Step8 - Step12 0.03422 0.0274 187 1.248 0.9842
Step9 - Step10 0.00471 0.0274 187 0.172 1.0000
Step9 - Step11 0.01948 0.0274 187 0.710 0.9999
Step9 - Step12 0.02840 0.0274 187 1.036 0.9967
Step10 - Step11 0.01477 0.0274 187 0.539 1.0000
Step10 - Step12 0.02369 0.0274 187 0.864 0.9994
Step11 - Step12 0.00892 0.0274 187 0.325 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.915640591 -0.002206877 -0.014727037 -0.019797229 -0.023035267 -0.026203243
Step7 Step8 Step9 Step10 Step11 Step12
-0.041224960 -0.051333071 -0.057158852 -0.061867452 -0.076638672 -0.085556183
Random Effects:
$subject
(Intercept)
2 0.18471939
3 0.37503726
4 -0.46215459
5 -0.43759428
7 -0.18823031
8 0.68909557
10 0.82952104
11 1.09340874
13 -0.25532207
14 0.09366402
15 -0.28172676
16 -0.11407996
17 -0.29039133
18 -0.20610963
19 -0.34856010
20 -0.25190308
22 -0.49217550
23 0.06280158
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.8862877 -0.8257382 -0.3788806 -0.5657424 0.1050657 -0.1231394
=============================================================
--- Mixed - Block 2 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.31403 0.028548 11 187 1.0622 0.3942
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.010127 0.0546 187 0.185 1.0000
Step1 - Step3 0.017660 0.0546 187 0.323 1.0000
Step1 - Step4 0.017799 0.0546 187 0.326 1.0000
Step1 - Step5 0.021011 0.0546 187 0.384 1.0000
Step1 - Step6 0.019690 0.0546 187 0.360 1.0000
Step1 - Step7 0.040106 0.0546 187 0.734 0.9999
Step1 - Step8 0.058965 0.0546 187 1.079 0.9952
Step1 - Step9 0.079766 0.0546 187 1.460 0.9494
Step1 - Step10 0.087186 0.0546 187 1.595 0.9088
Step1 - Step11 0.117830 0.0546 187 2.156 0.5833
Step1 - Step12 0.100389 0.0546 187 1.837 0.7954
Step2 - Step3 0.007533 0.0546 187 0.138 1.0000
Step2 - Step4 0.007672 0.0546 187 0.140 1.0000
Step2 - Step5 0.010884 0.0546 187 0.199 1.0000
Step2 - Step6 0.009563 0.0546 187 0.175 1.0000
Step2 - Step7 0.029979 0.0546 187 0.549 1.0000
Step2 - Step8 0.048838 0.0546 187 0.894 0.9991
Step2 - Step9 0.069639 0.0546 187 1.274 0.9814
Step2 - Step10 0.077059 0.0546 187 1.410 0.9603
Step2 - Step11 0.107703 0.0546 187 1.971 0.7124
Step2 - Step12 0.090262 0.0546 187 1.652 0.8871
Step3 - Step4 0.000138 0.0546 187 0.003 1.0000
Step3 - Step5 0.003351 0.0546 187 0.061 1.0000
Step3 - Step6 0.002030 0.0546 187 0.037 1.0000
Step3 - Step7 0.022445 0.0546 187 0.411 1.0000
Step3 - Step8 0.041305 0.0546 187 0.756 0.9998
Step3 - Step9 0.062106 0.0546 187 1.136 0.9926
Step3 - Step10 0.069526 0.0546 187 1.272 0.9816
Step3 - Step11 0.100169 0.0546 187 1.833 0.7977
Step3 - Step12 0.082729 0.0546 187 1.514 0.9351
Step4 - Step5 0.003212 0.0546 187 0.059 1.0000
Step4 - Step6 0.001892 0.0546 187 0.035 1.0000
Step4 - Step7 0.022307 0.0546 187 0.408 1.0000
Step4 - Step8 0.041166 0.0546 187 0.753 0.9998
Step4 - Step9 0.061967 0.0546 187 1.134 0.9927
Step4 - Step10 0.069387 0.0546 187 1.270 0.9819
Step4 - Step11 0.100031 0.0546 187 1.830 0.7991
Step4 - Step12 0.082590 0.0546 187 1.511 0.9358
Step5 - Step6 -0.001321 0.0546 187 -0.024 1.0000
Step5 - Step7 0.019095 0.0546 187 0.349 1.0000
Step5 - Step8 0.037954 0.0546 187 0.695 0.9999
Step5 - Step9 0.058755 0.0546 187 1.075 0.9954
Step5 - Step10 0.066175 0.0546 187 1.211 0.9875
Step5 - Step11 0.096819 0.0546 187 1.772 0.8311
Step5 - Step12 0.079378 0.0546 187 1.453 0.9510
Step6 - Step7 0.020415 0.0546 187 0.374 1.0000
Step6 - Step8 0.039274 0.0546 187 0.719 0.9999
Step6 - Step9 0.060075 0.0546 187 1.099 0.9944
Step6 - Step10 0.067496 0.0546 187 1.235 0.9854
Step6 - Step11 0.098139 0.0546 187 1.796 0.8183
Step6 - Step12 0.080698 0.0546 187 1.477 0.9451
Step7 - Step8 0.018859 0.0546 187 0.345 1.0000
Step7 - Step9 0.039660 0.0546 187 0.726 0.9999
Step7 - Step10 0.047080 0.0546 187 0.862 0.9994
Step7 - Step11 0.077724 0.0546 187 1.422 0.9578
Step7 - Step12 0.060283 0.0546 187 1.103 0.9942
Step8 - Step9 0.020801 0.0546 187 0.381 1.0000
Step8 - Step10 0.028221 0.0546 187 0.516 1.0000
Step8 - Step11 0.058865 0.0546 187 1.077 0.9953
Step8 - Step12 0.041424 0.0546 187 0.758 0.9998
Step9 - Step10 0.007420 0.0546 187 0.136 1.0000
Step9 - Step11 0.038064 0.0546 187 0.697 0.9999
Step9 - Step12 0.020623 0.0546 187 0.377 1.0000
Step10 - Step11 0.030644 0.0546 187 0.561 1.0000
Step10 - Step12 0.013203 0.0546 187 0.242 1.0000
Step11 - Step12 -0.017441 0.0546 187 -0.319 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.79057546 -0.01012696 -0.01766023 -0.01779866 -0.02101094 -0.01969042
Step7 Step8 Step9 Step10 Step11 Step12
-0.04010554 -0.05896485 -0.07976575 -0.08718597 -0.11782967 -0.10038882
Random Effects:
$subject
(Intercept)
2 -0.1474609
3 0.5520054
4 -0.8154371
5 -0.8007244
7 0.0919751
8 0.8892435
10 1.6019275
11 2.1068230
13 -0.4724234
14 -0.5384222
15 -0.3232169
16 0.4164849
17 -0.8794031
18 0.3431330
19 -0.7447090
20 -0.7086679
22 -0.6732561
23 0.1021287
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.31105538 0.17581098 0.19034833 0.21761241 0.12793070 0.01944703
=============================================================
--- Mixed - Block 3 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.233 0.013706 17 289 3.9247 5.812e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 3.31e-03 0.0197 289 0.168 1.0000
Step1 - Step3 1.18e-02 0.0197 289 0.600 1.0000
Step1 - Step4 1.38e-02 0.0197 289 0.700 1.0000
Step1 - Step5 1.06e-02 0.0197 289 0.538 1.0000
Step1 - Step6 1.10e-02 0.0197 289 0.557 1.0000
Step1 - Step7 1.55e-02 0.0197 289 0.789 1.0000
Step1 - Step8 3.04e-02 0.0197 289 1.541 0.9868
Step1 - Step9 3.31e-02 0.0197 289 1.681 0.9689
Step1 - Step10 5.11e-02 0.0197 289 2.596 0.4600
Step1 - Step11 5.15e-02 0.0197 289 2.617 0.4447
Step1 - Step12 6.10e-02 0.0197 289 3.096 0.1645
Step1 - Step13 6.02e-02 0.0197 289 3.058 0.1807
Step1 - Step14 5.76e-02 0.0197 289 2.926 0.2452
Step1 - Step15 6.02e-02 0.0197 289 3.056 0.1814
Step1 - Step16 7.09e-02 0.0197 289 3.598 0.0392
Step1 - Step17 8.00e-02 0.0197 289 4.062 0.0077
Step1 - Step18 8.13e-02 0.0197 289 4.126 0.0060
Step2 - Step3 8.50e-03 0.0197 289 0.432 1.0000
Step2 - Step4 1.05e-02 0.0197 289 0.532 1.0000
Step2 - Step5 7.30e-03 0.0197 289 0.371 1.0000
Step2 - Step6 7.66e-03 0.0197 289 0.389 1.0000
Step2 - Step7 1.22e-02 0.0197 289 0.621 1.0000
Step2 - Step8 2.70e-02 0.0197 289 1.373 0.9963
Step2 - Step9 2.98e-02 0.0197 289 1.513 0.9892
Step2 - Step10 4.78e-02 0.0197 289 2.428 0.5870
Step2 - Step11 4.82e-02 0.0197 289 2.449 0.5712
Step2 - Step12 5.77e-02 0.0197 289 2.928 0.2437
Step2 - Step13 5.69e-02 0.0197 289 2.890 0.2650
Step2 - Step14 5.43e-02 0.0197 289 2.758 0.3461
Step2 - Step15 5.69e-02 0.0197 289 2.888 0.2659
Step2 - Step16 6.76e-02 0.0197 289 3.430 0.0659
Step2 - Step17 7.67e-02 0.0197 289 3.894 0.0143
Step2 - Step18 7.80e-02 0.0197 289 3.958 0.0113
Step3 - Step4 1.98e-03 0.0197 289 0.100 1.0000
Step3 - Step5 -1.20e-03 0.0197 289 -0.061 1.0000
Step3 - Step6 -8.46e-04 0.0197 289 -0.043 1.0000
Step3 - Step7 3.73e-03 0.0197 289 0.189 1.0000
Step3 - Step8 1.85e-02 0.0197 289 0.941 1.0000
Step3 - Step9 2.13e-02 0.0197 289 1.081 0.9998
Step3 - Step10 3.93e-02 0.0197 289 1.997 0.8686
Step3 - Step11 3.97e-02 0.0197 289 2.017 0.8586
Step3 - Step12 4.92e-02 0.0197 289 2.497 0.5348
Step3 - Step13 4.84e-02 0.0197 289 2.458 0.5641
Step3 - Step14 4.58e-02 0.0197 289 2.326 0.6636
Step3 - Step15 4.84e-02 0.0197 289 2.457 0.5653
Step3 - Step16 5.91e-02 0.0197 289 2.999 0.2080
Step3 - Step17 6.82e-02 0.0197 289 3.463 0.0598
Step3 - Step18 6.95e-02 0.0197 289 3.527 0.0491
Step4 - Step5 -3.18e-03 0.0197 289 -0.161 1.0000
Step4 - Step6 -2.82e-03 0.0197 289 -0.143 1.0000
Step4 - Step7 1.75e-03 0.0197 289 0.089 1.0000
Step4 - Step8 1.66e-02 0.0197 289 0.841 1.0000
Step4 - Step9 1.93e-02 0.0197 289 0.981 1.0000
Step4 - Step10 3.74e-02 0.0197 289 1.896 0.9111
Step4 - Step11 3.78e-02 0.0197 289 1.917 0.9032
Step4 - Step12 4.72e-02 0.0197 289 2.396 0.6112
Step4 - Step13 4.64e-02 0.0197 289 2.358 0.6401
Step4 - Step14 4.38e-02 0.0197 289 2.226 0.7348
Step4 - Step15 4.64e-02 0.0197 289 2.356 0.6413
Step4 - Step16 5.71e-02 0.0197 289 2.898 0.2604
Step4 - Step17 6.62e-02 0.0197 289 3.362 0.0804
Step4 - Step18 6.75e-02 0.0197 289 3.426 0.0667
Step5 - Step6 3.58e-04 0.0197 289 0.018 1.0000
Step5 - Step7 4.93e-03 0.0197 289 0.250 1.0000
Step5 - Step8 1.97e-02 0.0197 289 1.003 0.9999
Step5 - Step9 2.25e-02 0.0197 289 1.142 0.9996
Step5 - Step10 4.05e-02 0.0197 289 2.058 0.8377
Step5 - Step11 4.09e-02 0.0197 289 2.078 0.8264
Step5 - Step12 5.04e-02 0.0197 289 2.558 0.4885
Step5 - Step13 4.96e-02 0.0197 289 2.519 0.5176
Step5 - Step14 4.70e-02 0.0197 289 2.387 0.6181
Step5 - Step15 4.96e-02 0.0197 289 2.518 0.5188
Step5 - Step16 6.03e-02 0.0197 289 3.060 0.1799
Step5 - Step17 6.94e-02 0.0197 289 3.524 0.0495
Step5 - Step18 7.07e-02 0.0197 289 3.588 0.0405
Step6 - Step7 4.57e-03 0.0197 289 0.232 1.0000
Step6 - Step8 1.94e-02 0.0197 289 0.984 0.9999
Step6 - Step9 2.21e-02 0.0197 289 1.124 0.9997
Step6 - Step10 4.02e-02 0.0197 289 2.040 0.8473
Step6 - Step11 4.06e-02 0.0197 289 2.060 0.8363
Step6 - Step12 5.00e-02 0.0197 289 2.540 0.5022
Step6 - Step13 4.93e-02 0.0197 289 2.501 0.5314
Step6 - Step14 4.67e-02 0.0197 289 2.369 0.6317
Step6 - Step15 4.92e-02 0.0197 289 2.500 0.5326
Step6 - Step16 5.99e-02 0.0197 289 3.041 0.1880
Step6 - Step17 6.91e-02 0.0197 289 3.506 0.0524
Step6 - Step18 7.03e-02 0.0197 289 3.570 0.0429
Step7 - Step8 1.48e-02 0.0197 289 0.752 1.0000
Step7 - Step9 1.76e-02 0.0197 289 0.892 1.0000
Step7 - Step10 3.56e-02 0.0197 289 1.807 0.9401
Step7 - Step11 3.60e-02 0.0197 289 1.828 0.9340
Step7 - Step12 4.55e-02 0.0197 289 2.307 0.6773
Step7 - Step13 4.47e-02 0.0197 289 2.269 0.7048
Step7 - Step14 4.21e-02 0.0197 289 2.137 0.7923
Step7 - Step15 4.47e-02 0.0197 289 2.267 0.7059
Step7 - Step16 5.53e-02 0.0197 289 2.809 0.3131
Step7 - Step17 6.45e-02 0.0197 289 3.273 0.1034
Step7 - Step18 6.57e-02 0.0197 289 3.337 0.0864
Step8 - Step9 2.75e-03 0.0197 289 0.140 1.0000
Step8 - Step10 2.08e-02 0.0197 289 1.055 0.9999
Step8 - Step11 2.12e-02 0.0197 289 1.076 0.9998
Step8 - Step12 3.06e-02 0.0197 289 1.555 0.9855
Step8 - Step13 2.99e-02 0.0197 289 1.517 0.9888
Step8 - Step14 2.73e-02 0.0197 289 1.385 0.9959
Step8 - Step15 2.98e-02 0.0197 289 1.515 0.9890
Step8 - Step16 4.05e-02 0.0197 289 2.057 0.8381
Step8 - Step17 4.97e-02 0.0197 289 2.521 0.5161
Step8 - Step18 5.09e-02 0.0197 289 2.585 0.4680
Step9 - Step10 1.80e-02 0.0197 289 0.916 1.0000
Step9 - Step11 1.84e-02 0.0197 289 0.936 1.0000
Step9 - Step12 2.79e-02 0.0197 289 1.416 0.9948
Step9 - Step13 2.71e-02 0.0197 289 1.377 0.9962
Step9 - Step14 2.45e-02 0.0197 289 1.245 0.9989
Step9 - Step15 2.71e-02 0.0197 289 1.376 0.9962
Step9 - Step16 3.78e-02 0.0197 289 1.917 0.9030
Step9 - Step17 4.69e-02 0.0197 289 2.382 0.6223
Step9 - Step18 4.82e-02 0.0197 289 2.446 0.5738
Step10 - Step11 4.09e-04 0.0197 289 0.021 1.0000
Step10 - Step12 9.85e-03 0.0197 289 0.500 1.0000
Step10 - Step13 9.09e-03 0.0197 289 0.462 1.0000
Step10 - Step14 6.49e-03 0.0197 289 0.330 1.0000
Step10 - Step15 9.06e-03 0.0197 289 0.460 1.0000
Step10 - Step16 1.97e-02 0.0197 289 1.002 0.9999
Step10 - Step17 2.89e-02 0.0197 289 1.466 0.9923
Step10 - Step18 3.01e-02 0.0197 289 1.530 0.9878
Step11 - Step12 9.44e-03 0.0197 289 0.479 1.0000
Step11 - Step13 8.69e-03 0.0197 289 0.441 1.0000
Step11 - Step14 6.08e-03 0.0197 289 0.309 1.0000
Step11 - Step15 8.65e-03 0.0197 289 0.439 1.0000
Step11 - Step16 1.93e-02 0.0197 289 0.981 1.0000
Step11 - Step17 2.85e-02 0.0197 289 1.445 0.9934
Step11 - Step18 2.97e-02 0.0197 289 1.509 0.9894
Step12 - Step13 -7.57e-04 0.0197 289 -0.038 1.0000
Step12 - Step14 -3.36e-03 0.0197 289 -0.171 1.0000
Step12 - Step15 -7.88e-04 0.0197 289 -0.040 1.0000
Step12 - Step16 9.88e-03 0.0197 289 0.502 1.0000
Step12 - Step17 1.90e-02 0.0197 289 0.966 1.0000
Step12 - Step18 2.03e-02 0.0197 289 1.030 0.9999
Step13 - Step14 -2.60e-03 0.0197 289 -0.132 1.0000
Step13 - Step15 -3.12e-05 0.0197 289 -0.002 1.0000
Step13 - Step16 1.06e-02 0.0197 289 0.540 1.0000
Step13 - Step17 1.98e-02 0.0197 289 1.004 0.9999
Step13 - Step18 2.10e-02 0.0197 289 1.068 0.9998
Step14 - Step15 2.57e-03 0.0197 289 0.131 1.0000
Step14 - Step16 1.32e-02 0.0197 289 0.672 1.0000
Step14 - Step17 2.24e-02 0.0197 289 1.137 0.9996
Step14 - Step18 2.36e-02 0.0197 289 1.201 0.9993
Step15 - Step16 1.07e-02 0.0197 289 0.542 1.0000
Step15 - Step17 1.98e-02 0.0197 289 1.006 0.9999
Step15 - Step18 2.11e-02 0.0197 289 1.070 0.9998
Step16 - Step17 9.15e-03 0.0197 289 0.464 1.0000
Step16 - Step18 1.04e-02 0.0197 289 0.528 1.0000
Step17 - Step18 1.26e-03 0.0197 289 0.064 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.689309168 -0.003305951 -0.011809312 -0.013786735 -0.010605600 -0.010963456
Step7 Step8 Step9 Step10 Step11 Step12
-0.015537692 -0.030353983 -0.033104519 -0.051139534 -0.051548403 -0.060991308
Step13 Step14 Step15 Step16 Step17 Step18
-0.060234324 -0.057630813 -0.060203113 -0.070874770 -0.080019924 -0.081279532
Random Effects:
$subject
(Intercept)
2 0.217037342
3 0.033555084
4 -0.234093010
5 -0.316646415
7 -0.069082186
8 0.087326188
10 0.652465179
11 0.490556976
13 -0.195562843
14 -0.045275608
15 -0.125049094
16 -0.047142158
17 -0.060202858
18 0.153796820
19 -0.212052954
20 -0.233419425
22 -0.103076962
23 0.006865923
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.9965127 -0.1189668 -0.4756679 -0.3119872 -0.5505712 -0.2530975
=============================================================
--- Mixed - Block 3 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.17203 0.01012 17 289 2.4861 0.001117 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.002131 0.0213 289 0.100 1.0000
Step1 - Step3 0.005563 0.0213 289 0.262 1.0000
Step1 - Step4 0.008644 0.0213 289 0.406 1.0000
Step1 - Step5 0.002865 0.0213 289 0.135 1.0000
Step1 - Step6 -0.001075 0.0213 289 -0.051 1.0000
Step1 - Step7 -0.006767 0.0213 289 -0.318 1.0000
Step1 - Step8 0.006123 0.0213 289 0.288 1.0000
Step1 - Step9 0.010348 0.0213 289 0.487 1.0000
Step1 - Step10 0.022694 0.0213 289 1.067 0.9998
Step1 - Step11 0.031230 0.0213 289 1.469 0.9921
Step1 - Step12 0.034406 0.0213 289 1.618 0.9784
Step1 - Step13 0.036427 0.0213 289 1.713 0.9628
Step1 - Step14 0.036046 0.0213 289 1.695 0.9663
Step1 - Step15 0.037173 0.0213 289 1.748 0.9553
Step1 - Step16 0.048228 0.0213 289 2.268 0.7057
Step1 - Step17 0.062916 0.0213 289 2.958 0.2280
Step1 - Step18 0.075799 0.0213 289 3.564 0.0436
Step2 - Step3 0.003432 0.0213 289 0.161 1.0000
Step2 - Step4 0.006513 0.0213 289 0.306 1.0000
Step2 - Step5 0.000734 0.0213 289 0.034 1.0000
Step2 - Step6 -0.003206 0.0213 289 -0.151 1.0000
Step2 - Step7 -0.008898 0.0213 289 -0.418 1.0000
Step2 - Step8 0.003992 0.0213 289 0.188 1.0000
Step2 - Step9 0.008217 0.0213 289 0.386 1.0000
Step2 - Step10 0.020563 0.0213 289 0.967 1.0000
Step2 - Step11 0.029099 0.0213 289 1.368 0.9964
Step2 - Step12 0.032275 0.0213 289 1.518 0.9888
Step2 - Step13 0.034295 0.0213 289 1.613 0.9791
Step2 - Step14 0.033915 0.0213 289 1.595 0.9813
Step2 - Step15 0.035042 0.0213 289 1.648 0.9742
Step2 - Step16 0.046096 0.0213 289 2.168 0.7731
Step2 - Step17 0.060784 0.0213 289 2.858 0.2833
Step2 - Step18 0.073668 0.0213 289 3.464 0.0595
Step3 - Step4 0.003081 0.0213 289 0.145 1.0000
Step3 - Step5 -0.002698 0.0213 289 -0.127 1.0000
Step3 - Step6 -0.006638 0.0213 289 -0.312 1.0000
Step3 - Step7 -0.012330 0.0213 289 -0.580 1.0000
Step3 - Step8 0.000560 0.0213 289 0.026 1.0000
Step3 - Step9 0.004785 0.0213 289 0.225 1.0000
Step3 - Step10 0.017131 0.0213 289 0.806 1.0000
Step3 - Step11 0.025667 0.0213 289 1.207 0.9992
Step3 - Step12 0.028843 0.0213 289 1.356 0.9968
Step3 - Step13 0.030864 0.0213 289 1.451 0.9931
Step3 - Step14 0.030483 0.0213 289 1.433 0.9940
Step3 - Step15 0.031610 0.0213 289 1.486 0.9910
Step3 - Step16 0.042665 0.0213 289 2.006 0.8641
Step3 - Step17 0.057353 0.0213 289 2.697 0.3875
Step3 - Step18 0.070236 0.0213 289 3.303 0.0953
Step4 - Step5 -0.005779 0.0213 289 -0.272 1.0000
Step4 - Step6 -0.009719 0.0213 289 -0.457 1.0000
Step4 - Step7 -0.015411 0.0213 289 -0.725 1.0000
Step4 - Step8 -0.002521 0.0213 289 -0.119 1.0000
Step4 - Step9 0.001704 0.0213 289 0.080 1.0000
Step4 - Step10 0.014050 0.0213 289 0.661 1.0000
Step4 - Step11 0.022586 0.0213 289 1.062 0.9999
Step4 - Step12 0.025762 0.0213 289 1.211 0.9992
Step4 - Step13 0.027783 0.0213 289 1.306 0.9979
Step4 - Step14 0.027402 0.0213 289 1.289 0.9983
Step4 - Step15 0.028529 0.0213 289 1.342 0.9972
Step4 - Step16 0.039584 0.0213 289 1.861 0.9234
Step4 - Step17 0.054272 0.0213 289 2.552 0.4930
Step4 - Step18 0.067155 0.0213 289 3.158 0.1407
Step5 - Step6 -0.003939 0.0213 289 -0.185 1.0000
Step5 - Step7 -0.009632 0.0213 289 -0.453 1.0000
Step5 - Step8 0.003258 0.0213 289 0.153 1.0000
Step5 - Step9 0.007484 0.0213 289 0.352 1.0000
Step5 - Step10 0.019830 0.0213 289 0.932 1.0000
Step5 - Step11 0.028365 0.0213 289 1.334 0.9974
Step5 - Step12 0.031542 0.0213 289 1.483 0.9912
Step5 - Step13 0.033562 0.0213 289 1.578 0.9832
Step5 - Step14 0.033181 0.0213 289 1.560 0.9850
Step5 - Step15 0.034309 0.0213 289 1.613 0.9790
Step5 - Step16 0.045363 0.0213 289 2.133 0.7946
Step5 - Step17 0.060051 0.0213 289 2.824 0.3041
Step5 - Step18 0.072935 0.0213 289 3.430 0.0660
Step6 - Step7 -0.005692 0.0213 289 -0.268 1.0000
Step6 - Step8 0.007198 0.0213 289 0.338 1.0000
Step6 - Step9 0.011423 0.0213 289 0.537 1.0000
Step6 - Step10 0.023769 0.0213 289 1.118 0.9997
Step6 - Step11 0.032305 0.0213 289 1.519 0.9887
Step6 - Step12 0.035481 0.0213 289 1.668 0.9709
Step6 - Step13 0.037501 0.0213 289 1.763 0.9517
Step6 - Step14 0.037121 0.0213 289 1.745 0.9559
Step6 - Step15 0.038248 0.0213 289 1.799 0.9426
Step6 - Step16 0.049302 0.0213 289 2.318 0.6694
Step6 - Step17 0.063990 0.0213 289 3.009 0.2030
Step6 - Step18 0.076874 0.0213 289 3.615 0.0371
Step7 - Step8 0.012890 0.0213 289 0.606 1.0000
Step7 - Step9 0.017115 0.0213 289 0.805 1.0000
Step7 - Step10 0.029461 0.0213 289 1.385 0.9959
Step7 - Step11 0.037997 0.0213 289 1.787 0.9458
Step7 - Step12 0.041173 0.0213 289 1.936 0.8955
Step7 - Step13 0.043193 0.0213 289 2.031 0.8517
Step7 - Step14 0.042813 0.0213 289 2.013 0.8606
Step7 - Step15 0.043940 0.0213 289 2.066 0.8332
Step7 - Step16 0.054994 0.0213 289 2.586 0.4675
Step7 - Step17 0.069683 0.0213 289 3.277 0.1025
Step7 - Step18 0.082566 0.0213 289 3.882 0.0149
Step8 - Step9 0.004225 0.0213 289 0.199 1.0000
Step8 - Step10 0.016571 0.0213 289 0.779 1.0000
Step8 - Step11 0.025107 0.0213 289 1.181 0.9994
Step8 - Step12 0.028283 0.0213 289 1.330 0.9975
Step8 - Step13 0.030304 0.0213 289 1.425 0.9944
Step8 - Step14 0.029923 0.0213 289 1.407 0.9951
Step8 - Step15 0.031051 0.0213 289 1.460 0.9926
Step8 - Step16 0.042105 0.0213 289 1.980 0.8765
Step8 - Step17 0.056793 0.0213 289 2.671 0.4060
Step8 - Step18 0.069676 0.0213 289 3.276 0.1025
Step9 - Step10 0.012346 0.0213 289 0.581 1.0000
Step9 - Step11 0.020882 0.0213 289 0.982 1.0000
Step9 - Step12 0.024058 0.0213 289 1.131 0.9997
Step9 - Step13 0.026078 0.0213 289 1.226 0.9991
Step9 - Step14 0.025698 0.0213 289 1.208 0.9992
Step9 - Step15 0.026825 0.0213 289 1.261 0.9987
Step9 - Step16 0.037879 0.0213 289 1.781 0.9472
Step9 - Step17 0.052567 0.0213 289 2.472 0.5538
Step9 - Step18 0.065451 0.0213 289 3.078 0.1722
Step10 - Step11 0.008536 0.0213 289 0.401 1.0000
Step10 - Step12 0.011712 0.0213 289 0.551 1.0000
Step10 - Step13 0.013732 0.0213 289 0.646 1.0000
Step10 - Step14 0.013352 0.0213 289 0.628 1.0000
Step10 - Step15 0.014479 0.0213 289 0.681 1.0000
Step10 - Step16 0.025533 0.0213 289 1.201 0.9993
Step10 - Step17 0.040221 0.0213 289 1.891 0.9129
Step10 - Step18 0.053105 0.0213 289 2.497 0.5345
Step11 - Step12 0.003176 0.0213 289 0.149 1.0000
Step11 - Step13 0.005196 0.0213 289 0.244 1.0000
Step11 - Step14 0.004816 0.0213 289 0.226 1.0000
Step11 - Step15 0.005943 0.0213 289 0.279 1.0000
Step11 - Step16 0.016997 0.0213 289 0.799 1.0000
Step11 - Step17 0.031686 0.0213 289 1.490 0.9908
Step11 - Step18 0.044569 0.0213 289 2.096 0.8166
Step12 - Step13 0.002020 0.0213 289 0.095 1.0000
Step12 - Step14 0.001640 0.0213 289 0.077 1.0000
Step12 - Step15 0.002767 0.0213 289 0.130 1.0000
Step12 - Step16 0.013821 0.0213 289 0.650 1.0000
Step12 - Step17 0.028509 0.0213 289 1.341 0.9972
Step12 - Step18 0.041393 0.0213 289 1.946 0.8912
Step13 - Step14 -0.000380 0.0213 289 -0.018 1.0000
Step13 - Step15 0.000747 0.0213 289 0.035 1.0000
Step13 - Step16 0.011801 0.0213 289 0.555 1.0000
Step13 - Step17 0.026489 0.0213 289 1.246 0.9989
Step13 - Step18 0.039373 0.0213 289 1.851 0.9267
Step14 - Step15 0.001127 0.0213 289 0.053 1.0000
Step14 - Step16 0.012181 0.0213 289 0.573 1.0000
Step14 - Step17 0.026870 0.0213 289 1.263 0.9986
Step14 - Step18 0.039753 0.0213 289 1.869 0.9207
Step15 - Step16 0.011054 0.0213 289 0.520 1.0000
Step15 - Step17 0.025742 0.0213 289 1.210 0.9992
Step15 - Step18 0.038626 0.0213 289 1.816 0.9376
Step16 - Step17 0.014688 0.0213 289 0.691 1.0000
Step16 - Step18 0.027572 0.0213 289 1.296 0.9981
Step17 - Step18 0.012884 0.0213 289 0.606 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.696902361 -0.002131264 -0.005563023 -0.008643998 -0.002864774 0.001074614
Step7 Step8 Step9 Step10 Step11 Step12
0.006766807 -0.006122937 -0.010348414 -0.022694347 -0.031230184 -0.034406319
Step13 Step14 Step15 Step16 Step17 Step18
-0.036426630 -0.036046142 -0.037173483 -0.048227557 -0.062915706 -0.075799312
Random Effects:
$subject
(Intercept)
2 0.11067362
3 0.24126818
4 -0.19756778
5 -0.21922887
7 -0.10876780
8 0.26530435
10 0.65696392
11 0.19910429
13 -0.18156031
14 0.02331389
15 0.01310774
16 -0.11719019
17 -0.02139368
18 -0.06177287
19 -0.23766503
20 -0.18475356
22 -0.27069470
23 0.09085881
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.8618287 -0.5153149 -0.8523797 -0.2206190 0.7062235 0.4722699
=============================================================
--- Mixed - Block 3 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.15751 0.0092653 17 289 0.832 0.6555
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.007128 0.0352 289 0.203 1.0000
Step1 - Step3 0.006744 0.0352 289 0.192 1.0000
Step1 - Step4 0.012191 0.0352 289 0.347 1.0000
Step1 - Step5 0.007362 0.0352 289 0.209 1.0000
Step1 - Step6 0.015308 0.0352 289 0.435 1.0000
Step1 - Step7 0.009666 0.0352 289 0.275 1.0000
Step1 - Step8 0.027661 0.0352 289 0.786 1.0000
Step1 - Step9 0.036206 0.0352 289 1.029 0.9999
Step1 - Step10 0.039308 0.0352 289 1.117 0.9997
Step1 - Step11 0.045058 0.0352 289 1.281 0.9984
Step1 - Step12 0.043526 0.0352 289 1.237 0.9989
Step1 - Step13 0.049684 0.0352 289 1.412 0.9949
Step1 - Step14 0.056215 0.0352 289 1.598 0.9809
Step1 - Step15 0.054530 0.0352 289 1.550 0.9860
Step1 - Step16 0.065661 0.0352 289 1.867 0.9217
Step1 - Step17 0.062591 0.0352 289 1.779 0.9477
Step1 - Step18 0.061268 0.0352 289 1.742 0.9567
Step2 - Step3 -0.000384 0.0352 289 -0.011 1.0000
Step2 - Step4 0.005063 0.0352 289 0.144 1.0000
Step2 - Step5 0.000234 0.0352 289 0.007 1.0000
Step2 - Step6 0.008180 0.0352 289 0.233 1.0000
Step2 - Step7 0.002538 0.0352 289 0.072 1.0000
Step2 - Step8 0.020533 0.0352 289 0.584 1.0000
Step2 - Step9 0.029078 0.0352 289 0.827 1.0000
Step2 - Step10 0.032180 0.0352 289 0.915 1.0000
Step2 - Step11 0.037930 0.0352 289 1.078 0.9998
Step2 - Step12 0.036398 0.0352 289 1.035 0.9999
Step2 - Step13 0.042556 0.0352 289 1.210 0.9992
Step2 - Step14 0.049087 0.0352 289 1.395 0.9955
Step2 - Step15 0.047402 0.0352 289 1.348 0.9970
Step2 - Step16 0.058533 0.0352 289 1.664 0.9717
Step2 - Step17 0.055463 0.0352 289 1.577 0.9833
Step2 - Step18 0.054140 0.0352 289 1.539 0.9870
Step3 - Step4 0.005447 0.0352 289 0.155 1.0000
Step3 - Step5 0.000618 0.0352 289 0.018 1.0000
Step3 - Step6 0.008564 0.0352 289 0.243 1.0000
Step3 - Step7 0.002922 0.0352 289 0.083 1.0000
Step3 - Step8 0.020917 0.0352 289 0.595 1.0000
Step3 - Step9 0.029462 0.0352 289 0.838 1.0000
Step3 - Step10 0.032564 0.0352 289 0.926 1.0000
Step3 - Step11 0.038314 0.0352 289 1.089 0.9998
Step3 - Step12 0.036782 0.0352 289 1.046 0.9999
Step3 - Step13 0.042940 0.0352 289 1.221 0.9991
Step3 - Step14 0.049471 0.0352 289 1.406 0.9951
Step3 - Step15 0.047786 0.0352 289 1.358 0.9967
Step3 - Step16 0.058917 0.0352 289 1.675 0.9698
Step3 - Step17 0.055847 0.0352 289 1.588 0.9821
Step3 - Step18 0.054524 0.0352 289 1.550 0.9860
Step4 - Step5 -0.004830 0.0352 289 -0.137 1.0000
Step4 - Step6 0.003117 0.0352 289 0.089 1.0000
Step4 - Step7 -0.002525 0.0352 289 -0.072 1.0000
Step4 - Step8 0.015470 0.0352 289 0.440 1.0000
Step4 - Step9 0.024015 0.0352 289 0.683 1.0000
Step4 - Step10 0.027117 0.0352 289 0.771 1.0000
Step4 - Step11 0.032867 0.0352 289 0.934 1.0000
Step4 - Step12 0.031335 0.0352 289 0.891 1.0000
Step4 - Step13 0.037493 0.0352 289 1.066 0.9998
Step4 - Step14 0.044024 0.0352 289 1.252 0.9988
Step4 - Step15 0.042339 0.0352 289 1.204 0.9993
Step4 - Step16 0.053470 0.0352 289 1.520 0.9886
Step4 - Step17 0.050400 0.0352 289 1.433 0.9940
Step4 - Step18 0.049077 0.0352 289 1.395 0.9956
Step5 - Step6 0.007946 0.0352 289 0.226 1.0000
Step5 - Step7 0.002305 0.0352 289 0.066 1.0000
Step5 - Step8 0.020299 0.0352 289 0.577 1.0000
Step5 - Step9 0.028844 0.0352 289 0.820 1.0000
Step5 - Step10 0.031947 0.0352 289 0.908 1.0000
Step5 - Step11 0.037697 0.0352 289 1.072 0.9998
Step5 - Step12 0.036164 0.0352 289 1.028 0.9999
Step5 - Step13 0.042322 0.0352 289 1.203 0.9993
Step5 - Step14 0.048854 0.0352 289 1.389 0.9958
Step5 - Step15 0.047169 0.0352 289 1.341 0.9972
Step5 - Step16 0.058300 0.0352 289 1.657 0.9727
Step5 - Step17 0.055230 0.0352 289 1.570 0.9840
Step5 - Step18 0.053906 0.0352 289 1.532 0.9876
Step6 - Step7 -0.005642 0.0352 289 -0.160 1.0000
Step6 - Step8 0.012353 0.0352 289 0.351 1.0000
Step6 - Step9 0.020898 0.0352 289 0.594 1.0000
Step6 - Step10 0.024000 0.0352 289 0.682 1.0000
Step6 - Step11 0.029751 0.0352 289 0.846 1.0000
Step6 - Step12 0.028218 0.0352 289 0.802 1.0000
Step6 - Step13 0.034376 0.0352 289 0.977 1.0000
Step6 - Step14 0.040908 0.0352 289 1.163 0.9995
Step6 - Step15 0.039222 0.0352 289 1.115 0.9997
Step6 - Step16 0.050353 0.0352 289 1.431 0.9941
Step6 - Step17 0.047283 0.0352 289 1.344 0.9971
Step6 - Step18 0.045960 0.0352 289 1.307 0.9979
Step7 - Step8 0.017995 0.0352 289 0.512 1.0000
Step7 - Step9 0.026540 0.0352 289 0.754 1.0000
Step7 - Step10 0.029642 0.0352 289 0.843 1.0000
Step7 - Step11 0.035392 0.0352 289 1.006 0.9999
Step7 - Step12 0.033860 0.0352 289 0.963 1.0000
Step7 - Step13 0.040018 0.0352 289 1.138 0.9996
Step7 - Step14 0.046549 0.0352 289 1.323 0.9976
Step7 - Step15 0.044864 0.0352 289 1.275 0.9985
Step7 - Step16 0.055995 0.0352 289 1.592 0.9817
Step7 - Step17 0.052925 0.0352 289 1.505 0.9898
Step7 - Step18 0.051602 0.0352 289 1.467 0.9922
Step8 - Step9 0.008545 0.0352 289 0.243 1.0000
Step8 - Step10 0.011647 0.0352 289 0.331 1.0000
Step8 - Step11 0.017398 0.0352 289 0.495 1.0000
Step8 - Step12 0.015865 0.0352 289 0.451 1.0000
Step8 - Step13 0.022023 0.0352 289 0.626 1.0000
Step8 - Step14 0.028555 0.0352 289 0.812 1.0000
Step8 - Step15 0.026869 0.0352 289 0.764 1.0000
Step8 - Step16 0.038000 0.0352 289 1.080 0.9998
Step8 - Step17 0.034930 0.0352 289 0.993 0.9999
Step8 - Step18 0.033607 0.0352 289 0.955 1.0000
Step9 - Step10 0.003102 0.0352 289 0.088 1.0000
Step9 - Step11 0.008852 0.0352 289 0.252 1.0000
Step9 - Step12 0.007320 0.0352 289 0.208 1.0000
Step9 - Step13 0.013478 0.0352 289 0.383 1.0000
Step9 - Step14 0.020009 0.0352 289 0.569 1.0000
Step9 - Step15 0.018324 0.0352 289 0.521 1.0000
Step9 - Step16 0.029455 0.0352 289 0.837 1.0000
Step9 - Step17 0.026385 0.0352 289 0.750 1.0000
Step9 - Step18 0.025062 0.0352 289 0.712 1.0000
Step10 - Step11 0.005750 0.0352 289 0.163 1.0000
Step10 - Step12 0.004218 0.0352 289 0.120 1.0000
Step10 - Step13 0.010376 0.0352 289 0.295 1.0000
Step10 - Step14 0.016907 0.0352 289 0.481 1.0000
Step10 - Step15 0.015222 0.0352 289 0.433 1.0000
Step10 - Step16 0.026353 0.0352 289 0.749 1.0000
Step10 - Step17 0.023283 0.0352 289 0.662 1.0000
Step10 - Step18 0.021960 0.0352 289 0.624 1.0000
Step11 - Step12 -0.001532 0.0352 289 -0.044 1.0000
Step11 - Step13 0.004626 0.0352 289 0.131 1.0000
Step11 - Step14 0.011157 0.0352 289 0.317 1.0000
Step11 - Step15 0.009472 0.0352 289 0.269 1.0000
Step11 - Step16 0.020603 0.0352 289 0.586 1.0000
Step11 - Step17 0.017533 0.0352 289 0.498 1.0000
Step11 - Step18 0.016209 0.0352 289 0.461 1.0000
Step12 - Step13 0.006158 0.0352 289 0.175 1.0000
Step12 - Step14 0.012689 0.0352 289 0.361 1.0000
Step12 - Step15 0.011004 0.0352 289 0.313 1.0000
Step12 - Step16 0.022135 0.0352 289 0.629 1.0000
Step12 - Step17 0.019065 0.0352 289 0.542 1.0000
Step12 - Step18 0.017742 0.0352 289 0.504 1.0000
Step13 - Step14 0.006531 0.0352 289 0.186 1.0000
Step13 - Step15 0.004846 0.0352 289 0.138 1.0000
Step13 - Step16 0.015977 0.0352 289 0.454 1.0000
Step13 - Step17 0.012907 0.0352 289 0.367 1.0000
Step13 - Step18 0.011584 0.0352 289 0.329 1.0000
Step14 - Step15 -0.001685 0.0352 289 -0.048 1.0000
Step14 - Step16 0.009446 0.0352 289 0.269 1.0000
Step14 - Step17 0.006376 0.0352 289 0.181 1.0000
Step14 - Step18 0.005052 0.0352 289 0.144 1.0000
Step15 - Step16 0.011131 0.0352 289 0.316 1.0000
Step15 - Step17 0.008061 0.0352 289 0.229 1.0000
Step15 - Step18 0.006738 0.0352 289 0.192 1.0000
Step16 - Step17 -0.003070 0.0352 289 -0.087 1.0000
Step16 - Step18 -0.004393 0.0352 289 -0.125 1.0000
Step17 - Step18 -0.001324 0.0352 289 -0.038 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.468854734 -0.007128076 -0.006744010 -0.012191149 -0.007361597 -0.015307936
Step7 Step8 Step9 Step10 Step11 Step12
-0.009666256 -0.027660958 -0.036206015 -0.039308206 -0.045058466 -0.043526034
Step13 Step14 Step15 Step16 Step17 Step18
-0.049684043 -0.056215458 -0.054530288 -0.065661112 -0.062591406 -0.061267824
Random Effects:
$subject
(Intercept)
2 0.11364790
3 0.48351802
4 -0.66326977
5 -0.73420340
7 0.27589996
8 0.13705590
10 2.04364135
11 0.39240357
13 -0.37328200
14 0.10553543
15 -0.24318679
16 0.17402938
17 -0.39162124
18 0.44451774
19 -0.60821764
20 -0.57887660
22 -0.52256179
23 -0.05503001
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.29851085 0.85188820 0.41045393 0.27290405 -0.08093394 -0.58195098
=============================================================
--- Mixed - Block 4 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.25215 0.014832 17 289 2.8141 0.0002125 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 1.72e-03 0.0242 289 0.071 1.0000
Step1 - Step3 -8.16e-03 0.0242 289 -0.337 1.0000
Step1 - Step4 -3.25e-03 0.0242 289 -0.134 1.0000
Step1 - Step5 1.55e-03 0.0242 289 0.064 1.0000
Step1 - Step6 -2.40e-03 0.0242 289 -0.099 1.0000
Step1 - Step7 -2.40e-03 0.0242 289 -0.099 1.0000
Step1 - Step8 4.05e-03 0.0242 289 0.168 1.0000
Step1 - Step9 1.61e-02 0.0242 289 0.665 1.0000
Step1 - Step10 2.05e-02 0.0242 289 0.847 1.0000
Step1 - Step11 1.95e-02 0.0242 289 0.804 1.0000
Step1 - Step12 4.37e-02 0.0242 289 1.806 0.9404
Step1 - Step13 6.25e-02 0.0242 289 2.582 0.4707
Step1 - Step14 5.02e-02 0.0242 289 2.075 0.8281
Step1 - Step15 4.52e-02 0.0242 289 1.866 0.9218
Step1 - Step16 7.47e-02 0.0242 289 3.086 0.1688
Step1 - Step17 7.03e-02 0.0242 289 2.905 0.2568
Step1 - Step18 5.67e-02 0.0242 289 2.344 0.6502
Step2 - Step3 -9.88e-03 0.0242 289 -0.408 1.0000
Step2 - Step4 -4.98e-03 0.0242 289 -0.206 1.0000
Step2 - Step5 -1.68e-04 0.0242 289 -0.007 1.0000
Step2 - Step6 -4.12e-03 0.0242 289 -0.170 1.0000
Step2 - Step7 -4.12e-03 0.0242 289 -0.170 1.0000
Step2 - Step8 2.33e-03 0.0242 289 0.096 1.0000
Step2 - Step9 1.44e-02 0.0242 289 0.594 1.0000
Step2 - Step10 1.88e-02 0.0242 289 0.776 1.0000
Step2 - Step11 1.77e-02 0.0242 289 0.733 1.0000
Step2 - Step12 4.20e-02 0.0242 289 1.735 0.9581
Step2 - Step13 6.08e-02 0.0242 289 2.511 0.5243
Step2 - Step14 4.85e-02 0.0242 289 2.004 0.8650
Step2 - Step15 4.34e-02 0.0242 289 1.795 0.9435
Step2 - Step16 7.30e-02 0.0242 289 3.015 0.2003
Step2 - Step17 6.86e-02 0.0242 289 2.833 0.2982
Step2 - Step18 5.50e-02 0.0242 289 2.273 0.7019
Step3 - Step4 4.90e-03 0.0242 289 0.203 1.0000
Step3 - Step5 9.71e-03 0.0242 289 0.401 1.0000
Step3 - Step6 5.75e-03 0.0242 289 0.238 1.0000
Step3 - Step7 5.75e-03 0.0242 289 0.238 1.0000
Step3 - Step8 1.22e-02 0.0242 289 0.505 1.0000
Step3 - Step9 2.42e-02 0.0242 289 1.002 0.9999
Step3 - Step10 2.87e-02 0.0242 289 1.184 0.9994
Step3 - Step11 2.76e-02 0.0242 289 1.141 0.9996
Step3 - Step12 5.19e-02 0.0242 289 2.143 0.7883
Step3 - Step13 7.06e-02 0.0242 289 2.919 0.2490
Step3 - Step14 5.84e-02 0.0242 289 2.412 0.5992
Step3 - Step15 5.33e-02 0.0242 289 2.203 0.7500
Step3 - Step16 8.28e-02 0.0242 289 3.423 0.0674
Step3 - Step17 7.84e-02 0.0242 289 3.242 0.1128
Step3 - Step18 6.49e-02 0.0242 289 2.681 0.3984
Step4 - Step5 4.81e-03 0.0242 289 0.199 1.0000
Step4 - Step6 8.51e-04 0.0242 289 0.035 1.0000
Step4 - Step7 8.52e-04 0.0242 289 0.035 1.0000
Step4 - Step8 7.31e-03 0.0242 289 0.302 1.0000
Step4 - Step9 1.93e-02 0.0242 289 0.799 1.0000
Step4 - Step10 2.38e-02 0.0242 289 0.981 1.0000
Step4 - Step11 2.27e-02 0.0242 289 0.938 1.0000
Step4 - Step12 4.70e-02 0.0242 289 1.941 0.8935
Step4 - Step13 6.57e-02 0.0242 289 2.716 0.3742
Step4 - Step14 5.35e-02 0.0242 289 2.210 0.7456
Step4 - Step15 4.84e-02 0.0242 289 2.001 0.8668
Step4 - Step16 7.79e-02 0.0242 289 3.220 0.1194
Step4 - Step17 7.35e-02 0.0242 289 3.039 0.1891
Step4 - Step18 6.00e-02 0.0242 289 2.479 0.5485
Step5 - Step6 -3.96e-03 0.0242 289 -0.163 1.0000
Step5 - Step7 -3.95e-03 0.0242 289 -0.163 1.0000
Step5 - Step8 2.50e-03 0.0242 289 0.103 1.0000
Step5 - Step9 1.45e-02 0.0242 289 0.601 1.0000
Step5 - Step10 1.89e-02 0.0242 289 0.783 1.0000
Step5 - Step11 1.79e-02 0.0242 289 0.740 1.0000
Step5 - Step12 4.22e-02 0.0242 289 1.742 0.9566
Step5 - Step13 6.09e-02 0.0242 289 2.518 0.5190
Step5 - Step14 4.87e-02 0.0242 289 2.011 0.8617
Step5 - Step15 4.36e-02 0.0242 289 1.802 0.9416
Step5 - Step16 7.31e-02 0.0242 289 3.022 0.1971
Step5 - Step17 6.87e-02 0.0242 289 2.840 0.2940
Step5 - Step18 5.52e-02 0.0242 289 2.280 0.6970
Step6 - Step7 1.01e-06 0.0242 289 0.000 1.0000
Step6 - Step8 6.46e-03 0.0242 289 0.267 1.0000
Step6 - Step9 1.85e-02 0.0242 289 0.764 1.0000
Step6 - Step10 2.29e-02 0.0242 289 0.946 1.0000
Step6 - Step11 2.19e-02 0.0242 289 0.903 1.0000
Step6 - Step12 4.61e-02 0.0242 289 1.906 0.9076
Step6 - Step13 6.49e-02 0.0242 289 2.681 0.3986
Step6 - Step14 5.26e-02 0.0242 289 2.175 0.7687
Step6 - Step15 4.76e-02 0.0242 289 1.965 0.8830
Step6 - Step16 7.71e-02 0.0242 289 3.185 0.1311
Step6 - Step17 7.27e-02 0.0242 289 3.004 0.2054
Step6 - Step18 5.91e-02 0.0242 289 2.444 0.5754
Step7 - Step8 6.46e-03 0.0242 289 0.267 1.0000
Step7 - Step9 1.85e-02 0.0242 289 0.764 1.0000
Step7 - Step10 2.29e-02 0.0242 289 0.946 1.0000
Step7 - Step11 2.19e-02 0.0242 289 0.903 1.0000
Step7 - Step12 4.61e-02 0.0242 289 1.906 0.9076
Step7 - Step13 6.49e-02 0.0242 289 2.681 0.3986
Step7 - Step14 5.26e-02 0.0242 289 2.175 0.7687
Step7 - Step15 4.76e-02 0.0242 289 1.965 0.8830
Step7 - Step16 7.71e-02 0.0242 289 3.185 0.1311
Step7 - Step17 7.27e-02 0.0242 289 3.004 0.2054
Step7 - Step18 5.91e-02 0.0242 289 2.444 0.5754
Step8 - Step9 1.20e-02 0.0242 289 0.497 1.0000
Step8 - Step10 1.64e-02 0.0242 289 0.680 1.0000
Step8 - Step11 1.54e-02 0.0242 289 0.636 1.0000
Step8 - Step12 3.97e-02 0.0242 289 1.639 0.9755
Step8 - Step13 5.84e-02 0.0242 289 2.414 0.5977
Step8 - Step14 4.62e-02 0.0242 289 1.908 0.9068
Step8 - Step15 4.11e-02 0.0242 289 1.699 0.9656
Step8 - Step16 7.06e-02 0.0242 289 2.918 0.2493
Step8 - Step17 6.62e-02 0.0242 289 2.737 0.3600
Step8 - Step18 5.27e-02 0.0242 289 2.177 0.7672
Step9 - Step10 4.41e-03 0.0242 289 0.182 1.0000
Step9 - Step11 3.36e-03 0.0242 289 0.139 1.0000
Step9 - Step12 2.76e-02 0.0242 289 1.142 0.9996
Step9 - Step13 4.64e-02 0.0242 289 1.917 0.9032
Step9 - Step14 3.41e-02 0.0242 289 1.410 0.9950
Step9 - Step15 2.91e-02 0.0242 289 1.201 0.9993
Step9 - Step16 5.86e-02 0.0242 289 2.421 0.5926
Step9 - Step17 5.42e-02 0.0242 289 2.240 0.7253
Step9 - Step18 4.06e-02 0.0242 289 1.679 0.9691
Step10 - Step11 -1.05e-03 0.0242 289 -0.043 1.0000
Step10 - Step12 2.32e-02 0.0242 289 0.959 1.0000
Step10 - Step13 4.20e-02 0.0242 289 1.735 0.9583
Step10 - Step14 2.97e-02 0.0242 289 1.228 0.9990
Step10 - Step15 2.47e-02 0.0242 289 1.019 0.9999
Step10 - Step16 5.42e-02 0.0242 289 2.239 0.7259
Step10 - Step17 4.98e-02 0.0242 289 2.058 0.8378
Step10 - Step18 3.62e-02 0.0242 289 1.497 0.9903
Step11 - Step12 2.43e-02 0.0242 289 1.003 0.9999
Step11 - Step13 4.30e-02 0.0242 289 1.778 0.9480
Step11 - Step14 3.08e-02 0.0242 289 1.272 0.9985
Step11 - Step15 2.57e-02 0.0242 289 1.062 0.9999
Step11 - Step16 5.52e-02 0.0242 289 2.282 0.6956
Step11 - Step17 5.08e-02 0.0242 289 2.101 0.8137
Step11 - Step18 3.73e-02 0.0242 289 1.541 0.9869
Step12 - Step13 1.88e-02 0.0242 289 0.775 1.0000
Step12 - Step14 6.51e-03 0.0242 289 0.269 1.0000
Step12 - Step15 1.45e-03 0.0242 289 0.060 1.0000
Step12 - Step16 3.10e-02 0.0242 289 1.279 0.9984
Step12 - Step17 2.66e-02 0.0242 289 1.098 0.9998
Step12 - Step18 1.30e-02 0.0242 289 0.538 1.0000
Step13 - Step14 -1.23e-02 0.0242 289 -0.506 1.0000
Step13 - Step15 -1.73e-02 0.0242 289 -0.716 1.0000
Step13 - Step16 1.22e-02 0.0242 289 0.504 1.0000
Step13 - Step17 7.81e-03 0.0242 289 0.323 1.0000
Step13 - Step18 -5.75e-03 0.0242 289 -0.237 1.0000
Step14 - Step15 -5.06e-03 0.0242 289 -0.209 1.0000
Step14 - Step16 2.45e-02 0.0242 289 1.010 0.9999
Step14 - Step17 2.01e-02 0.0242 289 0.829 1.0000
Step14 - Step18 6.51e-03 0.0242 289 0.269 1.0000
Step15 - Step16 2.95e-02 0.0242 289 1.220 0.9991
Step15 - Step17 2.51e-02 0.0242 289 1.038 0.9999
Step15 - Step18 1.16e-02 0.0242 289 0.478 1.0000
Step16 - Step17 -4.38e-03 0.0242 289 -0.181 1.0000
Step16 - Step18 -1.79e-02 0.0242 289 -0.741 1.0000
Step17 - Step18 -1.36e-02 0.0242 289 -0.560 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.778454008 -0.001722254 0.008154995 0.003252814 -0.001554268 0.002401562
Step7 Step8 Step9 Step10 Step11 Step12
0.002400557 -0.004054728 -0.016090644 -0.020498675 -0.019450045 -0.043714835
Step13 Step14 Step15 Step16 Step17 Step18
-0.062477643 -0.050222268 -0.045160930 -0.074675757 -0.070291020 -0.056732481
Random Effects:
$subject
(Intercept)
2 0.11709623
3 -0.10546447
4 -0.27101283
5 -0.42855871
7 -0.09708163
8 0.41056427
10 1.15545637
11 0.42071593
13 -0.21297071
14 -0.03185362
15 -0.21351277
16 0.13384627
17 -0.14468682
18 -0.01479793
19 -0.22654812
20 -0.25994927
22 -0.17740503
23 -0.05383716
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.08752551 -0.39168491 0.23427732 -0.23241553 -0.33719605 -0.06044152
=============================================================
--- Mixed - Block 4 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 1.0102 0.059424 17 289 6.3067 1.415e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.003459 0.0324 289 -0.107 1.0000
Step1 - Step3 0.028378 0.0324 289 0.877 1.0000
Step1 - Step4 0.024563 0.0324 289 0.759 1.0000
Step1 - Step5 0.026464 0.0324 289 0.818 1.0000
Step1 - Step6 0.053216 0.0324 289 1.645 0.9747
Step1 - Step7 0.037728 0.0324 289 1.166 0.9995
Step1 - Step8 0.072733 0.0324 289 2.248 0.7196
Step1 - Step9 0.075260 0.0324 289 2.326 0.6637
Step1 - Step10 0.088741 0.0324 289 2.743 0.3563
Step1 - Step11 0.101042 0.0324 289 3.123 0.1539
Step1 - Step12 0.123077 0.0324 289 3.804 0.0197
Step1 - Step13 0.157385 0.0324 289 4.864 0.0003
Step1 - Step14 0.135146 0.0324 289 4.177 0.0050
Step1 - Step15 0.122813 0.0324 289 3.796 0.0202
Step1 - Step16 0.169141 0.0324 289 5.227 <.0001
Step1 - Step17 0.160686 0.0324 289 4.966 0.0002
Step1 - Step18 0.144933 0.0324 289 4.479 0.0015
Step2 - Step3 0.031836 0.0324 289 0.984 0.9999
Step2 - Step4 0.028021 0.0324 289 0.866 1.0000
Step2 - Step5 0.029923 0.0324 289 0.925 1.0000
Step2 - Step6 0.056675 0.0324 289 1.752 0.9545
Step2 - Step7 0.041187 0.0324 289 1.273 0.9985
Step2 - Step8 0.076191 0.0324 289 2.355 0.6425
Step2 - Step9 0.078719 0.0324 289 2.433 0.5835
Step2 - Step10 0.092199 0.0324 289 2.850 0.2885
Step2 - Step11 0.104501 0.0324 289 3.230 0.1164
Step2 - Step12 0.126536 0.0324 289 3.911 0.0135
Step2 - Step13 0.160843 0.0324 289 4.971 0.0002
Step2 - Step14 0.138605 0.0324 289 4.284 0.0033
Step2 - Step15 0.126272 0.0324 289 3.903 0.0139
Step2 - Step16 0.172600 0.0324 289 5.334 <.0001
Step2 - Step17 0.164144 0.0324 289 5.073 0.0001
Step2 - Step18 0.148391 0.0324 289 4.586 0.0009
Step3 - Step4 -0.003815 0.0324 289 -0.118 1.0000
Step3 - Step5 -0.001914 0.0324 289 -0.059 1.0000
Step3 - Step6 0.024838 0.0324 289 0.768 1.0000
Step3 - Step7 0.009350 0.0324 289 0.289 1.0000
Step3 - Step8 0.044355 0.0324 289 1.371 0.9964
Step3 - Step9 0.046882 0.0324 289 1.449 0.9932
Step3 - Step10 0.060363 0.0324 289 1.866 0.9220
Step3 - Step11 0.072664 0.0324 289 2.246 0.7211
Step3 - Step12 0.094699 0.0324 289 2.927 0.2446
Step3 - Step13 0.129007 0.0324 289 3.987 0.0102
Step3 - Step14 0.106768 0.0324 289 3.300 0.0961
Step3 - Step15 0.094435 0.0324 289 2.919 0.2491
Step3 - Step16 0.140763 0.0324 289 4.350 0.0025
Step3 - Step17 0.132308 0.0324 289 4.089 0.0070
Step3 - Step18 0.116555 0.0324 289 3.602 0.0386
Step4 - Step5 0.001901 0.0324 289 0.059 1.0000
Step4 - Step6 0.028653 0.0324 289 0.886 1.0000
Step4 - Step7 0.013165 0.0324 289 0.407 1.0000
Step4 - Step8 0.048170 0.0324 289 1.489 0.9909
Step4 - Step9 0.050698 0.0324 289 1.567 0.9844
Step4 - Step10 0.064178 0.0324 289 1.983 0.8748
Step4 - Step11 0.076480 0.0324 289 2.364 0.6358
Step4 - Step12 0.098514 0.0324 289 3.045 0.1865
Step4 - Step13 0.132822 0.0324 289 4.105 0.0066
Step4 - Step14 0.110584 0.0324 289 3.418 0.0684
Step4 - Step15 0.098250 0.0324 289 3.037 0.1902
Step4 - Step16 0.144579 0.0324 289 4.468 0.0015
Step4 - Step17 0.136123 0.0324 289 4.207 0.0044
Step4 - Step18 0.120370 0.0324 289 3.720 0.0262
Step5 - Step6 0.026752 0.0324 289 0.827 1.0000
Step5 - Step7 0.011264 0.0324 289 0.348 1.0000
Step5 - Step8 0.046268 0.0324 289 1.430 0.9941
Step5 - Step9 0.048796 0.0324 289 1.508 0.9895
Step5 - Step10 0.062276 0.0324 289 1.925 0.9001
Step5 - Step11 0.074578 0.0324 289 2.305 0.6791
Step5 - Step12 0.096613 0.0324 289 2.986 0.2141
Step5 - Step13 0.130921 0.0324 289 4.046 0.0082
Step5 - Step14 0.108682 0.0324 289 3.359 0.0812
Step5 - Step15 0.096349 0.0324 289 2.978 0.2182
Step5 - Step16 0.142677 0.0324 289 4.410 0.0019
Step5 - Step17 0.134222 0.0324 289 4.148 0.0055
Step5 - Step18 0.118469 0.0324 289 3.661 0.0319
Step6 - Step7 -0.015488 0.0324 289 -0.479 1.0000
Step6 - Step8 0.019516 0.0324 289 0.603 1.0000
Step6 - Step9 0.022044 0.0324 289 0.681 1.0000
Step6 - Step10 0.035524 0.0324 289 1.098 0.9998
Step6 - Step11 0.047826 0.0324 289 1.478 0.9915
Step6 - Step12 0.069861 0.0324 289 2.159 0.7785
Step6 - Step13 0.104169 0.0324 289 3.219 0.1197
Step6 - Step14 0.081930 0.0324 289 2.532 0.5079
Step6 - Step15 0.069597 0.0324 289 2.151 0.7836
Step6 - Step16 0.115925 0.0324 289 3.583 0.0411
Step6 - Step17 0.107470 0.0324 289 3.321 0.0904
Step6 - Step18 0.091717 0.0324 289 2.835 0.2975
Step7 - Step8 0.035005 0.0324 289 1.082 0.9998
Step7 - Step9 0.037532 0.0324 289 1.160 0.9995
Step7 - Step10 0.051013 0.0324 289 1.577 0.9833
Step7 - Step11 0.063314 0.0324 289 1.957 0.8867
Step7 - Step12 0.085349 0.0324 289 2.638 0.4294
Step7 - Step13 0.119657 0.0324 289 3.698 0.0282
Step7 - Step14 0.097418 0.0324 289 3.011 0.2021
Step7 - Step15 0.085085 0.0324 289 2.630 0.4354
Step7 - Step16 0.131413 0.0324 289 4.061 0.0077
Step7 - Step17 0.122958 0.0324 289 3.800 0.0199
Step7 - Step18 0.107205 0.0324 289 3.313 0.0925
Step8 - Step9 0.002528 0.0324 289 0.078 1.0000
Step8 - Step10 0.016008 0.0324 289 0.495 1.0000
Step8 - Step11 0.028310 0.0324 289 0.875 1.0000
Step8 - Step12 0.050344 0.0324 289 1.556 0.9855
Step8 - Step13 0.084652 0.0324 289 2.616 0.4451
Step8 - Step14 0.062414 0.0324 289 1.929 0.8984
Step8 - Step15 0.050080 0.0324 289 1.548 0.9862
Step8 - Step16 0.096409 0.0324 289 2.980 0.2173
Step8 - Step17 0.087953 0.0324 289 2.718 0.3727
Step8 - Step18 0.072200 0.0324 289 2.231 0.7310
Step9 - Step10 0.013480 0.0324 289 0.417 1.0000
Step9 - Step11 0.025782 0.0324 289 0.797 1.0000
Step9 - Step12 0.047817 0.0324 289 1.478 0.9916
Step9 - Step13 0.082124 0.0324 289 2.538 0.5034
Step9 - Step14 0.059886 0.0324 289 1.851 0.9269
Step9 - Step15 0.047553 0.0324 289 1.470 0.9921
Step9 - Step16 0.093881 0.0324 289 2.901 0.2585
Step9 - Step17 0.085425 0.0324 289 2.640 0.4277
Step9 - Step18 0.069672 0.0324 289 2.153 0.7821
Step10 - Step11 0.012302 0.0324 289 0.380 1.0000
Step10 - Step12 0.034336 0.0324 289 1.061 0.9999
Step10 - Step13 0.068644 0.0324 289 2.122 0.8015
Step10 - Step14 0.046406 0.0324 289 1.434 0.9939
Step10 - Step15 0.034072 0.0324 289 1.053 0.9999
Step10 - Step16 0.080401 0.0324 289 2.485 0.5439
Step10 - Step17 0.071945 0.0324 289 2.224 0.7363
Step10 - Step18 0.056192 0.0324 289 1.737 0.9578
Step11 - Step12 0.022035 0.0324 289 0.681 1.0000
Step11 - Step13 0.056343 0.0324 289 1.741 0.9568
Step11 - Step14 0.034104 0.0324 289 1.054 0.9999
Step11 - Step15 0.021771 0.0324 289 0.673 1.0000
Step11 - Step16 0.068099 0.0324 289 2.105 0.8115
Step11 - Step17 0.059643 0.0324 289 1.843 0.9293
Step11 - Step18 0.043890 0.0324 289 1.356 0.9968
Step12 - Step13 0.034308 0.0324 289 1.060 0.9999
Step12 - Step14 0.012069 0.0324 289 0.373 1.0000
Step12 - Step15 -0.000264 0.0324 289 -0.008 1.0000
Step12 - Step16 0.046064 0.0324 289 1.424 0.9944
Step12 - Step17 0.037609 0.0324 289 1.162 0.9995
Step12 - Step18 0.021856 0.0324 289 0.675 1.0000
Step13 - Step14 -0.022239 0.0324 289 -0.687 1.0000
Step13 - Step15 -0.034572 0.0324 289 -1.068 0.9998
Step13 - Step16 0.011756 0.0324 289 0.363 1.0000
Step13 - Step17 0.003301 0.0324 289 0.102 1.0000
Step13 - Step18 -0.012452 0.0324 289 -0.385 1.0000
Step14 - Step15 -0.012333 0.0324 289 -0.381 1.0000
Step14 - Step16 0.033995 0.0324 289 1.051 0.9999
Step14 - Step17 0.025540 0.0324 289 0.789 1.0000
Step14 - Step18 0.009787 0.0324 289 0.302 1.0000
Step15 - Step16 0.046328 0.0324 289 1.432 0.9940
Step15 - Step17 0.037873 0.0324 289 1.170 0.9995
Step15 - Step18 0.022120 0.0324 289 0.684 1.0000
Step16 - Step17 -0.008456 0.0324 289 -0.261 1.0000
Step16 - Step18 -0.024209 0.0324 289 -0.748 1.0000
Step17 - Step18 -0.015753 0.0324 289 -0.487 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.88440842 0.00345862 -0.02837787 -0.02456268 -0.02646418 -0.05321614
Step7 Step8 Step9 Step10 Step11 Step12
-0.03772800 -0.07273255 -0.07526032 -0.08874055 -0.10104228 -0.12307700
Step13 Step14 Step15 Step16 Step17 Step18
-0.15738481 -0.13514620 -0.12281291 -0.16914123 -0.16068571 -0.14493272
Random Effects:
$subject
(Intercept)
2 0.36975526
3 0.14786499
4 -0.27686909
5 -0.36168291
7 -0.28216811
8 0.47134441
10 0.98329144
11 0.43057146
13 -0.27065304
14 -0.08534180
15 -0.21444622
16 0.02414633
17 -0.12734390
18 0.12308542
19 -0.38318217
20 -0.27250425
22 -0.34491318
23 0.06904535
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.82993157 -0.05439119 -0.11599365 -0.85471963 -0.01832145 0.22418505
=============================================================
--- Mixed - Block 4 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 2.681 0.15771 17 289 6.8711 6.998e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.013435 0.0505 289 0.266 1.0000
Step1 - Step3 0.038242 0.0505 289 0.757 1.0000
Step1 - Step4 0.037796 0.0505 289 0.748 1.0000
Step1 - Step5 0.052683 0.0505 289 1.043 0.9999
Step1 - Step6 0.052975 0.0505 289 1.049 0.9999
Step1 - Step7 0.059776 0.0505 289 1.184 0.9994
Step1 - Step8 0.072437 0.0505 289 1.434 0.9939
Step1 - Step9 0.092874 0.0505 289 1.839 0.9307
Step1 - Step10 0.123616 0.0505 289 2.448 0.5721
Step1 - Step11 0.118163 0.0505 289 2.340 0.6535
Step1 - Step12 0.185349 0.0505 289 3.670 0.0309
Step1 - Step13 0.246680 0.0505 289 4.885 0.0002
Step1 - Step14 0.218323 0.0505 289 4.323 0.0028
Step1 - Step15 0.180664 0.0505 289 3.578 0.0418
Step1 - Step16 0.279145 0.0505 289 5.528 <.0001
Step1 - Step17 0.283546 0.0505 289 5.615 <.0001
Step1 - Step18 0.214983 0.0505 289 4.257 0.0036
Step2 - Step3 0.024807 0.0505 289 0.491 1.0000
Step2 - Step4 0.024361 0.0505 289 0.482 1.0000
Step2 - Step5 0.039248 0.0505 289 0.777 1.0000
Step2 - Step6 0.039540 0.0505 289 0.783 1.0000
Step2 - Step7 0.046341 0.0505 289 0.918 1.0000
Step2 - Step8 0.059002 0.0505 289 1.168 0.9995
Step2 - Step9 0.079439 0.0505 289 1.573 0.9837
Step2 - Step10 0.110180 0.0505 289 2.182 0.7640
Step2 - Step11 0.104728 0.0505 289 2.074 0.8290
Step2 - Step12 0.171913 0.0505 289 3.404 0.0712
Step2 - Step13 0.233244 0.0505 289 4.619 0.0008
Step2 - Step14 0.204888 0.0505 289 4.057 0.0079
Step2 - Step15 0.167229 0.0505 289 3.311 0.0930
Step2 - Step16 0.265710 0.0505 289 5.262 <.0001
Step2 - Step17 0.270111 0.0505 289 5.349 <.0001
Step2 - Step18 0.201548 0.0505 289 3.991 0.0101
Step3 - Step4 -0.000446 0.0505 289 -0.009 1.0000
Step3 - Step5 0.014441 0.0505 289 0.286 1.0000
Step3 - Step6 0.014733 0.0505 289 0.292 1.0000
Step3 - Step7 0.021534 0.0505 289 0.426 1.0000
Step3 - Step8 0.034195 0.0505 289 0.677 1.0000
Step3 - Step9 0.054632 0.0505 289 1.082 0.9998
Step3 - Step10 0.085373 0.0505 289 1.691 0.9671
Step3 - Step11 0.079921 0.0505 289 1.583 0.9827
Step3 - Step12 0.147106 0.0505 289 2.913 0.2521
Step3 - Step13 0.208437 0.0505 289 4.127 0.0060
Step3 - Step14 0.180081 0.0505 289 3.566 0.0434
Step3 - Step15 0.142422 0.0505 289 2.820 0.3063
Step3 - Step16 0.240903 0.0505 289 4.770 0.0004
Step3 - Step17 0.245304 0.0505 289 4.858 0.0003
Step3 - Step18 0.176741 0.0505 289 3.500 0.0534
Step4 - Step5 0.014887 0.0505 289 0.295 1.0000
Step4 - Step6 0.015179 0.0505 289 0.301 1.0000
Step4 - Step7 0.021980 0.0505 289 0.435 1.0000
Step4 - Step8 0.034641 0.0505 289 0.686 1.0000
Step4 - Step9 0.055079 0.0505 289 1.091 0.9998
Step4 - Step10 0.085820 0.0505 289 1.699 0.9654
Step4 - Step11 0.080367 0.0505 289 1.591 0.9817
Step4 - Step12 0.147553 0.0505 289 2.922 0.2473
Step4 - Step13 0.208884 0.0505 289 4.136 0.0058
Step4 - Step14 0.180527 0.0505 289 3.575 0.0422
Step4 - Step15 0.142868 0.0505 289 2.829 0.3008
Step4 - Step16 0.241349 0.0505 289 4.779 0.0004
Step4 - Step17 0.245750 0.0505 289 4.866 0.0003
Step4 - Step18 0.177187 0.0505 289 3.509 0.0519
Step5 - Step6 0.000292 0.0505 289 0.006 1.0000
Step5 - Step7 0.007093 0.0505 289 0.140 1.0000
Step5 - Step8 0.019754 0.0505 289 0.391 1.0000
Step5 - Step9 0.040191 0.0505 289 0.796 1.0000
Step5 - Step10 0.070933 0.0505 289 1.405 0.9952
Step5 - Step11 0.065480 0.0505 289 1.297 0.9981
Step5 - Step12 0.132666 0.0505 289 2.627 0.4373
Step5 - Step13 0.193997 0.0505 289 3.842 0.0172
Step5 - Step14 0.165640 0.0505 289 3.280 0.1015
Step5 - Step15 0.127981 0.0505 289 2.534 0.5063
Step5 - Step16 0.226462 0.0505 289 4.484 0.0014
Step5 - Step17 0.230863 0.0505 289 4.572 0.0010
Step5 - Step18 0.162300 0.0505 289 3.214 0.1215
Step6 - Step7 0.006801 0.0505 289 0.135 1.0000
Step6 - Step8 0.019462 0.0505 289 0.385 1.0000
Step6 - Step9 0.039900 0.0505 289 0.790 1.0000
Step6 - Step10 0.070641 0.0505 289 1.399 0.9954
Step6 - Step11 0.065188 0.0505 289 1.291 0.9982
Step6 - Step12 0.132374 0.0505 289 2.621 0.4415
Step6 - Step13 0.193705 0.0505 289 3.836 0.0176
Step6 - Step14 0.165348 0.0505 289 3.274 0.1031
Step6 - Step15 0.127690 0.0505 289 2.529 0.5107
Step6 - Step16 0.226170 0.0505 289 4.479 0.0015
Step6 - Step17 0.230571 0.0505 289 4.566 0.0010
Step6 - Step18 0.162008 0.0505 289 3.208 0.1234
Step7 - Step8 0.012661 0.0505 289 0.251 1.0000
Step7 - Step9 0.033099 0.0505 289 0.655 1.0000
Step7 - Step10 0.063840 0.0505 289 1.264 0.9986
Step7 - Step11 0.058387 0.0505 289 1.156 0.9996
Step7 - Step12 0.125573 0.0505 289 2.487 0.5426
Step7 - Step13 0.186904 0.0505 289 3.701 0.0279
Step7 - Step14 0.158547 0.0505 289 3.140 0.1475
Step7 - Step15 0.120889 0.0505 289 2.394 0.6131
Step7 - Step16 0.219369 0.0505 289 4.344 0.0026
Step7 - Step17 0.223770 0.0505 289 4.431 0.0018
Step7 - Step18 0.155207 0.0505 289 3.073 0.1740
Step8 - Step9 0.020437 0.0505 289 0.405 1.0000
Step8 - Step10 0.051179 0.0505 289 1.013 0.9999
Step8 - Step11 0.045726 0.0505 289 0.905 1.0000
Step8 - Step12 0.112912 0.0505 289 2.236 0.7279
Step8 - Step13 0.174243 0.0505 289 3.450 0.0620
Step8 - Step14 0.145886 0.0505 289 2.889 0.2656
Step8 - Step15 0.108227 0.0505 289 2.143 0.7884
Step8 - Step16 0.206708 0.0505 289 4.093 0.0069
Step8 - Step17 0.211109 0.0505 289 4.180 0.0049
Step8 - Step18 0.142546 0.0505 289 2.823 0.3048
Step9 - Step10 0.030741 0.0505 289 0.609 1.0000
Step9 - Step11 0.025288 0.0505 289 0.501 1.0000
Step9 - Step12 0.092474 0.0505 289 1.831 0.9331
Step9 - Step13 0.153805 0.0505 289 3.046 0.1861
Step9 - Step14 0.125448 0.0505 289 2.484 0.5444
Step9 - Step15 0.087790 0.0505 289 1.738 0.9574
Step9 - Step16 0.186271 0.0505 289 3.689 0.0291
Step9 - Step17 0.190672 0.0505 289 3.776 0.0217
Step9 - Step18 0.122108 0.0505 289 2.418 0.5948
Step10 - Step11 -0.005453 0.0505 289 -0.108 1.0000
Step10 - Step12 0.061733 0.0505 289 1.222 0.9991
Step10 - Step13 0.123064 0.0505 289 2.437 0.5804
Step10 - Step14 0.094707 0.0505 289 1.875 0.9186
Step10 - Step15 0.057049 0.0505 289 1.130 0.9997
Step10 - Step16 0.155530 0.0505 289 3.080 0.1713
Step10 - Step17 0.159931 0.0505 289 3.167 0.1375
Step10 - Step18 0.091367 0.0505 289 1.809 0.9396
Step11 - Step12 0.067186 0.0505 289 1.330 0.9974
Step11 - Step13 0.128517 0.0505 289 2.545 0.4983
Step11 - Step14 0.100160 0.0505 289 1.983 0.8748
Step11 - Step15 0.062502 0.0505 289 1.238 0.9989
Step11 - Step16 0.160982 0.0505 289 3.188 0.1302
Step11 - Step17 0.165383 0.0505 289 3.275 0.1029
Step11 - Step18 0.096820 0.0505 289 1.917 0.9031
Step12 - Step13 0.061331 0.0505 289 1.214 0.9992
Step12 - Step14 0.032974 0.0505 289 0.653 1.0000
Step12 - Step15 -0.004684 0.0505 289 -0.093 1.0000
Step12 - Step16 0.093797 0.0505 289 1.857 0.9248
Step12 - Step17 0.098197 0.0505 289 1.945 0.8920
Step12 - Step18 0.029634 0.0505 289 0.587 1.0000
Step13 - Step14 -0.028357 0.0505 289 -0.562 1.0000
Step13 - Step15 -0.066015 0.0505 289 -1.307 0.9979
Step13 - Step16 0.032466 0.0505 289 0.643 1.0000
Step13 - Step17 0.036867 0.0505 289 0.730 1.0000
Step13 - Step18 -0.031697 0.0505 289 -0.628 1.0000
Step14 - Step15 -0.037658 0.0505 289 -0.746 1.0000
Step14 - Step16 0.060822 0.0505 289 1.204 0.9992
Step14 - Step17 0.065223 0.0505 289 1.292 0.9982
Step14 - Step18 -0.003340 0.0505 289 -0.066 1.0000
Step15 - Step16 0.098481 0.0505 289 1.950 0.8896
Step15 - Step17 0.102882 0.0505 289 2.037 0.8485
Step15 - Step18 0.034318 0.0505 289 0.680 1.0000
Step16 - Step17 0.004401 0.0505 289 0.087 1.0000
Step16 - Step18 -0.064162 0.0505 289 -1.271 0.9985
Step17 - Step18 -0.068563 0.0505 289 -1.358 0.9968
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.75672442 -0.01343518 -0.03824215 -0.03779586 -0.05268298 -0.05297480
Step7 Step8 Step9 Step10 Step11 Step12
-0.05977578 -0.07243701 -0.09287447 -0.12361557 -0.11816280 -0.18534861
Step13 Step14 Step15 Step16 Step17 Step18
-0.24667958 -0.21832283 -0.18066434 -0.27914522 -0.28354608 -0.21498274
Random Effects:
$subject
(Intercept)
2 -0.13093283
3 0.08152113
4 -0.62660875
5 -0.84994062
7 0.24815050
8 0.78580340
10 2.08091719
11 0.72704043
13 -0.43079730
14 -0.04942483
15 -0.50578548
16 0.08669507
17 -0.45794858
18 0.69413455
19 -0.77126730
20 -0.48946414
22 -0.67588648
23 0.28379404
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.4958609 1.1146709 0.5987113 0.3269831 0.8249149 -0.1443813
=============================================================
--- Mixed - Block 5 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.097393 0.005729 17 289 2.0206 0.01036 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.003791 0.0177 289 -0.214 1.0000
Step1 - Step3 -0.012747 0.0177 289 -0.718 1.0000
Step1 - Step4 0.005586 0.0177 289 0.315 1.0000
Step1 - Step5 0.007840 0.0177 289 0.442 1.0000
Step1 - Step6 -0.014272 0.0177 289 -0.804 1.0000
Step1 - Step7 0.014057 0.0177 289 0.792 1.0000
Step1 - Step8 0.019433 0.0177 289 1.095 0.9998
Step1 - Step9 0.020009 0.0177 289 1.127 0.9997
Step1 - Step10 0.018370 0.0177 289 1.035 0.9999
Step1 - Step11 0.016539 0.0177 289 0.932 1.0000
Step1 - Step12 0.029785 0.0177 289 1.678 0.9693
Step1 - Step13 0.033647 0.0177 289 1.896 0.9113
Step1 - Step14 0.032737 0.0177 289 1.844 0.9290
Step1 - Step15 0.035594 0.0177 289 2.005 0.8645
Step1 - Step16 0.038640 0.0177 289 2.177 0.7671
Step1 - Step17 0.043180 0.0177 289 2.433 0.5836
Step1 - Step18 0.037328 0.0177 289 2.103 0.8124
Step2 - Step3 -0.008956 0.0177 289 -0.505 1.0000
Step2 - Step4 0.009377 0.0177 289 0.528 1.0000
Step2 - Step5 0.011631 0.0177 289 0.655 1.0000
Step2 - Step6 -0.010481 0.0177 289 -0.591 1.0000
Step2 - Step7 0.017848 0.0177 289 1.006 0.9999
Step2 - Step8 0.023224 0.0177 289 1.308 0.9979
Step2 - Step9 0.023800 0.0177 289 1.341 0.9972
Step2 - Step10 0.022161 0.0177 289 1.249 0.9988
Step2 - Step11 0.020330 0.0177 289 1.145 0.9996
Step2 - Step12 0.033576 0.0177 289 1.892 0.9128
Step2 - Step13 0.037438 0.0177 289 2.109 0.8088
Step2 - Step14 0.036527 0.0177 289 2.058 0.8376
Step2 - Step15 0.039384 0.0177 289 2.219 0.7394
Step2 - Step16 0.042431 0.0177 289 2.391 0.6156
Step2 - Step17 0.046971 0.0177 289 2.646 0.4232
Step2 - Step18 0.041119 0.0177 289 2.317 0.6706
Step3 - Step4 0.018333 0.0177 289 1.033 0.9999
Step3 - Step5 0.020587 0.0177 289 1.160 0.9995
Step3 - Step6 -0.001525 0.0177 289 -0.086 1.0000
Step3 - Step7 0.026804 0.0177 289 1.510 0.9894
Step3 - Step8 0.032180 0.0177 289 1.813 0.9385
Step3 - Step9 0.032756 0.0177 289 1.845 0.9286
Step3 - Step10 0.031117 0.0177 289 1.753 0.9541
Step3 - Step11 0.029286 0.0177 289 1.650 0.9739
Step3 - Step12 0.042532 0.0177 289 2.396 0.6113
Step3 - Step13 0.046394 0.0177 289 2.614 0.4469
Step3 - Step14 0.045484 0.0177 289 2.563 0.4850
Step3 - Step15 0.048341 0.0177 289 2.724 0.3691
Step3 - Step16 0.051387 0.0177 289 2.895 0.2620
Step3 - Step17 0.055927 0.0177 289 3.151 0.1432
Step3 - Step18 0.050075 0.0177 289 2.821 0.3057
Step4 - Step5 0.002254 0.0177 289 0.127 1.0000
Step4 - Step6 -0.019858 0.0177 289 -1.119 0.9997
Step4 - Step7 0.008471 0.0177 289 0.477 1.0000
Step4 - Step8 0.013847 0.0177 289 0.780 1.0000
Step4 - Step9 0.014423 0.0177 289 0.813 1.0000
Step4 - Step10 0.012784 0.0177 289 0.720 1.0000
Step4 - Step11 0.010954 0.0177 289 0.617 1.0000
Step4 - Step12 0.024199 0.0177 289 1.363 0.9966
Step4 - Step13 0.028061 0.0177 289 1.581 0.9829
Step4 - Step14 0.027151 0.0177 289 1.530 0.9878
Step4 - Step15 0.030008 0.0177 289 1.691 0.9671
Step4 - Step16 0.033054 0.0177 289 1.862 0.9231
Step4 - Step17 0.037594 0.0177 289 2.118 0.8036
Step4 - Step18 0.031742 0.0177 289 1.788 0.9453
Step5 - Step6 -0.022112 0.0177 289 -1.246 0.9988
Step5 - Step7 0.006216 0.0177 289 0.350 1.0000
Step5 - Step8 0.011593 0.0177 289 0.653 1.0000
Step5 - Step9 0.012169 0.0177 289 0.686 1.0000
Step5 - Step10 0.010530 0.0177 289 0.593 1.0000
Step5 - Step11 0.008699 0.0177 289 0.490 1.0000
Step5 - Step12 0.021945 0.0177 289 1.236 0.9990
Step5 - Step13 0.025806 0.0177 289 1.454 0.9929
Step5 - Step14 0.024896 0.0177 289 1.403 0.9953
Step5 - Step15 0.027753 0.0177 289 1.564 0.9847
Step5 - Step16 0.030800 0.0177 289 1.735 0.9581
Step5 - Step17 0.035340 0.0177 289 1.991 0.8713
Step5 - Step18 0.029487 0.0177 289 1.661 0.9721
Step6 - Step7 0.028329 0.0177 289 1.596 0.9812
Step6 - Step8 0.033705 0.0177 289 1.899 0.9101
Step6 - Step9 0.034281 0.0177 289 1.931 0.8974
Step6 - Step10 0.032642 0.0177 289 1.839 0.9307
Step6 - Step11 0.030811 0.0177 289 1.736 0.9580
Step6 - Step12 0.044057 0.0177 289 2.482 0.5459
Step6 - Step13 0.047919 0.0177 289 2.700 0.3855
Step6 - Step14 0.047008 0.0177 289 2.648 0.4217
Step6 - Step15 0.049865 0.0177 289 2.809 0.3130
Step6 - Step16 0.052912 0.0177 289 2.981 0.2165
Step6 - Step17 0.057452 0.0177 289 3.237 0.1142
Step6 - Step18 0.051600 0.0177 289 2.907 0.2554
Step7 - Step8 0.005376 0.0177 289 0.303 1.0000
Step7 - Step9 0.005952 0.0177 289 0.335 1.0000
Step7 - Step10 0.004313 0.0177 289 0.243 1.0000
Step7 - Step11 0.002483 0.0177 289 0.140 1.0000
Step7 - Step12 0.015728 0.0177 289 0.886 1.0000
Step7 - Step13 0.019590 0.0177 289 1.104 0.9998
Step7 - Step14 0.018680 0.0177 289 1.052 0.9999
Step7 - Step15 0.021537 0.0177 289 1.213 0.9992
Step7 - Step16 0.024583 0.0177 289 1.385 0.9959
Step7 - Step17 0.029124 0.0177 289 1.641 0.9752
Step7 - Step18 0.023271 0.0177 289 1.311 0.9979
Step8 - Step9 0.000576 0.0177 289 0.032 1.0000
Step8 - Step10 -0.001063 0.0177 289 -0.060 1.0000
Step8 - Step11 -0.002894 0.0177 289 -0.163 1.0000
Step8 - Step12 0.010352 0.0177 289 0.583 1.0000
Step8 - Step13 0.014214 0.0177 289 0.801 1.0000
Step8 - Step14 0.013303 0.0177 289 0.750 1.0000
Step8 - Step15 0.016160 0.0177 289 0.910 1.0000
Step8 - Step16 0.019207 0.0177 289 1.082 0.9998
Step8 - Step17 0.023747 0.0177 289 1.338 0.9973
Step8 - Step18 0.017895 0.0177 289 1.008 0.9999
Step9 - Step10 -0.001639 0.0177 289 -0.092 1.0000
Step9 - Step11 -0.003470 0.0177 289 -0.195 1.0000
Step9 - Step12 0.009776 0.0177 289 0.551 1.0000
Step9 - Step13 0.013638 0.0177 289 0.768 1.0000
Step9 - Step14 0.012728 0.0177 289 0.717 1.0000
Step9 - Step15 0.015585 0.0177 289 0.878 1.0000
Step9 - Step16 0.018631 0.0177 289 1.050 0.9999
Step9 - Step17 0.023171 0.0177 289 1.305 0.9980
Step9 - Step18 0.017319 0.0177 289 0.976 1.0000
Step10 - Step11 -0.001831 0.0177 289 -0.103 1.0000
Step10 - Step12 0.011415 0.0177 289 0.643 1.0000
Step10 - Step13 0.015277 0.0177 289 0.861 1.0000
Step10 - Step14 0.014366 0.0177 289 0.809 1.0000
Step10 - Step15 0.017223 0.0177 289 0.970 1.0000
Step10 - Step16 0.020270 0.0177 289 1.142 0.9996
Step10 - Step17 0.024810 0.0177 289 1.398 0.9955
Step10 - Step18 0.018957 0.0177 289 1.068 0.9998
Step11 - Step12 0.013246 0.0177 289 0.746 1.0000
Step11 - Step13 0.017107 0.0177 289 0.964 1.0000
Step11 - Step14 0.016197 0.0177 289 0.913 1.0000
Step11 - Step15 0.019054 0.0177 289 1.074 0.9998
Step11 - Step16 0.022101 0.0177 289 1.245 0.9989
Step11 - Step17 0.026641 0.0177 289 1.501 0.9900
Step11 - Step18 0.020788 0.0177 289 1.171 0.9995
Step12 - Step13 0.003862 0.0177 289 0.218 1.0000
Step12 - Step14 0.002952 0.0177 289 0.166 1.0000
Step12 - Step15 0.005808 0.0177 289 0.327 1.0000
Step12 - Step16 0.008855 0.0177 289 0.499 1.0000
Step12 - Step17 0.013395 0.0177 289 0.755 1.0000
Step12 - Step18 0.007543 0.0177 289 0.425 1.0000
Step13 - Step14 -0.000910 0.0177 289 -0.051 1.0000
Step13 - Step15 0.001947 0.0177 289 0.110 1.0000
Step13 - Step16 0.004993 0.0177 289 0.281 1.0000
Step13 - Step17 0.009534 0.0177 289 0.537 1.0000
Step13 - Step18 0.003681 0.0177 289 0.207 1.0000
Step14 - Step15 0.002857 0.0177 289 0.161 1.0000
Step14 - Step16 0.005904 0.0177 289 0.333 1.0000
Step14 - Step17 0.010444 0.0177 289 0.588 1.0000
Step14 - Step18 0.004591 0.0177 289 0.259 1.0000
Step15 - Step16 0.003047 0.0177 289 0.172 1.0000
Step15 - Step17 0.007587 0.0177 289 0.427 1.0000
Step15 - Step18 0.001734 0.0177 289 0.098 1.0000
Step16 - Step17 0.004540 0.0177 289 0.256 1.0000
Step16 - Step18 -0.001313 0.0177 289 -0.074 1.0000
Step17 - Step18 -0.005853 0.0177 289 -0.330 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.668041723 0.003790932 0.012746978 -0.005585973 -0.007840425 0.014271877
Step7 Step8 Step9 Step10 Step11 Step12
-0.014056901 -0.019433124 -0.020009011 -0.018370347 -0.016539502 -0.029785060
Step13 Step14 Step15 Step16 Step17 Step18
-0.033646887 -0.032736557 -0.035593548 -0.038640227 -0.043180462 -0.037327651
Random Effects:
$subject
(Intercept)
2 0.0271046434
3 -0.0525603679
4 -0.1363756416
5 -0.3210430066
7 -0.2690103005
8 0.4867411220
10 0.6352690182
11 0.0648859518
13 -0.0598412680
14 -0.0005446846
15 0.1932573874
16 -0.1145501218
17 -0.1277414736
18 -0.0490605740
19 -0.2559087842
20 -0.1675573393
22 -0.0672064567
23 0.2141418959
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
1.2126186 2.0728146 1.3868142 1.3727675 1.4555417 0.2742303
=============================================================
--- Mixed - Block 5 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.85141 0.050083 17 289 1.5759 0.06956 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000754 0.0594 289 0.013 1.0000
Step1 - Step3 -0.058706 0.0594 289 -0.988 0.9999
Step1 - Step4 -0.020994 0.0594 289 -0.353 1.0000
Step1 - Step5 -0.022466 0.0594 289 -0.378 1.0000
Step1 - Step6 -0.095249 0.0594 289 -1.603 0.9803
Step1 - Step7 -0.028306 0.0594 289 -0.476 1.0000
Step1 - Step8 -0.024976 0.0594 289 -0.420 1.0000
Step1 - Step9 0.012246 0.0594 289 0.206 1.0000
Step1 - Step10 0.019084 0.0594 289 0.321 1.0000
Step1 - Step11 -0.009623 0.0594 289 -0.162 1.0000
Step1 - Step12 0.026015 0.0594 289 0.438 1.0000
Step1 - Step13 -0.017257 0.0594 289 -0.290 1.0000
Step1 - Step14 0.040221 0.0594 289 0.677 1.0000
Step1 - Step15 0.066884 0.0594 289 1.126 0.9997
Step1 - Step16 0.039247 0.0594 289 0.660 1.0000
Step1 - Step17 0.121730 0.0594 289 2.049 0.8426
Step1 - Step18 0.097830 0.0594 289 1.646 0.9744
Step2 - Step3 -0.059460 0.0594 289 -1.001 0.9999
Step2 - Step4 -0.021749 0.0594 289 -0.366 1.0000
Step2 - Step5 -0.023221 0.0594 289 -0.391 1.0000
Step2 - Step6 -0.096003 0.0594 289 -1.616 0.9787
Step2 - Step7 -0.029060 0.0594 289 -0.489 1.0000
Step2 - Step8 -0.025731 0.0594 289 -0.433 1.0000
Step2 - Step9 0.011492 0.0594 289 0.193 1.0000
Step2 - Step10 0.018329 0.0594 289 0.308 1.0000
Step2 - Step11 -0.010377 0.0594 289 -0.175 1.0000
Step2 - Step12 0.025261 0.0594 289 0.425 1.0000
Step2 - Step13 -0.018012 0.0594 289 -0.303 1.0000
Step2 - Step14 0.039466 0.0594 289 0.664 1.0000
Step2 - Step15 0.066130 0.0594 289 1.113 0.9997
Step2 - Step16 0.038493 0.0594 289 0.648 1.0000
Step2 - Step17 0.120975 0.0594 289 2.036 0.8492
Step2 - Step18 0.097076 0.0594 289 1.634 0.9763
Step3 - Step4 0.037712 0.0594 289 0.635 1.0000
Step3 - Step5 0.036240 0.0594 289 0.610 1.0000
Step3 - Step6 -0.036543 0.0594 289 -0.615 1.0000
Step3 - Step7 0.030400 0.0594 289 0.512 1.0000
Step3 - Step8 0.033730 0.0594 289 0.568 1.0000
Step3 - Step9 0.070952 0.0594 289 1.194 0.9993
Step3 - Step10 0.077790 0.0594 289 1.309 0.9979
Step3 - Step11 0.049084 0.0594 289 0.826 1.0000
Step3 - Step12 0.084721 0.0594 289 1.426 0.9943
Step3 - Step13 0.041449 0.0594 289 0.698 1.0000
Step3 - Step14 0.098927 0.0594 289 1.665 0.9715
Step3 - Step15 0.125590 0.0594 289 2.113 0.8063
Step3 - Step16 0.097953 0.0594 289 1.648 0.9741
Step3 - Step17 0.180436 0.0594 289 3.036 0.1902
Step3 - Step18 0.156536 0.0594 289 2.634 0.4320
Step4 - Step5 -0.001472 0.0594 289 -0.025 1.0000
Step4 - Step6 -0.074254 0.0594 289 -1.250 0.9988
Step4 - Step7 -0.007312 0.0594 289 -0.123 1.0000
Step4 - Step8 -0.003982 0.0594 289 -0.067 1.0000
Step4 - Step9 0.033241 0.0594 289 0.559 1.0000
Step4 - Step10 0.040078 0.0594 289 0.674 1.0000
Step4 - Step11 0.011372 0.0594 289 0.191 1.0000
Step4 - Step12 0.047010 0.0594 289 0.791 1.0000
Step4 - Step13 0.003737 0.0594 289 0.063 1.0000
Step4 - Step14 0.061215 0.0594 289 1.030 0.9999
Step4 - Step15 0.087878 0.0594 289 1.479 0.9915
Step4 - Step16 0.060241 0.0594 289 1.014 0.9999
Step4 - Step17 0.142724 0.0594 289 2.402 0.6071
Step4 - Step18 0.118825 0.0594 289 2.000 0.8672
Step5 - Step6 -0.072782 0.0594 289 -1.225 0.9991
Step5 - Step7 -0.005840 0.0594 289 -0.098 1.0000
Step5 - Step8 -0.002510 0.0594 289 -0.042 1.0000
Step5 - Step9 0.034713 0.0594 289 0.584 1.0000
Step5 - Step10 0.041550 0.0594 289 0.699 1.0000
Step5 - Step11 0.012844 0.0594 289 0.216 1.0000
Step5 - Step12 0.048481 0.0594 289 0.816 1.0000
Step5 - Step13 0.005209 0.0594 289 0.088 1.0000
Step5 - Step14 0.062687 0.0594 289 1.055 0.9999
Step5 - Step15 0.089350 0.0594 289 1.504 0.9898
Step5 - Step16 0.061713 0.0594 289 1.039 0.9999
Step5 - Step17 0.144196 0.0594 289 2.427 0.5883
Step5 - Step18 0.120297 0.0594 289 2.024 0.8551
Step6 - Step7 0.066943 0.0594 289 1.127 0.9997
Step6 - Step8 0.070272 0.0594 289 1.183 0.9994
Step6 - Step9 0.107495 0.0594 289 1.809 0.9397
Step6 - Step10 0.114332 0.0594 289 1.924 0.9004
Step6 - Step11 0.085626 0.0594 289 1.441 0.9936
Step6 - Step12 0.121264 0.0594 289 2.041 0.8467
Step6 - Step13 0.077991 0.0594 289 1.312 0.9978
Step6 - Step14 0.135469 0.0594 289 2.280 0.6972
Step6 - Step15 0.162132 0.0594 289 2.728 0.3658
Step6 - Step16 0.134496 0.0594 289 2.263 0.7088
Step6 - Step17 0.216978 0.0594 289 3.651 0.0329
Step6 - Step18 0.193079 0.0594 289 3.249 0.1105
Step7 - Step8 0.003330 0.0594 289 0.056 1.0000
Step7 - Step9 0.040552 0.0594 289 0.682 1.0000
Step7 - Step10 0.047390 0.0594 289 0.797 1.0000
Step7 - Step11 0.018684 0.0594 289 0.314 1.0000
Step7 - Step12 0.054321 0.0594 289 0.914 1.0000
Step7 - Step13 0.011049 0.0594 289 0.186 1.0000
Step7 - Step14 0.068527 0.0594 289 1.153 0.9996
Step7 - Step15 0.095190 0.0594 289 1.602 0.9805
Step7 - Step16 0.067553 0.0594 289 1.137 0.9996
Step7 - Step17 0.150036 0.0594 289 2.525 0.5134
Step7 - Step18 0.126136 0.0594 289 2.123 0.8008
Step8 - Step9 0.037223 0.0594 289 0.626 1.0000
Step8 - Step10 0.044060 0.0594 289 0.741 1.0000
Step8 - Step11 0.015354 0.0594 289 0.258 1.0000
Step8 - Step12 0.050992 0.0594 289 0.858 1.0000
Step8 - Step13 0.007719 0.0594 289 0.130 1.0000
Step8 - Step14 0.065197 0.0594 289 1.097 0.9998
Step8 - Step15 0.091860 0.0594 289 1.546 0.9864
Step8 - Step16 0.064223 0.0594 289 1.081 0.9998
Step8 - Step17 0.146706 0.0594 289 2.469 0.5561
Step8 - Step18 0.122807 0.0594 289 2.067 0.8329
Step9 - Step10 0.006838 0.0594 289 0.115 1.0000
Step9 - Step11 -0.021869 0.0594 289 -0.368 1.0000
Step9 - Step12 0.013769 0.0594 289 0.232 1.0000
Step9 - Step13 -0.029503 0.0594 289 -0.496 1.0000
Step9 - Step14 0.027974 0.0594 289 0.471 1.0000
Step9 - Step15 0.054638 0.0594 289 0.919 1.0000
Step9 - Step16 0.027001 0.0594 289 0.454 1.0000
Step9 - Step17 0.109484 0.0594 289 1.842 0.9296
Step9 - Step18 0.085584 0.0594 289 1.440 0.9936
Step10 - Step11 -0.028706 0.0594 289 -0.483 1.0000
Step10 - Step12 0.006931 0.0594 289 0.117 1.0000
Step10 - Step13 -0.036341 0.0594 289 -0.612 1.0000
Step10 - Step14 0.021137 0.0594 289 0.356 1.0000
Step10 - Step15 0.047800 0.0594 289 0.804 1.0000
Step10 - Step16 0.020163 0.0594 289 0.339 1.0000
Step10 - Step17 0.102646 0.0594 289 1.727 0.9598
Step10 - Step18 0.078746 0.0594 289 1.325 0.9976
Step11 - Step12 0.035638 0.0594 289 0.600 1.0000
Step11 - Step13 -0.007635 0.0594 289 -0.128 1.0000
Step11 - Step14 0.049843 0.0594 289 0.839 1.0000
Step11 - Step15 0.076506 0.0594 289 1.287 0.9983
Step11 - Step16 0.048869 0.0594 289 0.822 1.0000
Step11 - Step17 0.131352 0.0594 289 2.210 0.7451
Step11 - Step18 0.107453 0.0594 289 1.808 0.9399
Step12 - Step13 -0.043272 0.0594 289 -0.728 1.0000
Step12 - Step14 0.014205 0.0594 289 0.239 1.0000
Step12 - Step15 0.040869 0.0594 289 0.688 1.0000
Step12 - Step16 0.013232 0.0594 289 0.223 1.0000
Step12 - Step17 0.095715 0.0594 289 1.611 0.9794
Step12 - Step18 0.071815 0.0594 289 1.209 0.9992
Step13 - Step14 0.057478 0.0594 289 0.967 1.0000
Step13 - Step15 0.084141 0.0594 289 1.416 0.9947
Step13 - Step16 0.056504 0.0594 289 0.951 1.0000
Step13 - Step17 0.138987 0.0594 289 2.339 0.6542
Step13 - Step18 0.115088 0.0594 289 1.937 0.8952
Step14 - Step15 0.026663 0.0594 289 0.449 1.0000
Step14 - Step16 -0.000974 0.0594 289 -0.016 1.0000
Step14 - Step17 0.081509 0.0594 289 1.372 0.9963
Step14 - Step18 0.057610 0.0594 289 0.969 1.0000
Step15 - Step16 -0.027637 0.0594 289 -0.465 1.0000
Step15 - Step17 0.054846 0.0594 289 0.923 1.0000
Step15 - Step18 0.030946 0.0594 289 0.521 1.0000
Step16 - Step17 0.082483 0.0594 289 1.388 0.9958
Step16 - Step18 0.058583 0.0594 289 0.986 0.9999
Step17 - Step18 -0.023899 0.0594 289 -0.402 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
0.7546625750 -0.0007543218 0.0587060795 0.0209944734 0.0224663889
Step6 Step7 Step8 Step9 Step10
0.0952485963 0.0283060176 0.0249764333 -0.0122462075 -0.0190837961
Step11 Step12 Step13 Step14 Step15
0.0096225114 -0.0260151007 0.0172572535 -0.0402205866 -0.0668838439
Step16 Step17 Step18
-0.0392469753 -0.1217297759 -0.0978302879
Random Effects:
$subject
(Intercept)
2 0.373768949
3 0.078446709
4 -0.217018794
5 -0.398779410
7 -0.175416496
8 0.267636015
10 0.420884094
11 -0.222318892
13 -0.131290447
14 -0.110547150
15 -0.021798274
16 0.001914506
17 -0.120023899
18 -0.132924416
19 -0.382571068
20 -0.377740419
22 -0.310866532
23 1.458645525
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.44447609 0.70476553 0.27048745 0.45147177 0.47182202 -0.07954699
=============================================================
--- Mixed - Block 5 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.66058 0.038858 17 289 2.7237 0.0003376 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -2.22e-02 0.0398 289 -0.557 1.0000
Step1 - Step3 -6.46e-02 0.0398 289 -1.622 0.9779
Step1 - Step4 7.57e-03 0.0398 289 0.190 1.0000
Step1 - Step5 7.53e-03 0.0398 289 0.189 1.0000
Step1 - Step6 -2.99e-02 0.0398 289 -0.751 1.0000
Step1 - Step7 2.66e-02 0.0398 289 0.668 1.0000
Step1 - Step8 1.77e-02 0.0398 289 0.445 1.0000
Step1 - Step9 5.36e-02 0.0398 289 1.345 0.9971
Step1 - Step10 5.78e-02 0.0398 289 1.451 0.9931
Step1 - Step11 2.18e-02 0.0398 289 0.549 1.0000
Step1 - Step12 7.23e-02 0.0398 289 1.816 0.9375
Step1 - Step13 5.16e-02 0.0398 289 1.296 0.9981
Step1 - Step14 9.37e-02 0.0398 289 2.353 0.6437
Step1 - Step15 7.73e-02 0.0398 289 1.941 0.8933
Step1 - Step16 5.58e-02 0.0398 289 1.401 0.9953
Step1 - Step17 1.05e-01 0.0398 289 2.630 0.4349
Step1 - Step18 8.96e-02 0.0398 289 2.250 0.7182
Step2 - Step3 -4.24e-02 0.0398 289 -1.065 0.9998
Step2 - Step4 2.97e-02 0.0398 289 0.747 1.0000
Step2 - Step5 2.97e-02 0.0398 289 0.746 1.0000
Step2 - Step6 -7.72e-03 0.0398 289 -0.194 1.0000
Step2 - Step7 4.87e-02 0.0398 289 1.224 0.9991
Step2 - Step8 3.99e-02 0.0398 289 1.002 0.9999
Step2 - Step9 7.57e-02 0.0398 289 1.902 0.9090
Step2 - Step10 7.99e-02 0.0398 289 2.007 0.8635
Step2 - Step11 4.40e-02 0.0398 289 1.105 0.9998
Step2 - Step12 9.45e-02 0.0398 289 2.373 0.6289
Step2 - Step13 7.38e-02 0.0398 289 1.853 0.9263
Step2 - Step14 1.16e-01 0.0398 289 2.910 0.2540
Step2 - Step15 9.95e-02 0.0398 289 2.498 0.5339
Step2 - Step16 7.80e-02 0.0398 289 1.958 0.8862
Step2 - Step17 1.27e-01 0.0398 289 3.187 0.1305
Step2 - Step18 1.12e-01 0.0398 289 2.806 0.3149
Step3 - Step4 7.21e-02 0.0398 289 1.812 0.9388
Step3 - Step5 7.21e-02 0.0398 289 1.811 0.9391
Step3 - Step6 3.47e-02 0.0398 289 0.871 1.0000
Step3 - Step7 9.12e-02 0.0398 289 2.290 0.6902
Step3 - Step8 8.23e-02 0.0398 289 2.067 0.8327
Step3 - Step9 1.18e-01 0.0398 289 2.967 0.2235
Step3 - Step10 1.22e-01 0.0398 289 3.073 0.1743
Step3 - Step11 8.64e-02 0.0398 289 2.171 0.7713
Step3 - Step12 1.37e-01 0.0398 289 3.438 0.0643
Step3 - Step13 1.16e-01 0.0398 289 2.918 0.2493
Step3 - Step14 1.58e-01 0.0398 289 3.975 0.0107
Step3 - Step15 1.42e-01 0.0398 289 3.563 0.0438
Step3 - Step16 1.20e-01 0.0398 289 3.023 0.1962
Step3 - Step17 1.69e-01 0.0398 289 4.252 0.0037
Step3 - Step18 1.54e-01 0.0398 289 3.872 0.0155
Step4 - Step5 -3.61e-05 0.0398 289 -0.001 1.0000
Step4 - Step6 -3.74e-02 0.0398 289 -0.941 1.0000
Step4 - Step7 1.90e-02 0.0398 289 0.478 1.0000
Step4 - Step8 1.02e-02 0.0398 289 0.255 1.0000
Step4 - Step9 4.60e-02 0.0398 289 1.155 0.9996
Step4 - Step10 5.02e-02 0.0398 289 1.261 0.9987
Step4 - Step11 1.43e-02 0.0398 289 0.359 1.0000
Step4 - Step12 6.47e-02 0.0398 289 1.626 0.9773
Step4 - Step13 4.40e-02 0.0398 289 1.106 0.9998
Step4 - Step14 8.61e-02 0.0398 289 2.163 0.7760
Step4 - Step15 6.97e-02 0.0398 289 1.751 0.9545
Step4 - Step16 4.82e-02 0.0398 289 1.211 0.9992
Step4 - Step17 9.72e-02 0.0398 289 2.440 0.5779
Step4 - Step18 8.20e-02 0.0398 289 2.060 0.8366
Step5 - Step6 -3.74e-02 0.0398 289 -0.940 1.0000
Step5 - Step7 1.90e-02 0.0398 289 0.478 1.0000
Step5 - Step8 1.02e-02 0.0398 289 0.256 1.0000
Step5 - Step9 4.60e-02 0.0398 289 1.156 0.9996
Step5 - Step10 5.02e-02 0.0398 289 1.262 0.9987
Step5 - Step11 1.43e-02 0.0398 289 0.359 1.0000
Step5 - Step12 6.48e-02 0.0398 289 1.627 0.9772
Step5 - Step13 4.41e-02 0.0398 289 1.107 0.9997
Step5 - Step14 8.62e-02 0.0398 289 2.164 0.7754
Step5 - Step15 6.98e-02 0.0398 289 1.752 0.9543
Step5 - Step16 4.83e-02 0.0398 289 1.212 0.9992
Step5 - Step17 9.72e-02 0.0398 289 2.441 0.5772
Step5 - Step18 8.20e-02 0.0398 289 2.061 0.8361
Step6 - Step7 5.65e-02 0.0398 289 1.418 0.9947
Step6 - Step8 4.76e-02 0.0398 289 1.196 0.9993
Step6 - Step9 8.34e-02 0.0398 289 2.096 0.8166
Step6 - Step10 8.76e-02 0.0398 289 2.201 0.7512
Step6 - Step11 5.17e-02 0.0398 289 1.299 0.9981
Step6 - Step12 1.02e-01 0.0398 289 2.567 0.4818
Step6 - Step13 8.15e-02 0.0398 289 2.047 0.8435
Step6 - Step14 1.24e-01 0.0398 289 3.104 0.1615
Step6 - Step15 1.07e-01 0.0398 289 2.692 0.3909
Step6 - Step16 8.57e-02 0.0398 289 2.152 0.7830
Step6 - Step17 1.35e-01 0.0398 289 3.381 0.0762
Step6 - Step18 1.19e-01 0.0398 289 3.000 0.2071
Step7 - Step8 -8.86e-03 0.0398 289 -0.223 1.0000
Step7 - Step9 2.70e-02 0.0398 289 0.678 1.0000
Step7 - Step10 3.12e-02 0.0398 289 0.783 1.0000
Step7 - Step11 -4.74e-03 0.0398 289 -0.119 1.0000
Step7 - Step12 4.57e-02 0.0398 289 1.149 0.9996
Step7 - Step13 2.50e-02 0.0398 289 0.629 1.0000
Step7 - Step14 6.71e-02 0.0398 289 1.686 0.9680
Step7 - Step15 5.07e-02 0.0398 289 1.274 0.9985
Step7 - Step16 2.92e-02 0.0398 289 0.734 1.0000
Step7 - Step17 7.81e-02 0.0398 289 1.963 0.8841
Step7 - Step18 6.30e-02 0.0398 289 1.582 0.9827
Step8 - Step9 3.58e-02 0.0398 289 0.900 1.0000
Step8 - Step10 4.00e-02 0.0398 289 1.006 0.9999
Step8 - Step11 4.12e-03 0.0398 289 0.104 1.0000
Step8 - Step12 5.46e-02 0.0398 289 1.371 0.9964
Step8 - Step13 3.39e-02 0.0398 289 0.851 1.0000
Step8 - Step14 7.60e-02 0.0398 289 1.908 0.9066
Step8 - Step15 5.96e-02 0.0398 289 1.496 0.9904
Step8 - Step16 3.81e-02 0.0398 289 0.956 1.0000
Step8 - Step17 8.70e-02 0.0398 289 2.185 0.7617
Step8 - Step18 7.19e-02 0.0398 289 1.805 0.9408
Step9 - Step10 4.20e-03 0.0398 289 0.105 1.0000
Step9 - Step11 -3.17e-02 0.0398 289 -0.797 1.0000
Step9 - Step12 1.88e-02 0.0398 289 0.471 1.0000
Step9 - Step13 -1.95e-03 0.0398 289 -0.049 1.0000
Step9 - Step14 4.01e-02 0.0398 289 1.008 0.9999
Step9 - Step15 2.37e-02 0.0398 289 0.596 1.0000
Step9 - Step16 2.24e-03 0.0398 289 0.056 1.0000
Step9 - Step17 5.12e-02 0.0398 289 1.285 0.9983
Step9 - Step18 3.60e-02 0.0398 289 0.905 1.0000
Step10 - Step11 -3.59e-02 0.0398 289 -0.902 1.0000
Step10 - Step12 1.46e-02 0.0398 289 0.366 1.0000
Step10 - Step13 -6.15e-03 0.0398 289 -0.154 1.0000
Step10 - Step14 3.59e-02 0.0398 289 0.902 1.0000
Step10 - Step15 1.95e-02 0.0398 289 0.491 1.0000
Step10 - Step16 -1.96e-03 0.0398 289 -0.049 1.0000
Step10 - Step17 4.70e-02 0.0398 289 1.180 0.9994
Step10 - Step18 3.18e-02 0.0398 289 0.799 1.0000
Step11 - Step12 5.05e-02 0.0398 289 1.268 0.9986
Step11 - Step13 2.98e-02 0.0398 289 0.748 1.0000
Step11 - Step14 7.18e-02 0.0398 289 1.805 0.9409
Step11 - Step15 5.55e-02 0.0398 289 1.393 0.9956
Step11 - Step16 3.40e-02 0.0398 289 0.853 1.0000
Step11 - Step17 8.29e-02 0.0398 289 2.082 0.8245
Step11 - Step18 6.77e-02 0.0398 289 1.701 0.9651
Step12 - Step13 -2.07e-02 0.0398 289 -0.520 1.0000
Step12 - Step14 2.14e-02 0.0398 289 0.537 1.0000
Step12 - Step15 4.98e-03 0.0398 289 0.125 1.0000
Step12 - Step16 -1.65e-02 0.0398 289 -0.415 1.0000
Step12 - Step17 3.24e-02 0.0398 289 0.814 1.0000
Step12 - Step18 1.73e-02 0.0398 289 0.434 1.0000
Step13 - Step14 4.21e-02 0.0398 289 1.057 0.9999
Step13 - Step15 2.57e-02 0.0398 289 0.645 1.0000
Step13 - Step16 4.19e-03 0.0398 289 0.105 1.0000
Step13 - Step17 5.31e-02 0.0398 289 1.334 0.9974
Step13 - Step18 3.80e-02 0.0398 289 0.954 1.0000
Step14 - Step15 -1.64e-02 0.0398 289 -0.412 1.0000
Step14 - Step16 -3.79e-02 0.0398 289 -0.952 1.0000
Step14 - Step17 1.10e-02 0.0398 289 0.277 1.0000
Step14 - Step18 -4.11e-03 0.0398 289 -0.103 1.0000
Step15 - Step16 -2.15e-02 0.0398 289 -0.540 1.0000
Step15 - Step17 2.74e-02 0.0398 289 0.689 1.0000
Step15 - Step18 1.23e-02 0.0398 289 0.309 1.0000
Step16 - Step17 4.89e-02 0.0398 289 1.229 0.9990
Step16 - Step18 3.38e-02 0.0398 289 0.848 1.0000
Step17 - Step18 -1.51e-02 0.0398 289 -0.380 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.461502752 0.022159659 0.064577364 -0.007565349 -0.007529253 0.029882603
Step7 Step8 Step9 Step10 Step11 Step12
-0.026577448 -0.017717318 -0.053560481 -0.057759057 -0.021839775 -0.072314852
Step13 Step14 Step15 Step16 Step17 Step18
-0.051608266 -0.093684670 -0.077293385 -0.055796126 -0.104722932 -0.089576850
Random Effects:
$subject
(Intercept)
2 0.02226734
3 -0.08605940
4 -0.54223730
5 -0.83152443
7 -0.10652281
8 0.40901975
10 2.35461013
11 -0.13459313
13 0.44173402
14 -0.47233599
15 0.79049181
16 0.26695004
17 -0.66571231
18 -0.08715183
19 -0.72708449
20 -0.55644830
22 -0.46304718
23 0.38764408
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.5110612 1.8450813 1.2149304 1.6275619 1.2508821 0.1380450
=============================================================#3.3 Step Pairwise Model SD
# -------- Suppress lmerTest and pbkrtest warnings globally --------
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# -------- Extended Step-Wise SD LMM + Diagnostics per Block & Axis --------
run_stepwise_sd_lmm_full_diagnostics <- function(tagged_data, dataset_name = "Mixed") {
step_markers <- c(14, 15, 16, 17)
buffer <- 5
step_data <- tagged_data %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_block() %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup()
step_indices <- step_data %>%
select(subject, Block, trial, row_id, Step)
window_data <- map_dfr(1:nrow(step_indices), function(i) {
step <- step_indices[i, ]
rows <- (step$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$Step)
})
step_sd_summary <- window_data %>%
group_by(subject, Block, Step) %>%
summarise(
sd_x = sd(CoM.acc.x, na.rm = TRUE),
sd_y = sd(CoM.acc.y, na.rm = TRUE),
sd_z = sd(CoM.acc.z, na.rm = TRUE),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("sd_"), names_to = "Axis", values_to = "SD") %>%
mutate(
Axis = toupper(gsub("sd_", "", Axis)),
Step = factor(Step),
Block = factor(Block),
subject = factor(subject)
)
axis_labels <- c("X", "Y", "Z")
blocks <- unique(step_sd_summary$Block)
results <- list()
for (blk in blocks) {
for (axis in axis_labels) {
data_sub <- step_sd_summary %>%
filter(Block == blk, Axis == axis)
model <- lmer(SD ~ Step + (1 | subject), data = data_sub)
aov_tbl <- anova(model)
emmeans_out <- emmeans(model, pairwise ~ Step)
key <- glue::glue("{dataset_name} - SD - Block {blk} - Axis {axis}")
results[[key]] <- list(
ANOVA = aov_tbl,
Pairwise = summary(emmeans_out$contrasts),
Emmeans = summary(emmeans_out$emmeans),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
}
return(results)
}
# -------- Run Full Diagnostics --------
stepwise_sd_lmm_diag_results <- run_stepwise_sd_lmm_full_diagnostics(tagged_data)
# -------- Print SD LMM Diagnostics --------
print_stepwise_sd_lmm_diagnostics <- function(results_list, dataset_name = "Mixed") {
cat(glue::glue("\n=========== STEPWISE SD LMM DIAGNOSTICS: {dataset_name} ===========\n"))
for (key in names(results_list)) {
cat("\n---", key, "---\n")
cat("ANOVA:\n")
print(results_list[[key]]$ANOVA)
cat("\nPairwise Comparisons:\n")
print(results_list[[key]]$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")
}
}
# -------- Output Extended SD Model Diagnostics --------
print_stepwise_sd_lmm_diagnostics(stepwise_sd_lmm_diag_results)=========== STEPWISE SD LMM DIAGNOSTICS: Mixed ===========
--- Mixed - SD - Block 1 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 5.3496e-05 1.0699e-05 5 85 0.6472 0.6644
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000000 0.00136 85 0.000 1.0000
Step1 - Step3 -0.000239 0.00136 85 -0.177 1.0000
Step1 - Step4 0.001771 0.00136 85 1.307 0.7807
Step1 - Step5 -0.000239 0.00136 85 -0.177 1.0000
Step1 - Step6 0.000000 0.00136 85 0.000 1.0000
Step2 - Step3 -0.000239 0.00136 85 -0.177 1.0000
Step2 - Step4 0.001771 0.00136 85 1.307 0.7807
Step2 - Step5 -0.000239 0.00136 85 -0.177 1.0000
Step2 - Step6 0.000000 0.00136 85 0.000 1.0000
Step3 - Step4 0.002010 0.00136 85 1.483 0.6758
Step3 - Step5 0.000000 0.00136 85 0.000 1.0000
Step3 - Step6 0.000239 0.00136 85 0.177 1.0000
Step4 - Step5 -0.002010 0.00136 85 -1.483 0.6758
Step4 - Step6 -0.001771 0.00136 85 -1.307 0.7807
Step5 - Step6 0.000239 0.00136 85 0.177 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
8.452024e-01 -2.688710e-15 2.393599e-04 -1.770771e-03 2.393599e-04
Step6
-2.688773e-15
Random Effects:
$subject
(Intercept)
2 -0.2550918
3 0.1567868
4 -0.3506646
5 -0.3829182
7 -0.2292004
8 0.4913867
10 0.8586571
11 1.2340718
13 -0.2800431
14 0.3300590
15 -0.1917024
16 -0.2355887
17 -0.4973447
18 -0.3919900
19 -0.5341743
20 -0.3014273
22 -0.3497042
23 0.9288883
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.05355587 -0.05355587 -0.11242593 0.38196136 -0.11242593 -0.05355587
=============================================================
--- Mixed - SD - Block 1 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 5.9192e-05 1.1838e-05 5 85 1.1111 0.3606
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000000 0.00109 85 0.000 1.0000
Step1 - Step3 -0.000616 0.00109 85 -0.566 0.9929
Step1 - Step4 -0.002090 0.00109 85 -1.921 0.3967
Step1 - Step5 -0.000616 0.00109 85 -0.566 0.9929
Step1 - Step6 0.000000 0.00109 85 0.000 1.0000
Step2 - Step3 -0.000616 0.00109 85 -0.566 0.9929
Step2 - Step4 -0.002090 0.00109 85 -1.921 0.3967
Step2 - Step5 -0.000616 0.00109 85 -0.566 0.9929
Step2 - Step6 0.000000 0.00109 85 0.000 1.0000
Step3 - Step4 -0.001474 0.00109 85 -1.355 0.7534
Step3 - Step5 0.000000 0.00109 85 0.000 1.0000
Step3 - Step6 0.000616 0.00109 85 0.566 0.9929
Step4 - Step5 0.001474 0.00109 85 1.355 0.7534
Step4 - Step6 0.002090 0.00109 85 1.921 0.3967
Step5 - Step6 0.000616 0.00109 85 0.566 0.9929
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
8.813106e-01 1.016484e-14 6.160745e-04 2.090224e-03 6.160745e-04 1.033857e-14
Random Effects:
$subject
(Intercept)
2 -0.303793183
3 0.003871254
4 -0.482994299
5 -0.430014430
7 -0.312624567
8 0.526805755
10 1.506732996
11 1.408859403
13 -0.039626579
14 0.364923077
15 -0.350871092
16 -0.407872592
17 -0.511733542
18 -0.303952183
19 -0.560920437
20 -0.306794247
22 -0.558357534
23 0.758362208
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.16925243 0.16925243 -0.01948979 -0.47111415 -0.01948979 0.16925243
=============================================================
--- Mixed - SD - Block 1 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.00012435 2.487e-05 5 85 1.5972 0.1696
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000000 0.00132 85 0.000 1.0000
Step1 - Step3 0.000327 0.00132 85 0.248 0.9999
Step1 - Step4 -0.002722 0.00132 85 -2.069 0.3132
Step1 - Step5 0.000327 0.00132 85 0.248 0.9999
Step1 - Step6 0.000000 0.00132 85 0.000 1.0000
Step2 - Step3 0.000327 0.00132 85 0.248 0.9999
Step2 - Step4 -0.002722 0.00132 85 -2.069 0.3132
Step2 - Step5 0.000327 0.00132 85 0.248 0.9999
Step2 - Step6 0.000000 0.00132 85 0.000 1.0000
Step3 - Step4 -0.003048 0.00132 85 -2.318 0.1985
Step3 - Step5 0.000000 0.00132 85 0.000 1.0000
Step3 - Step6 -0.000327 0.00132 85 -0.248 0.9999
Step4 - Step5 0.003048 0.00132 85 2.318 0.1985
Step4 - Step6 0.002722 0.00132 85 2.069 0.3132
Step5 - Step6 -0.000327 0.00132 85 -0.248 0.9999
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 6 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
1.469192e+00 -2.911766e-15 -3.265772e-04 2.721796e-03 -3.265772e-04
Step6
-2.911782e-15
Random Effects:
$subject
(Intercept)
2 -0.54120954
3 0.24588589
4 -0.64890393
5 -0.71199325
7 -0.03406864
8 1.36138122
10 1.49947612
11 2.40310888
13 0.14589447
14 -0.69327026
15 -0.20038146
16 -0.42901791
17 -1.13723045
18 -0.51858629
19 -0.71222633
20 -0.67059853
22 -0.84122595
23 1.48296597
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.08702494 0.08702494 0.16978797 -0.60274793 0.16978797 0.08702494
=============================================================
--- Mixed - SD - Block 2 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.34866 0.031697 11 187 6.9576 8.147e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.013502 0.0225 187 0.600 1.0000
Step1 - Step3 0.028275 0.0225 187 1.257 0.9833
Step1 - Step4 0.034181 0.0225 187 1.519 0.9336
Step1 - Step5 0.038240 0.0225 187 1.700 0.8663
Step1 - Step6 0.045177 0.0225 187 2.008 0.6875
Step1 - Step7 0.045440 0.0225 187 2.020 0.6795
Step1 - Step8 0.065137 0.0225 187 2.895 0.1513
Step1 - Step9 0.098068 0.0225 187 4.359 0.0013
Step1 - Step10 0.106033 0.0225 187 4.713 0.0003
Step1 - Step11 0.117109 0.0225 187 5.205 <.0001
Step1 - Step12 0.124615 0.0225 187 5.539 <.0001
Step2 - Step3 0.014773 0.0225 187 0.657 1.0000
Step2 - Step4 0.020679 0.0225 187 0.919 0.9989
Step2 - Step5 0.024738 0.0225 187 1.100 0.9944
Step2 - Step6 0.031675 0.0225 187 1.408 0.9607
Step2 - Step7 0.031938 0.0225 187 1.420 0.9583
Step2 - Step8 0.051635 0.0225 187 2.295 0.4839
Step2 - Step9 0.084566 0.0225 187 3.759 0.0119
Step2 - Step10 0.092531 0.0225 187 4.113 0.0033
Step2 - Step11 0.103607 0.0225 187 4.605 0.0005
Step2 - Step12 0.111113 0.0225 187 4.939 0.0001
Step3 - Step4 0.005906 0.0225 187 0.262 1.0000
Step3 - Step5 0.009965 0.0225 187 0.443 1.0000
Step3 - Step6 0.016902 0.0225 187 0.751 0.9998
Step3 - Step7 0.017165 0.0225 187 0.763 0.9998
Step3 - Step8 0.036862 0.0225 187 1.638 0.8925
Step3 - Step9 0.069793 0.0225 187 3.102 0.0896
Step3 - Step10 0.077758 0.0225 187 3.456 0.0321
Step3 - Step11 0.088834 0.0225 187 3.948 0.0061
Step3 - Step12 0.096341 0.0225 187 4.282 0.0017
Step4 - Step5 0.004059 0.0225 187 0.180 1.0000
Step4 - Step6 0.010996 0.0225 187 0.489 1.0000
Step4 - Step7 0.011259 0.0225 187 0.500 1.0000
Step4 - Step8 0.030957 0.0225 187 1.376 0.9667
Step4 - Step9 0.063887 0.0225 187 2.840 0.1724
Step4 - Step10 0.071853 0.0225 187 3.194 0.0698
Step4 - Step11 0.082928 0.0225 187 3.686 0.0153
Step4 - Step12 0.090435 0.0225 187 4.020 0.0047
Step5 - Step6 0.006936 0.0225 187 0.308 1.0000
Step5 - Step7 0.007200 0.0225 187 0.320 1.0000
Step5 - Step8 0.026897 0.0225 187 1.196 0.9888
Step5 - Step9 0.059828 0.0225 187 2.659 0.2554
Step5 - Step10 0.067793 0.0225 187 3.013 0.1130
Step5 - Step11 0.078869 0.0225 187 3.506 0.0275
Step5 - Step12 0.086375 0.0225 187 3.839 0.0090
Step6 - Step7 0.000263 0.0225 187 0.012 1.0000
Step6 - Step8 0.019961 0.0225 187 0.887 0.9992
Step6 - Step9 0.052891 0.0225 187 2.351 0.4448
Step6 - Step10 0.060857 0.0225 187 2.705 0.2322
Step6 - Step11 0.071933 0.0225 187 3.197 0.0691
Step6 - Step12 0.079439 0.0225 187 3.531 0.0254
Step7 - Step8 0.019697 0.0225 187 0.875 0.9993
Step7 - Step9 0.052628 0.0225 187 2.339 0.4529
Step7 - Step10 0.060593 0.0225 187 2.693 0.2380
Step7 - Step11 0.071669 0.0225 187 3.185 0.0714
Step7 - Step12 0.079175 0.0225 187 3.519 0.0264
Step8 - Step9 0.032931 0.0225 187 1.464 0.9484
Step8 - Step10 0.040896 0.0225 187 1.818 0.8063
Step8 - Step11 0.051972 0.0225 187 2.310 0.4733
Step8 - Step12 0.059478 0.0225 187 2.644 0.2635
Step9 - Step10 0.007965 0.0225 187 0.354 1.0000
Step9 - Step11 0.019041 0.0225 187 0.846 0.9995
Step9 - Step12 0.026548 0.0225 187 1.180 0.9899
Step10 - Step11 0.011076 0.0225 187 0.492 1.0000
Step10 - Step12 0.018582 0.0225 187 0.826 0.9996
Step11 - Step12 0.007506 0.0225 187 0.334 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.85324240 -0.01350188 -0.02827476 -0.03418065 -0.03824011 -0.04517651
Step7 Step8 Step9 Step10 Step11 Step12
-0.04543987 -0.06513724 -0.09806778 -0.10603317 -0.11710905 -0.12461532
Random Effects:
$subject
(Intercept)
2 0.29031083
3 0.12991359
4 -0.33571298
5 -0.29128186
7 -0.18423060
8 0.18815896
10 0.85540252
11 0.99644663
13 -0.27328728
14 0.21489533
15 -0.18891518
16 -0.16585298
17 -0.30144778
18 -0.17037536
19 -0.33163909
20 -0.28980507
22 -0.18367761
23 0.04109791
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.3690467 -0.9543075 -1.3790925 -0.5782817 -0.3422331 0.3918117
=============================================================
--- Mixed - SD - Block 2 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.19762 0.017966 11 187 2.5201 0.005539 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.000712 0.0281 187 0.025 1.0000
Step1 - Step3 0.015052 0.0281 187 0.535 1.0000
Step1 - Step4 0.021699 0.0281 187 0.771 0.9998
Step1 - Step5 0.024820 0.0281 187 0.882 0.9992
Step1 - Step6 0.027977 0.0281 187 0.994 0.9977
Step1 - Step7 0.041982 0.0281 187 1.492 0.9412
Step1 - Step8 0.052133 0.0281 187 1.852 0.7865
Step1 - Step9 0.062481 0.0281 187 2.220 0.5374
Step1 - Step10 0.066571 0.0281 187 2.365 0.4349
Step1 - Step11 0.084567 0.0281 187 3.005 0.1155
Step1 - Step12 0.096316 0.0281 187 3.422 0.0357
Step2 - Step3 0.014341 0.0281 187 0.510 1.0000
Step2 - Step4 0.020987 0.0281 187 0.746 0.9998
Step2 - Step5 0.024109 0.0281 187 0.857 0.9994
Step2 - Step6 0.027266 0.0281 187 0.969 0.9982
Step2 - Step7 0.041271 0.0281 187 1.466 0.9477
Step2 - Step8 0.051421 0.0281 187 1.827 0.8011
Step2 - Step9 0.061769 0.0281 187 2.195 0.5556
Step2 - Step10 0.065859 0.0281 187 2.340 0.4523
Step2 - Step11 0.083855 0.0281 187 2.979 0.1231
Step2 - Step12 0.095605 0.0281 187 3.397 0.0386
Step3 - Step4 0.006647 0.0281 187 0.236 1.0000
Step3 - Step5 0.009768 0.0281 187 0.347 1.0000
Step3 - Step6 0.012925 0.0281 187 0.459 1.0000
Step3 - Step7 0.026930 0.0281 187 0.957 0.9984
Step3 - Step8 0.037081 0.0281 187 1.318 0.9759
Step3 - Step9 0.047428 0.0281 187 1.685 0.8728
Step3 - Step10 0.051519 0.0281 187 1.831 0.7991
Step3 - Step11 0.069514 0.0281 187 2.470 0.3655
Step3 - Step12 0.081264 0.0281 187 2.887 0.1541
Step4 - Step5 0.003121 0.0281 187 0.111 1.0000
Step4 - Step6 0.006278 0.0281 187 0.223 1.0000
Step4 - Step7 0.020283 0.0281 187 0.721 0.9999
Step4 - Step8 0.030434 0.0281 187 1.081 0.9951
Step4 - Step9 0.040781 0.0281 187 1.449 0.9519
Step4 - Step10 0.044872 0.0281 187 1.594 0.9092
Step4 - Step11 0.062868 0.0281 187 2.234 0.5275
Step4 - Step12 0.074617 0.0281 187 2.651 0.2595
Step5 - Step6 0.003157 0.0281 187 0.112 1.0000
Step5 - Step7 0.017162 0.0281 187 0.610 1.0000
Step5 - Step8 0.027313 0.0281 187 0.970 0.9981
Step5 - Step9 0.037660 0.0281 187 1.338 0.9729
Step5 - Step10 0.041751 0.0281 187 1.483 0.9434
Step5 - Step11 0.059746 0.0281 187 2.123 0.6072
Step5 - Step12 0.071496 0.0281 187 2.540 0.3220
Step6 - Step7 0.014005 0.0281 187 0.498 1.0000
Step6 - Step8 0.024156 0.0281 187 0.858 0.9994
Step6 - Step9 0.034503 0.0281 187 1.226 0.9863
Step6 - Step10 0.038594 0.0281 187 1.371 0.9676
Step6 - Step11 0.056589 0.0281 187 2.011 0.6856
Step6 - Step12 0.068339 0.0281 187 2.428 0.3926
Step7 - Step8 0.010151 0.0281 187 0.361 1.0000
Step7 - Step9 0.020498 0.0281 187 0.728 0.9999
Step7 - Step10 0.024589 0.0281 187 0.874 0.9993
Step7 - Step11 0.042584 0.0281 187 1.513 0.9353
Step7 - Step12 0.054334 0.0281 187 1.931 0.7386
Step8 - Step9 0.010348 0.0281 187 0.368 1.0000
Step8 - Step10 0.014438 0.0281 187 0.513 1.0000
Step8 - Step11 0.032434 0.0281 187 1.152 0.9917
Step8 - Step12 0.044183 0.0281 187 1.570 0.9177
Step9 - Step10 0.004091 0.0281 187 0.145 1.0000
Step9 - Step11 0.022086 0.0281 187 0.785 0.9997
Step9 - Step12 0.033836 0.0281 187 1.202 0.9882
Step10 - Step11 0.017995 0.0281 187 0.639 1.0000
Step10 - Step12 0.029745 0.0281 187 1.057 0.9960
Step11 - Step12 0.011750 0.0281 187 0.417 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
0.8982466572 -0.0007116643 -0.0150524558 -0.0216990573 -0.0248203182
Step6 Step7 Step8 Step9 Step10
-0.0279773472 -0.0419824515 -0.0521330118 -0.0624805350 -0.0665711440
Step11 Step12
-0.0845666082 -0.0963163554
Random Effects:
$subject
(Intercept)
2 0.18653446
3 0.34213339
4 -0.44326650
5 -0.42667438
7 -0.16748677
8 0.67112682
10 0.82135597
11 1.09558842
13 -0.23906867
14 0.11156655
15 -0.32290000
16 -0.11070846
17 -0.31646800
18 -0.19083545
19 -0.37153796
20 -0.23112626
22 -0.47600583
23 0.06777269
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.78914079 -0.75721479 -0.40655597 -0.58005427 0.18967103 -0.09101536
=============================================================
--- Mixed - SD - Block 2 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.18404 0.016731 11 187 0.6722 0.7637
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.003283 0.0526 187 0.062 1.0000
Step1 - Step3 0.014907 0.0526 187 0.283 1.0000
Step1 - Step4 0.007145 0.0526 187 0.136 1.0000
Step1 - Step5 0.005955 0.0526 187 0.113 1.0000
Step1 - Step6 0.006532 0.0526 187 0.124 1.0000
Step1 - Step7 0.010944 0.0526 187 0.208 1.0000
Step1 - Step8 0.031299 0.0526 187 0.595 1.0000
Step1 - Step9 0.057560 0.0526 187 1.095 0.9946
Step1 - Step10 0.061252 0.0526 187 1.165 0.9909
Step1 - Step11 0.081782 0.0526 187 1.555 0.9226
Step1 - Step12 0.074173 0.0526 187 1.410 0.9602
Step2 - Step3 0.011624 0.0526 187 0.221 1.0000
Step2 - Step4 0.003862 0.0526 187 0.073 1.0000
Step2 - Step5 0.002672 0.0526 187 0.051 1.0000
Step2 - Step6 0.003249 0.0526 187 0.062 1.0000
Step2 - Step7 0.007661 0.0526 187 0.146 1.0000
Step2 - Step8 0.028016 0.0526 187 0.533 1.0000
Step2 - Step9 0.054277 0.0526 187 1.032 0.9968
Step2 - Step10 0.057969 0.0526 187 1.102 0.9943
Step2 - Step11 0.078499 0.0526 187 1.493 0.9410
Step2 - Step12 0.070890 0.0526 187 1.348 0.9714
Step3 - Step4 -0.007762 0.0526 187 -0.148 1.0000
Step3 - Step5 -0.008952 0.0526 187 -0.170 1.0000
Step3 - Step6 -0.008375 0.0526 187 -0.159 1.0000
Step3 - Step7 -0.003963 0.0526 187 -0.075 1.0000
Step3 - Step8 0.016392 0.0526 187 0.312 1.0000
Step3 - Step9 0.042653 0.0526 187 0.811 0.9996
Step3 - Step10 0.046345 0.0526 187 0.881 0.9992
Step3 - Step11 0.066875 0.0526 187 1.272 0.9817
Step3 - Step12 0.059266 0.0526 187 1.127 0.9931
Step4 - Step5 -0.001190 0.0526 187 -0.023 1.0000
Step4 - Step6 -0.000613 0.0526 187 -0.012 1.0000
Step4 - Step7 0.003799 0.0526 187 0.072 1.0000
Step4 - Step8 0.024154 0.0526 187 0.459 1.0000
Step4 - Step9 0.050415 0.0526 187 0.959 0.9983
Step4 - Step10 0.054107 0.0526 187 1.029 0.9968
Step4 - Step11 0.074637 0.0526 187 1.419 0.9584
Step4 - Step12 0.067028 0.0526 187 1.275 0.9813
Step5 - Step6 0.000577 0.0526 187 0.011 1.0000
Step5 - Step7 0.004989 0.0526 187 0.095 1.0000
Step5 - Step8 0.025344 0.0526 187 0.482 1.0000
Step5 - Step9 0.051605 0.0526 187 0.981 0.9979
Step5 - Step10 0.055298 0.0526 187 1.052 0.9962
Step5 - Step11 0.075827 0.0526 187 1.442 0.9535
Step5 - Step12 0.068218 0.0526 187 1.297 0.9786
Step6 - Step7 0.004412 0.0526 187 0.084 1.0000
Step6 - Step8 0.024767 0.0526 187 0.471 1.0000
Step6 - Step9 0.051028 0.0526 187 0.970 0.9981
Step6 - Step10 0.054720 0.0526 187 1.041 0.9965
Step6 - Step11 0.075250 0.0526 187 1.431 0.9559
Step6 - Step12 0.067641 0.0526 187 1.286 0.9800
Step7 - Step8 0.020355 0.0526 187 0.387 1.0000
Step7 - Step9 0.046616 0.0526 187 0.886 0.9992
Step7 - Step10 0.050309 0.0526 187 0.957 0.9984
Step7 - Step11 0.070838 0.0526 187 1.347 0.9716
Step7 - Step12 0.063229 0.0526 187 1.202 0.9882
Step8 - Step9 0.026261 0.0526 187 0.499 1.0000
Step8 - Step10 0.029953 0.0526 187 0.570 1.0000
Step8 - Step11 0.050483 0.0526 187 0.960 0.9983
Step8 - Step12 0.042874 0.0526 187 0.815 0.9996
Step9 - Step10 0.003692 0.0526 187 0.070 1.0000
Step9 - Step11 0.024222 0.0526 187 0.461 1.0000
Step9 - Step12 0.016613 0.0526 187 0.316 1.0000
Step10 - Step11 0.020530 0.0526 187 0.390 1.0000
Step10 - Step12 0.012921 0.0526 187 0.246 1.0000
Step11 - Step12 -0.007609 0.0526 187 -0.145 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 12 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.595264622 -0.003282699 -0.014907015 -0.007144805 -0.005954529 -0.006531658
Step7 Step8 Step9 Step10 Step11 Step12
-0.010943604 -0.031298750 -0.057559943 -0.061252162 -0.081781987 -0.074172916
Random Effects:
$subject
(Intercept)
2 -0.09961552
3 0.41897130
4 -0.67642800
5 -0.66663682
7 0.08098175
8 1.01795885
10 1.47994446
11 2.02761024
13 -0.42120344
14 -0.41265002
15 -0.36469037
16 0.27914076
17 -0.84977608
18 0.09748478
19 -0.70398338
20 -0.75889634
22 -0.69028739
23 0.24207521
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.462627499 0.117996086 0.092894093 0.004184111 0.069502311 0.064436305
=============================================================
--- Mixed - SD - Block 3 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.24895 0.014644 17 289 3.8546 8.496e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.002850 0.0205 289 0.139 1.0000
Step1 - Step3 0.010492 0.0205 289 0.511 1.0000
Step1 - Step4 0.012216 0.0205 289 0.595 1.0000
Step1 - Step5 0.008727 0.0205 289 0.425 1.0000
Step1 - Step6 0.009718 0.0205 289 0.473 1.0000
Step1 - Step7 0.011441 0.0205 289 0.557 1.0000
Step1 - Step8 0.026344 0.0205 289 1.282 0.9984
Step1 - Step9 0.030209 0.0205 289 1.470 0.9920
Step1 - Step10 0.049561 0.0205 289 2.412 0.5992
Step1 - Step11 0.047711 0.0205 289 2.322 0.6665
Step1 - Step12 0.058382 0.0205 289 2.842 0.2933
Step1 - Step13 0.059656 0.0205 289 2.904 0.2573
Step1 - Step14 0.058031 0.0205 289 2.824 0.3037
Step1 - Step15 0.061013 0.0205 289 2.970 0.2223
Step1 - Step16 0.072288 0.0205 289 3.518 0.0504
Step1 - Step17 0.081534 0.0205 289 3.968 0.0109
Step1 - Step18 0.083350 0.0205 289 4.057 0.0079
Step2 - Step3 0.007642 0.0205 289 0.372 1.0000
Step2 - Step4 0.009366 0.0205 289 0.456 1.0000
Step2 - Step5 0.005877 0.0205 289 0.286 1.0000
Step2 - Step6 0.006868 0.0205 289 0.334 1.0000
Step2 - Step7 0.008591 0.0205 289 0.418 1.0000
Step2 - Step8 0.023494 0.0205 289 1.143 0.9996
Step2 - Step9 0.027359 0.0205 289 1.332 0.9974
Step2 - Step10 0.046711 0.0205 289 2.274 0.7016
Step2 - Step11 0.044861 0.0205 289 2.183 0.7629
Step2 - Step12 0.055532 0.0205 289 2.703 0.3833
Step2 - Step13 0.056806 0.0205 289 2.765 0.3415
Step2 - Step14 0.055181 0.0205 289 2.686 0.3952
Step2 - Step15 0.058163 0.0205 289 2.831 0.2997
Step2 - Step16 0.069438 0.0205 289 3.380 0.0765
Step2 - Step17 0.078684 0.0205 289 3.830 0.0180
Step2 - Step18 0.080500 0.0205 289 3.918 0.0131
Step3 - Step4 0.001725 0.0205 289 0.084 1.0000
Step3 - Step5 -0.001765 0.0205 289 -0.086 1.0000
Step3 - Step6 -0.000774 0.0205 289 -0.038 1.0000
Step3 - Step7 0.000949 0.0205 289 0.046 1.0000
Step3 - Step8 0.015852 0.0205 289 0.772 1.0000
Step3 - Step9 0.019717 0.0205 289 0.960 1.0000
Step3 - Step10 0.039069 0.0205 289 1.902 0.9091
Step3 - Step11 0.037219 0.0205 289 1.812 0.9389
Step3 - Step12 0.047890 0.0205 289 2.331 0.6601
Step3 - Step13 0.049164 0.0205 289 2.393 0.6138
Step3 - Step14 0.047539 0.0205 289 2.314 0.6726
Step3 - Step15 0.050521 0.0205 289 2.459 0.5636
Step3 - Step16 0.061796 0.0205 289 3.008 0.2036
Step3 - Step17 0.071042 0.0205 289 3.458 0.0607
Step3 - Step18 0.072858 0.0205 289 3.546 0.0462
Step4 - Step5 -0.003489 0.0205 289 -0.170 1.0000
Step4 - Step6 -0.002499 0.0205 289 -0.122 1.0000
Step4 - Step7 -0.000776 0.0205 289 -0.038 1.0000
Step4 - Step8 0.014127 0.0205 289 0.688 1.0000
Step4 - Step9 0.017992 0.0205 289 0.876 1.0000
Step4 - Step10 0.037344 0.0205 289 1.818 0.9372
Step4 - Step11 0.035495 0.0205 289 1.728 0.9598
Step4 - Step12 0.046166 0.0205 289 2.247 0.7202
Step4 - Step13 0.047440 0.0205 289 2.309 0.6762
Step4 - Step14 0.045814 0.0205 289 2.230 0.7320
Step4 - Step15 0.048797 0.0205 289 2.375 0.6273
Step4 - Step16 0.060072 0.0205 289 2.924 0.2462
Step4 - Step17 0.069317 0.0205 289 3.374 0.0778
Step4 - Step18 0.071133 0.0205 289 3.462 0.0598
Step5 - Step6 0.000991 0.0205 289 0.048 1.0000
Step5 - Step7 0.002713 0.0205 289 0.132 1.0000
Step5 - Step8 0.017616 0.0205 289 0.857 1.0000
Step5 - Step9 0.021481 0.0205 289 1.046 0.9999
Step5 - Step10 0.040833 0.0205 289 1.987 0.8730
Step5 - Step11 0.038984 0.0205 289 1.897 0.9107
Step5 - Step12 0.049655 0.0205 289 2.417 0.5957
Step5 - Step13 0.050929 0.0205 289 2.479 0.5485
Step5 - Step14 0.049303 0.0205 289 2.400 0.6087
Step5 - Step15 0.052286 0.0205 289 2.545 0.4983
Step5 - Step16 0.063561 0.0205 289 3.094 0.1655
Step5 - Step17 0.072806 0.0205 289 3.544 0.0466
Step5 - Step18 0.074623 0.0205 289 3.632 0.0351
Step6 - Step7 0.001723 0.0205 289 0.084 1.0000
Step6 - Step8 0.016626 0.0205 289 0.809 1.0000
Step6 - Step9 0.020491 0.0205 289 0.997 0.9999
Step6 - Step10 0.039843 0.0205 289 1.939 0.8942
Step6 - Step11 0.037993 0.0205 289 1.849 0.9274
Step6 - Step12 0.048664 0.0205 289 2.369 0.6321
Step6 - Step13 0.049939 0.0205 289 2.431 0.5852
Step6 - Step14 0.048313 0.0205 289 2.351 0.6449
Step6 - Step15 0.051296 0.0205 289 2.497 0.5349
Step6 - Step16 0.062570 0.0205 289 3.045 0.1862
Step6 - Step17 0.071816 0.0205 289 3.495 0.0541
Step6 - Step18 0.073632 0.0205 289 3.584 0.0410
Step7 - Step8 0.014903 0.0205 289 0.725 1.0000
Step7 - Step9 0.018768 0.0205 289 0.913 1.0000
Step7 - Step10 0.038120 0.0205 289 1.855 0.9254
Step7 - Step11 0.036270 0.0205 289 1.765 0.9512
Step7 - Step12 0.046942 0.0205 289 2.285 0.6936
Step7 - Step13 0.048216 0.0205 289 2.347 0.6484
Step7 - Step14 0.046590 0.0205 289 2.268 0.7058
Step7 - Step15 0.049573 0.0205 289 2.413 0.5988
Step7 - Step16 0.060847 0.0205 289 2.962 0.2264
Step7 - Step17 0.070093 0.0205 289 3.412 0.0696
Step7 - Step18 0.071909 0.0205 289 3.500 0.0533
Step8 - Step9 0.003865 0.0205 289 0.188 1.0000
Step8 - Step10 0.023217 0.0205 289 1.130 0.9997
Step8 - Step11 0.021367 0.0205 289 1.040 0.9999
Step8 - Step12 0.032039 0.0205 289 1.559 0.9851
Step8 - Step13 0.033313 0.0205 289 1.621 0.9780
Step8 - Step14 0.031687 0.0205 289 1.542 0.9867
Step8 - Step15 0.034670 0.0205 289 1.687 0.9676
Step8 - Step16 0.045944 0.0205 289 2.236 0.7277
Step8 - Step17 0.055190 0.0205 289 2.686 0.3949
Step8 - Step18 0.057006 0.0205 289 2.775 0.3352
Step9 - Step10 0.019352 0.0205 289 0.942 1.0000
Step9 - Step11 0.017502 0.0205 289 0.852 1.0000
Step9 - Step12 0.028173 0.0205 289 1.371 0.9964
Step9 - Step13 0.029448 0.0205 289 1.433 0.9940
Step9 - Step14 0.027822 0.0205 289 1.354 0.9969
Step9 - Step15 0.030805 0.0205 289 1.499 0.9901
Step9 - Step16 0.042079 0.0205 289 2.048 0.8428
Step9 - Step17 0.051325 0.0205 289 2.498 0.5338
Step9 - Step18 0.053141 0.0205 289 2.586 0.4671
Step10 - Step11 -0.001849 0.0205 289 -0.090 1.0000
Step10 - Step12 0.008822 0.0205 289 0.429 1.0000
Step10 - Step13 0.010096 0.0205 289 0.491 1.0000
Step10 - Step14 0.008470 0.0205 289 0.412 1.0000
Step10 - Step15 0.011453 0.0205 289 0.557 1.0000
Step10 - Step16 0.022727 0.0205 289 1.106 0.9998
Step10 - Step17 0.031973 0.0205 289 1.556 0.9854
Step10 - Step18 0.033789 0.0205 289 1.645 0.9747
Step11 - Step12 0.010671 0.0205 289 0.519 1.0000
Step11 - Step13 0.011945 0.0205 289 0.581 1.0000
Step11 - Step14 0.010320 0.0205 289 0.502 1.0000
Step11 - Step15 0.013302 0.0205 289 0.647 1.0000
Step11 - Step16 0.024577 0.0205 289 1.196 0.9993
Step11 - Step17 0.033822 0.0205 289 1.646 0.9744
Step11 - Step18 0.035639 0.0205 289 1.735 0.9583
Step12 - Step13 0.001274 0.0205 289 0.062 1.0000
Step12 - Step14 -0.000351 0.0205 289 -0.017 1.0000
Step12 - Step15 0.002631 0.0205 289 0.128 1.0000
Step12 - Step16 0.013906 0.0205 289 0.677 1.0000
Step12 - Step17 0.023151 0.0205 289 1.127 0.9997
Step12 - Step18 0.024968 0.0205 289 1.215 0.9992
Step13 - Step14 -0.001626 0.0205 289 -0.079 1.0000
Step13 - Step15 0.001357 0.0205 289 0.066 1.0000
Step13 - Step16 0.012632 0.0205 289 0.615 1.0000
Step13 - Step17 0.021877 0.0205 289 1.065 0.9999
Step13 - Step18 0.023694 0.0205 289 1.153 0.9996
Step14 - Step15 0.002983 0.0205 289 0.145 1.0000
Step14 - Step16 0.014257 0.0205 289 0.694 1.0000
Step14 - Step17 0.023503 0.0205 289 1.144 0.9996
Step14 - Step18 0.025319 0.0205 289 1.232 0.9990
Step15 - Step16 0.011275 0.0205 289 0.549 1.0000
Step15 - Step17 0.020520 0.0205 289 0.999 0.9999
Step15 - Step18 0.022337 0.0205 289 1.087 0.9998
Step16 - Step17 0.009246 0.0205 289 0.450 1.0000
Step16 - Step18 0.011062 0.0205 289 0.538 1.0000
Step17 - Step18 0.001816 0.0205 289 0.088 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.671461377 -0.002850006 -0.010491967 -0.012216496 -0.008727327 -0.009717854
Step7 Step8 Step9 Step10 Step11 Step12
-0.011440754 -0.026343724 -0.030208819 -0.049560694 -0.047711203 -0.058382263
Step13 Step14 Step15 Step16 Step17 Step18
-0.059656444 -0.058030780 -0.061013449 -0.072288136 -0.081533669 -0.083349970
Random Effects:
$subject
(Intercept)
2 0.23289732
3 0.02696411
4 -0.22775546
5 -0.29972565
7 -0.06629733
8 0.07711327
10 0.65172520
11 0.50326115
13 -0.18110343
14 -0.02842196
15 -0.11070271
16 -0.04576267
17 -0.05449078
18 0.09659745
19 -0.21532113
20 -0.22205811
22 -0.15956441
23 0.02264515
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.88765296 -0.06935408 -0.42180346 -0.27011748 -0.50476822 -0.22822550
=============================================================
--- Mixed - SD - Block 3 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.14985 0.0088144 17 289 1.893 0.01839 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 2.11e-03 0.0227 289 0.093 1.0000
Step1 - Step3 6.56e-03 0.0227 289 0.288 1.0000
Step1 - Step4 1.01e-02 0.0227 289 0.444 1.0000
Step1 - Step5 2.15e-03 0.0227 289 0.095 1.0000
Step1 - Step6 -2.31e-03 0.0227 289 -0.101 1.0000
Step1 - Step7 -1.21e-02 0.0227 289 -0.531 1.0000
Step1 - Step8 -3.13e-04 0.0227 289 -0.014 1.0000
Step1 - Step9 5.91e-03 0.0227 289 0.260 1.0000
Step1 - Step10 1.90e-02 0.0227 289 0.834 1.0000
Step1 - Step11 2.68e-02 0.0227 289 1.177 0.9994
Step1 - Step12 2.93e-02 0.0227 289 1.289 0.9983
Step1 - Step13 3.11e-02 0.0227 289 1.369 0.9964
Step1 - Step14 2.96e-02 0.0227 289 1.302 0.9980
Step1 - Step15 2.94e-02 0.0227 289 1.291 0.9982
Step1 - Step16 4.15e-02 0.0227 289 1.825 0.9348
Step1 - Step17 5.65e-02 0.0227 289 2.483 0.5452
Step1 - Step18 7.14e-02 0.0227 289 3.141 0.1469
Step2 - Step3 4.45e-03 0.0227 289 0.196 1.0000
Step2 - Step4 8.00e-03 0.0227 289 0.352 1.0000
Step2 - Step5 4.59e-05 0.0227 289 0.002 1.0000
Step2 - Step6 -4.41e-03 0.0227 289 -0.194 1.0000
Step2 - Step7 -1.42e-02 0.0227 289 -0.624 1.0000
Step2 - Step8 -2.42e-03 0.0227 289 -0.106 1.0000
Step2 - Step9 3.80e-03 0.0227 289 0.167 1.0000
Step2 - Step10 1.69e-02 0.0227 289 0.742 1.0000
Step2 - Step11 2.47e-02 0.0227 289 1.084 0.9998
Step2 - Step12 2.72e-02 0.0227 289 1.196 0.9993
Step2 - Step13 2.90e-02 0.0227 289 1.277 0.9984
Step2 - Step14 2.75e-02 0.0227 289 1.210 0.9992
Step2 - Step15 2.73e-02 0.0227 289 1.199 0.9993
Step2 - Step16 3.94e-02 0.0227 289 1.733 0.9586
Step2 - Step17 5.44e-02 0.0227 289 2.391 0.6156
Step2 - Step18 6.93e-02 0.0227 289 3.048 0.1848
Step3 - Step4 3.54e-03 0.0227 289 0.156 1.0000
Step3 - Step5 -4.41e-03 0.0227 289 -0.194 1.0000
Step3 - Step6 -8.87e-03 0.0227 289 -0.390 1.0000
Step3 - Step7 -1.86e-02 0.0227 289 -0.820 1.0000
Step3 - Step8 -6.87e-03 0.0227 289 -0.302 1.0000
Step3 - Step9 -6.52e-04 0.0227 289 -0.029 1.0000
Step3 - Step10 1.24e-02 0.0227 289 0.546 1.0000
Step3 - Step11 2.02e-02 0.0227 289 0.889 1.0000
Step3 - Step12 2.28e-02 0.0227 289 1.001 0.9999
Step3 - Step13 2.46e-02 0.0227 289 1.081 0.9998
Step3 - Step14 2.31e-02 0.0227 289 1.014 0.9999
Step3 - Step15 2.28e-02 0.0227 289 1.003 0.9999
Step3 - Step16 3.50e-02 0.0227 289 1.537 0.9872
Step3 - Step17 4.99e-02 0.0227 289 2.195 0.7555
Step3 - Step18 6.49e-02 0.0227 289 2.853 0.2866
Step4 - Step5 -7.95e-03 0.0227 289 -0.350 1.0000
Step4 - Step6 -1.24e-02 0.0227 289 -0.546 1.0000
Step4 - Step7 -2.22e-02 0.0227 289 -0.976 1.0000
Step4 - Step8 -1.04e-02 0.0227 289 -0.458 1.0000
Step4 - Step9 -4.20e-03 0.0227 289 -0.184 1.0000
Step4 - Step10 8.87e-03 0.0227 289 0.390 1.0000
Step4 - Step11 1.67e-02 0.0227 289 0.733 1.0000
Step4 - Step12 1.92e-02 0.0227 289 0.845 1.0000
Step4 - Step13 2.10e-02 0.0227 289 0.925 1.0000
Step4 - Step14 1.95e-02 0.0227 289 0.858 1.0000
Step4 - Step15 1.93e-02 0.0227 289 0.847 1.0000
Step4 - Step16 3.14e-02 0.0227 289 1.381 0.9960
Step4 - Step17 4.64e-02 0.0227 289 2.039 0.8476
Step4 - Step18 6.13e-02 0.0227 289 2.697 0.3875
Step5 - Step6 -4.46e-03 0.0227 289 -0.196 1.0000
Step5 - Step7 -1.42e-02 0.0227 289 -0.626 1.0000
Step5 - Step8 -2.46e-03 0.0227 289 -0.108 1.0000
Step5 - Step9 3.76e-03 0.0227 289 0.165 1.0000
Step5 - Step10 1.68e-02 0.0227 289 0.740 1.0000
Step5 - Step11 2.46e-02 0.0227 289 1.082 0.9998
Step5 - Step12 2.72e-02 0.0227 289 1.194 0.9993
Step5 - Step13 2.90e-02 0.0227 289 1.275 0.9985
Step5 - Step14 2.75e-02 0.0227 289 1.208 0.9992
Step5 - Step15 2.72e-02 0.0227 289 1.197 0.9993
Step5 - Step16 3.94e-02 0.0227 289 1.731 0.9591
Step5 - Step17 5.43e-02 0.0227 289 2.389 0.6172
Step5 - Step18 6.93e-02 0.0227 289 3.046 0.1857
Step6 - Step7 -9.78e-03 0.0227 289 -0.430 1.0000
Step6 - Step8 1.99e-03 0.0227 289 0.088 1.0000
Step6 - Step9 8.21e-03 0.0227 289 0.361 1.0000
Step6 - Step10 2.13e-02 0.0227 289 0.936 1.0000
Step6 - Step11 2.91e-02 0.0227 289 1.278 0.9984
Step6 - Step12 3.16e-02 0.0227 289 1.390 0.9957
Step6 - Step13 3.35e-02 0.0227 289 1.471 0.9920
Step6 - Step14 3.19e-02 0.0227 289 1.404 0.9952
Step6 - Step15 3.17e-02 0.0227 289 1.393 0.9957
Step6 - Step16 4.38e-02 0.0227 289 1.927 0.8992
Step6 - Step17 5.88e-02 0.0227 289 2.585 0.4686
Step6 - Step18 7.38e-02 0.0227 289 3.243 0.1125
Step7 - Step8 1.18e-02 0.0227 289 0.518 1.0000
Step7 - Step9 1.80e-02 0.0227 289 0.791 1.0000
Step7 - Step10 3.11e-02 0.0227 289 1.366 0.9965
Step7 - Step11 3.89e-02 0.0227 289 1.708 0.9637
Step7 - Step12 4.14e-02 0.0227 289 1.820 0.9364
Step7 - Step13 4.32e-02 0.0227 289 1.901 0.9095
Step7 - Step14 4.17e-02 0.0227 289 1.834 0.9324
Step7 - Step15 4.15e-02 0.0227 289 1.822 0.9357
Step7 - Step16 5.36e-02 0.0227 289 2.357 0.6409
Step7 - Step17 6.86e-02 0.0227 289 3.014 0.2004
Step7 - Step18 8.35e-02 0.0227 289 3.672 0.0307
Step8 - Step9 6.22e-03 0.0227 289 0.273 1.0000
Step8 - Step10 1.93e-02 0.0227 289 0.848 1.0000
Step8 - Step11 2.71e-02 0.0227 289 1.191 0.9993
Step8 - Step12 2.96e-02 0.0227 289 1.303 0.9980
Step8 - Step13 3.15e-02 0.0227 289 1.383 0.9960
Step8 - Step14 2.99e-02 0.0227 289 1.316 0.9978
Step8 - Step15 2.97e-02 0.0227 289 1.305 0.9980
Step8 - Step16 4.18e-02 0.0227 289 1.839 0.9306
Step8 - Step17 5.68e-02 0.0227 289 2.497 0.5347
Step8 - Step18 7.18e-02 0.0227 289 3.155 0.1418
Step9 - Step10 1.31e-02 0.0227 289 0.575 1.0000
Step9 - Step11 2.09e-02 0.0227 289 0.917 1.0000
Step9 - Step12 2.34e-02 0.0227 289 1.029 0.9999
Step9 - Step13 2.52e-02 0.0227 289 1.110 0.9997
Step9 - Step14 2.37e-02 0.0227 289 1.042 0.9999
Step9 - Step15 2.35e-02 0.0227 289 1.031 0.9999
Step9 - Step16 3.56e-02 0.0227 289 1.566 0.9845
Step9 - Step17 5.06e-02 0.0227 289 2.223 0.7364
Step9 - Step18 6.55e-02 0.0227 289 2.881 0.2699
Step10 - Step11 7.80e-03 0.0227 289 0.343 1.0000
Step10 - Step12 1.03e-02 0.0227 289 0.455 1.0000
Step10 - Step13 1.22e-02 0.0227 289 0.535 1.0000
Step10 - Step14 1.06e-02 0.0227 289 0.468 1.0000
Step10 - Step15 1.04e-02 0.0227 289 0.457 1.0000
Step10 - Step16 2.25e-02 0.0227 289 0.991 0.9999
Step10 - Step17 3.75e-02 0.0227 289 1.649 0.9740
Step10 - Step18 5.25e-02 0.0227 289 2.307 0.6777
Step11 - Step12 2.54e-03 0.0227 289 0.112 1.0000
Step11 - Step13 4.37e-03 0.0227 289 0.192 1.0000
Step11 - Step14 2.85e-03 0.0227 289 0.125 1.0000
Step11 - Step15 2.59e-03 0.0227 289 0.114 1.0000
Step11 - Step16 1.48e-02 0.0227 289 0.649 1.0000
Step11 - Step17 2.97e-02 0.0227 289 1.306 0.9980
Step11 - Step18 4.47e-02 0.0227 289 1.964 0.8836
Step12 - Step13 1.83e-03 0.0227 289 0.080 1.0000
Step12 - Step14 3.03e-04 0.0227 289 0.013 1.0000
Step12 - Step15 5.04e-05 0.0227 289 0.002 1.0000
Step12 - Step16 1.22e-02 0.0227 289 0.537 1.0000
Step12 - Step17 2.72e-02 0.0227 289 1.194 0.9993
Step12 - Step18 4.21e-02 0.0227 289 1.852 0.9265
Step13 - Step14 -1.53e-03 0.0227 289 -0.067 1.0000
Step13 - Step15 -1.78e-03 0.0227 289 -0.078 1.0000
Step13 - Step16 1.04e-02 0.0227 289 0.456 1.0000
Step13 - Step17 2.53e-02 0.0227 289 1.114 0.9997
Step13 - Step18 4.03e-02 0.0227 289 1.772 0.9496
Step14 - Step15 -2.52e-04 0.0227 289 -0.011 1.0000
Step14 - Step16 1.19e-02 0.0227 289 0.523 1.0000
Step14 - Step17 2.69e-02 0.0227 289 1.181 0.9994
Step14 - Step18 4.18e-02 0.0227 289 1.839 0.9307
Step15 - Step16 1.22e-02 0.0227 289 0.534 1.0000
Step15 - Step17 2.71e-02 0.0227 289 1.192 0.9993
Step15 - Step18 4.21e-02 0.0227 289 1.850 0.9272
Step16 - Step17 1.50e-02 0.0227 289 0.658 1.0000
Step16 - Step18 2.99e-02 0.0227 289 1.316 0.9978
Step17 - Step18 1.50e-02 0.0227 289 0.658 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.676665387 -0.002105039 -0.006558100 -0.010102947 -0.002150915 0.002308275
Step7 Step8 Step9 Step10 Step11 Step12
0.012086261 0.000313495 -0.005906507 -0.018974636 -0.026771168 -0.029315705
Step13 Step14 Step15 Step16 Step17 Step18
-0.031144131 -0.029618499 -0.029366154 -0.041522036 -0.056479318 -0.071444602
Random Effects:
$subject
(Intercept)
2 0.124686034
3 0.219202692
4 -0.186134444
5 -0.208807724
7 -0.093053285
8 0.219535949
10 0.663814077
11 0.168616554
13 -0.166097181
14 0.022505551
15 0.003140649
16 -0.119170801
17 -0.034699363
18 -0.055796293
19 -0.242271180
20 -0.169201275
22 -0.253962753
23 0.107692792
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-0.80843506 -0.48892347 -0.71336998 -0.09702261 0.73889975 0.52047023
=============================================================
--- Mixed - SD - Block 3 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.054738 0.0032199 17 289 0.2935 0.9976
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.004711 0.0349 289 -0.135 1.0000
Step1 - Step3 -0.003429 0.0349 289 -0.098 1.0000
Step1 - Step4 0.000581 0.0349 289 0.017 1.0000
Step1 - Step5 -0.009733 0.0349 289 -0.279 1.0000
Step1 - Step6 -0.007225 0.0349 289 -0.207 1.0000
Step1 - Step7 -0.029757 0.0349 289 -0.852 1.0000
Step1 - Step8 -0.008478 0.0349 289 -0.243 1.0000
Step1 - Step9 -0.001171 0.0349 289 -0.034 1.0000
Step1 - Step10 0.002458 0.0349 289 0.070 1.0000
Step1 - Step11 0.005889 0.0349 289 0.169 1.0000
Step1 - Step12 -0.002879 0.0349 289 -0.082 1.0000
Step1 - Step13 0.008429 0.0349 289 0.241 1.0000
Step1 - Step14 0.011739 0.0349 289 0.336 1.0000
Step1 - Step15 0.007507 0.0349 289 0.215 1.0000
Step1 - Step16 0.020483 0.0349 289 0.587 1.0000
Step1 - Step17 0.022165 0.0349 289 0.635 1.0000
Step1 - Step18 0.027616 0.0349 289 0.791 1.0000
Step2 - Step3 0.001282 0.0349 289 0.037 1.0000
Step2 - Step4 0.005292 0.0349 289 0.152 1.0000
Step2 - Step5 -0.005022 0.0349 289 -0.144 1.0000
Step2 - Step6 -0.002514 0.0349 289 -0.072 1.0000
Step2 - Step7 -0.025046 0.0349 289 -0.717 1.0000
Step2 - Step8 -0.003767 0.0349 289 -0.108 1.0000
Step2 - Step9 0.003540 0.0349 289 0.101 1.0000
Step2 - Step10 0.007169 0.0349 289 0.205 1.0000
Step2 - Step11 0.010600 0.0349 289 0.304 1.0000
Step2 - Step12 0.001832 0.0349 289 0.052 1.0000
Step2 - Step13 0.013140 0.0349 289 0.376 1.0000
Step2 - Step14 0.016450 0.0349 289 0.471 1.0000
Step2 - Step15 0.012218 0.0349 289 0.350 1.0000
Step2 - Step16 0.025194 0.0349 289 0.722 1.0000
Step2 - Step17 0.026876 0.0349 289 0.770 1.0000
Step2 - Step18 0.032327 0.0349 289 0.926 1.0000
Step3 - Step4 0.004010 0.0349 289 0.115 1.0000
Step3 - Step5 -0.006305 0.0349 289 -0.181 1.0000
Step3 - Step6 -0.003796 0.0349 289 -0.109 1.0000
Step3 - Step7 -0.026328 0.0349 289 -0.754 1.0000
Step3 - Step8 -0.005049 0.0349 289 -0.145 1.0000
Step3 - Step9 0.002258 0.0349 289 0.065 1.0000
Step3 - Step10 0.005886 0.0349 289 0.169 1.0000
Step3 - Step11 0.009318 0.0349 289 0.267 1.0000
Step3 - Step12 0.000550 0.0349 289 0.016 1.0000
Step3 - Step13 0.011857 0.0349 289 0.340 1.0000
Step3 - Step14 0.015168 0.0349 289 0.434 1.0000
Step3 - Step15 0.010935 0.0349 289 0.313 1.0000
Step3 - Step16 0.023911 0.0349 289 0.685 1.0000
Step3 - Step17 0.025594 0.0349 289 0.733 1.0000
Step3 - Step18 0.031045 0.0349 289 0.889 1.0000
Step4 - Step5 -0.010315 0.0349 289 -0.295 1.0000
Step4 - Step6 -0.007806 0.0349 289 -0.224 1.0000
Step4 - Step7 -0.030338 0.0349 289 -0.869 1.0000
Step4 - Step8 -0.009059 0.0349 289 -0.259 1.0000
Step4 - Step9 -0.001752 0.0349 289 -0.050 1.0000
Step4 - Step10 0.001876 0.0349 289 0.054 1.0000
Step4 - Step11 0.005308 0.0349 289 0.152 1.0000
Step4 - Step12 -0.003460 0.0349 289 -0.099 1.0000
Step4 - Step13 0.007847 0.0349 289 0.225 1.0000
Step4 - Step14 0.011158 0.0349 289 0.320 1.0000
Step4 - Step15 0.006925 0.0349 289 0.198 1.0000
Step4 - Step16 0.019901 0.0349 289 0.570 1.0000
Step4 - Step17 0.021584 0.0349 289 0.618 1.0000
Step4 - Step18 0.027035 0.0349 289 0.774 1.0000
Step5 - Step6 0.002508 0.0349 289 0.072 1.0000
Step5 - Step7 -0.020023 0.0349 289 -0.573 1.0000
Step5 - Step8 0.001256 0.0349 289 0.036 1.0000
Step5 - Step9 0.008562 0.0349 289 0.245 1.0000
Step5 - Step10 0.012191 0.0349 289 0.349 1.0000
Step5 - Step11 0.015622 0.0349 289 0.447 1.0000
Step5 - Step12 0.006854 0.0349 289 0.196 1.0000
Step5 - Step13 0.018162 0.0349 289 0.520 1.0000
Step5 - Step14 0.021472 0.0349 289 0.615 1.0000
Step5 - Step15 0.017240 0.0349 289 0.494 1.0000
Step5 - Step16 0.030216 0.0349 289 0.865 1.0000
Step5 - Step17 0.031899 0.0349 289 0.914 1.0000
Step5 - Step18 0.037349 0.0349 289 1.070 0.9998
Step6 - Step7 -0.022531 0.0349 289 -0.645 1.0000
Step6 - Step8 -0.001253 0.0349 289 -0.036 1.0000
Step6 - Step9 0.006054 0.0349 289 0.173 1.0000
Step6 - Step10 0.009683 0.0349 289 0.277 1.0000
Step6 - Step11 0.013114 0.0349 289 0.376 1.0000
Step6 - Step12 0.004346 0.0349 289 0.124 1.0000
Step6 - Step13 0.015654 0.0349 289 0.448 1.0000
Step6 - Step14 0.018964 0.0349 289 0.543 1.0000
Step6 - Step15 0.014732 0.0349 289 0.422 1.0000
Step6 - Step16 0.027708 0.0349 289 0.794 1.0000
Step6 - Step17 0.029391 0.0349 289 0.842 1.0000
Step6 - Step18 0.034841 0.0349 289 0.998 0.9999
Step7 - Step8 0.021279 0.0349 289 0.609 1.0000
Step7 - Step9 0.028585 0.0349 289 0.819 1.0000
Step7 - Step10 0.032214 0.0349 289 0.923 1.0000
Step7 - Step11 0.035645 0.0349 289 1.021 0.9999
Step7 - Step12 0.026877 0.0349 289 0.770 1.0000
Step7 - Step13 0.038185 0.0349 289 1.094 0.9998
Step7 - Step14 0.041496 0.0349 289 1.188 0.9994
Step7 - Step15 0.037263 0.0349 289 1.067 0.9998
Step7 - Step16 0.050239 0.0349 289 1.439 0.9937
Step7 - Step17 0.051922 0.0349 289 1.487 0.9910
Step7 - Step18 0.057372 0.0349 289 1.643 0.9749
Step8 - Step9 0.007307 0.0349 289 0.209 1.0000
Step8 - Step10 0.010935 0.0349 289 0.313 1.0000
Step8 - Step11 0.014367 0.0349 289 0.411 1.0000
Step8 - Step12 0.005599 0.0349 289 0.160 1.0000
Step8 - Step13 0.016906 0.0349 289 0.484 1.0000
Step8 - Step14 0.020217 0.0349 289 0.579 1.0000
Step8 - Step15 0.015984 0.0349 289 0.458 1.0000
Step8 - Step16 0.028961 0.0349 289 0.829 1.0000
Step8 - Step17 0.030643 0.0349 289 0.878 1.0000
Step8 - Step18 0.036094 0.0349 289 1.034 0.9999
Step9 - Step10 0.003629 0.0349 289 0.104 1.0000
Step9 - Step11 0.007060 0.0349 289 0.202 1.0000
Step9 - Step12 -0.001708 0.0349 289 -0.049 1.0000
Step9 - Step13 0.009600 0.0349 289 0.275 1.0000
Step9 - Step14 0.012910 0.0349 289 0.370 1.0000
Step9 - Step15 0.008678 0.0349 289 0.249 1.0000
Step9 - Step16 0.021654 0.0349 289 0.620 1.0000
Step9 - Step17 0.023337 0.0349 289 0.668 1.0000
Step9 - Step18 0.028787 0.0349 289 0.824 1.0000
Step10 - Step11 0.003431 0.0349 289 0.098 1.0000
Step10 - Step12 -0.005337 0.0349 289 -0.153 1.0000
Step10 - Step13 0.005971 0.0349 289 0.171 1.0000
Step10 - Step14 0.009282 0.0349 289 0.266 1.0000
Step10 - Step15 0.005049 0.0349 289 0.145 1.0000
Step10 - Step16 0.018025 0.0349 289 0.516 1.0000
Step10 - Step17 0.019708 0.0349 289 0.564 1.0000
Step10 - Step18 0.025158 0.0349 289 0.721 1.0000
Step11 - Step12 -0.008768 0.0349 289 -0.251 1.0000
Step11 - Step13 0.002540 0.0349 289 0.073 1.0000
Step11 - Step14 0.005850 0.0349 289 0.168 1.0000
Step11 - Step15 0.001618 0.0349 289 0.046 1.0000
Step11 - Step16 0.014594 0.0349 289 0.418 1.0000
Step11 - Step17 0.016276 0.0349 289 0.466 1.0000
Step11 - Step18 0.021727 0.0349 289 0.622 1.0000
Step12 - Step13 0.011308 0.0349 289 0.324 1.0000
Step12 - Step14 0.014618 0.0349 289 0.419 1.0000
Step12 - Step15 0.010386 0.0349 289 0.297 1.0000
Step12 - Step16 0.023362 0.0349 289 0.669 1.0000
Step12 - Step17 0.025045 0.0349 289 0.717 1.0000
Step12 - Step18 0.030495 0.0349 289 0.873 1.0000
Step13 - Step14 0.003310 0.0349 289 0.095 1.0000
Step13 - Step15 -0.000922 0.0349 289 -0.026 1.0000
Step13 - Step16 0.012054 0.0349 289 0.345 1.0000
Step13 - Step17 0.013737 0.0349 289 0.393 1.0000
Step13 - Step18 0.019187 0.0349 289 0.550 1.0000
Step14 - Step15 -0.004232 0.0349 289 -0.121 1.0000
Step14 - Step16 0.008744 0.0349 289 0.250 1.0000
Step14 - Step17 0.010426 0.0349 289 0.299 1.0000
Step14 - Step18 0.015877 0.0349 289 0.455 1.0000
Step15 - Step16 0.012976 0.0349 289 0.372 1.0000
Step15 - Step17 0.014659 0.0349 289 0.420 1.0000
Step15 - Step18 0.020109 0.0349 289 0.576 1.0000
Step16 - Step17 0.001683 0.0349 289 0.048 1.0000
Step16 - Step18 0.007133 0.0349 289 0.204 1.0000
Step17 - Step18 0.005450 0.0349 289 0.156 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
1.3175413701 0.0047110150 0.0034287776 -0.0005812146 0.0097333153
Step6 Step7 Step8 Step9 Step10
0.0072252295 0.0297565650 0.0084777989 0.0011712252 -0.0024575753
Step11 Step12 Step13 Step14 Step15
-0.0058889160 0.0028792565 -0.0084286014 -0.0117390951 -0.0075066189
Step16 Step17 Step18
-0.0204827125 -0.0221653387 -0.0276158268
Random Effects:
$subject
(Intercept)
2 0.13291393
3 0.48434932
4 -0.55370065
5 -0.62504671
7 0.26931118
8 0.16547275
10 1.84656947
11 0.32818874
13 -0.27907137
14 0.10368586
15 -0.19161125
16 0.06298122
17 -0.35856743
18 0.31999253
19 -0.59917057
20 -0.56464026
22 -0.56576503
23 0.02410827
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.29342298 0.98103947 0.39299442 0.22379449 -0.01686636 -0.45801462
=============================================================
--- Mixed - SD - Block 4 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.2558 0.015047 17 289 2.7456 0.0003019 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.004082 0.0247 289 0.165 1.0000
Step1 - Step3 -0.010434 0.0247 289 -0.423 1.0000
Step1 - Step4 -0.003139 0.0247 289 -0.127 1.0000
Step1 - Step5 0.002250 0.0247 289 0.091 1.0000
Step1 - Step6 -0.006750 0.0247 289 -0.274 1.0000
Step1 - Step7 -0.006006 0.0247 289 -0.243 1.0000
Step1 - Step8 -0.002087 0.0247 289 -0.085 1.0000
Step1 - Step9 0.014821 0.0247 289 0.601 1.0000
Step1 - Step10 0.019053 0.0247 289 0.772 1.0000
Step1 - Step11 0.015871 0.0247 289 0.643 1.0000
Step1 - Step12 0.041450 0.0247 289 1.680 0.9690
Step1 - Step13 0.059539 0.0247 289 2.413 0.5988
Step1 - Step14 0.049240 0.0247 289 1.995 0.8692
Step1 - Step15 0.043660 0.0247 289 1.769 0.9502
Step1 - Step16 0.072092 0.0247 289 2.921 0.2475
Step1 - Step17 0.069764 0.0247 289 2.827 0.3021
Step1 - Step18 0.057912 0.0247 289 2.347 0.6484
Step2 - Step3 -0.014515 0.0247 289 -0.588 1.0000
Step2 - Step4 -0.007221 0.0247 289 -0.293 1.0000
Step2 - Step5 -0.001832 0.0247 289 -0.074 1.0000
Step2 - Step6 -0.010832 0.0247 289 -0.439 1.0000
Step2 - Step7 -0.010088 0.0247 289 -0.409 1.0000
Step2 - Step8 -0.006169 0.0247 289 -0.250 1.0000
Step2 - Step9 0.010739 0.0247 289 0.435 1.0000
Step2 - Step10 0.014971 0.0247 289 0.607 1.0000
Step2 - Step11 0.011789 0.0247 289 0.478 1.0000
Step2 - Step12 0.037368 0.0247 289 1.514 0.9890
Step2 - Step13 0.055457 0.0247 289 2.247 0.7200
Step2 - Step14 0.045158 0.0247 289 1.830 0.9335
Step2 - Step15 0.039578 0.0247 289 1.604 0.9802
Step2 - Step16 0.068010 0.0247 289 2.756 0.3473
Step2 - Step17 0.065682 0.0247 289 2.662 0.4123
Step2 - Step18 0.053830 0.0247 289 2.181 0.7643
Step3 - Step4 0.007294 0.0247 289 0.296 1.0000
Step3 - Step5 0.012683 0.0247 289 0.514 1.0000
Step3 - Step6 0.003684 0.0247 289 0.149 1.0000
Step3 - Step7 0.004428 0.0247 289 0.179 1.0000
Step3 - Step8 0.008346 0.0247 289 0.338 1.0000
Step3 - Step9 0.025255 0.0247 289 1.023 0.9999
Step3 - Step10 0.029486 0.0247 289 1.195 0.9993
Step3 - Step11 0.026305 0.0247 289 1.066 0.9998
Step3 - Step12 0.051883 0.0247 289 2.103 0.8127
Step3 - Step13 0.069973 0.0247 289 2.836 0.2969
Step3 - Step14 0.059673 0.0247 289 2.418 0.5947
Step3 - Step15 0.054094 0.0247 289 2.192 0.7573
Step3 - Step16 0.082526 0.0247 289 3.344 0.0847
Step3 - Step17 0.080197 0.0247 289 3.250 0.1102
Step3 - Step18 0.068345 0.0247 289 2.770 0.3384
Step4 - Step5 0.005389 0.0247 289 0.218 1.0000
Step4 - Step6 -0.003611 0.0247 289 -0.146 1.0000
Step4 - Step7 -0.002867 0.0247 289 -0.116 1.0000
Step4 - Step8 0.001052 0.0247 289 0.043 1.0000
Step4 - Step9 0.017960 0.0247 289 0.728 1.0000
Step4 - Step10 0.022192 0.0247 289 0.899 1.0000
Step4 - Step11 0.019010 0.0247 289 0.770 1.0000
Step4 - Step12 0.044589 0.0247 289 1.807 0.9402
Step4 - Step13 0.062678 0.0247 289 2.540 0.5020
Step4 - Step14 0.052379 0.0247 289 2.123 0.8009
Step4 - Step15 0.046799 0.0247 289 1.896 0.9110
Step4 - Step16 0.075231 0.0247 289 3.049 0.1847
Step4 - Step17 0.072903 0.0247 289 2.954 0.2301
Step4 - Step18 0.061051 0.0247 289 2.474 0.5522
Step5 - Step6 -0.009000 0.0247 289 -0.365 1.0000
Step5 - Step7 -0.008255 0.0247 289 -0.335 1.0000
Step5 - Step8 -0.004337 0.0247 289 -0.176 1.0000
Step5 - Step9 0.012572 0.0247 289 0.509 1.0000
Step5 - Step10 0.016803 0.0247 289 0.681 1.0000
Step5 - Step11 0.013622 0.0247 289 0.552 1.0000
Step5 - Step12 0.039200 0.0247 289 1.589 0.9820
Step5 - Step13 0.057290 0.0247 289 2.322 0.6670
Step5 - Step14 0.046990 0.0247 289 1.904 0.9081
Step5 - Step15 0.041411 0.0247 289 1.678 0.9693
Step5 - Step16 0.069843 0.0247 289 2.830 0.3001
Step5 - Step17 0.067514 0.0247 289 2.736 0.3607
Step5 - Step18 0.055662 0.0247 289 2.256 0.7142
Step6 - Step7 0.000744 0.0247 289 0.030 1.0000
Step6 - Step8 0.004663 0.0247 289 0.189 1.0000
Step6 - Step9 0.021571 0.0247 289 0.874 1.0000
Step6 - Step10 0.025803 0.0247 289 1.046 0.9999
Step6 - Step11 0.022621 0.0247 289 0.917 1.0000
Step6 - Step12 0.048200 0.0247 289 1.953 0.8883
Step6 - Step13 0.066289 0.0247 289 2.686 0.3949
Step6 - Step14 0.055990 0.0247 289 2.269 0.7049
Step6 - Step15 0.050410 0.0247 289 2.043 0.8456
Step6 - Step16 0.078842 0.0247 289 3.195 0.1277
Step6 - Step17 0.076514 0.0247 289 3.101 0.1627
Step6 - Step18 0.064662 0.0247 289 2.620 0.4422
Step7 - Step8 0.003918 0.0247 289 0.159 1.0000
Step7 - Step9 0.020827 0.0247 289 0.844 1.0000
Step7 - Step10 0.025059 0.0247 289 1.015 0.9999
Step7 - Step11 0.021877 0.0247 289 0.887 1.0000
Step7 - Step12 0.047455 0.0247 289 1.923 0.9008
Step7 - Step13 0.065545 0.0247 289 2.656 0.4162
Step7 - Step14 0.055245 0.0247 289 2.239 0.7259
Step7 - Step15 0.049666 0.0247 289 2.013 0.8609
Step7 - Step16 0.078098 0.0247 289 3.165 0.1382
Step7 - Step17 0.075770 0.0247 289 3.070 0.1752
Step7 - Step18 0.063917 0.0247 289 2.590 0.4644
Step8 - Step9 0.016908 0.0247 289 0.685 1.0000
Step8 - Step10 0.021140 0.0247 289 0.857 1.0000
Step8 - Step11 0.017959 0.0247 289 0.728 1.0000
Step8 - Step12 0.043537 0.0247 289 1.764 0.9514
Step8 - Step13 0.061627 0.0247 289 2.497 0.5344
Step8 - Step14 0.051327 0.0247 289 2.080 0.8255
Step8 - Step15 0.045748 0.0247 289 1.854 0.9259
Step8 - Step16 0.074180 0.0247 289 3.006 0.2044
Step8 - Step17 0.071851 0.0247 289 2.912 0.2528
Step8 - Step18 0.059999 0.0247 289 2.431 0.5847
Step9 - Step10 0.004232 0.0247 289 0.171 1.0000
Step9 - Step11 0.001050 0.0247 289 0.043 1.0000
Step9 - Step12 0.026629 0.0247 289 1.079 0.9998
Step9 - Step13 0.044718 0.0247 289 1.812 0.9387
Step9 - Step14 0.034419 0.0247 289 1.395 0.9956
Step9 - Step15 0.028839 0.0247 289 1.169 0.9995
Step9 - Step16 0.057271 0.0247 289 2.321 0.6675
Step9 - Step17 0.054943 0.0247 289 2.226 0.7343
Step9 - Step18 0.043091 0.0247 289 1.746 0.9557
Step10 - Step11 -0.003181 0.0247 289 -0.129 1.0000
Step10 - Step12 0.022397 0.0247 289 0.908 1.0000
Step10 - Step13 0.040487 0.0247 289 1.641 0.9753
Step10 - Step14 0.030187 0.0247 289 1.223 0.9991
Step10 - Step15 0.024607 0.0247 289 0.997 0.9999
Step10 - Step16 0.053039 0.0247 289 2.149 0.7846
Step10 - Step17 0.050711 0.0247 289 2.055 0.8392
Step10 - Step18 0.038859 0.0247 289 1.575 0.9836
Step11 - Step12 0.025578 0.0247 289 1.037 0.9999
Step11 - Step13 0.043668 0.0247 289 1.770 0.9501
Step11 - Step14 0.033368 0.0247 289 1.352 0.9969
Step11 - Step15 0.027789 0.0247 289 1.126 0.9997
Step11 - Step16 0.056221 0.0247 289 2.278 0.6983
Step11 - Step17 0.053893 0.0247 289 2.184 0.7626
Step11 - Step18 0.042040 0.0247 289 1.704 0.9646
Step12 - Step13 0.018090 0.0247 289 0.733 1.0000
Step12 - Step14 0.007790 0.0247 289 0.316 1.0000
Step12 - Step15 0.002211 0.0247 289 0.090 1.0000
Step12 - Step16 0.030643 0.0247 289 1.242 0.9989
Step12 - Step17 0.028314 0.0247 289 1.147 0.9996
Step12 - Step18 0.016462 0.0247 289 0.667 1.0000
Step13 - Step14 -0.010300 0.0247 289 -0.417 1.0000
Step13 - Step15 -0.015879 0.0247 289 -0.643 1.0000
Step13 - Step16 0.012553 0.0247 289 0.509 1.0000
Step13 - Step17 0.010225 0.0247 289 0.414 1.0000
Step13 - Step18 -0.001628 0.0247 289 -0.066 1.0000
Step14 - Step15 -0.005579 0.0247 289 -0.226 1.0000
Step14 - Step16 0.022853 0.0247 289 0.926 1.0000
Step14 - Step17 0.020524 0.0247 289 0.832 1.0000
Step14 - Step18 0.008672 0.0247 289 0.351 1.0000
Step15 - Step16 0.028432 0.0247 289 1.152 0.9996
Step15 - Step17 0.026104 0.0247 289 1.058 0.9999
Step15 - Step18 0.014251 0.0247 289 0.578 1.0000
Step16 - Step17 -0.002328 0.0247 289 -0.094 1.0000
Step16 - Step18 -0.014181 0.0247 289 -0.575 1.0000
Step17 - Step18 -0.011852 0.0247 289 -0.480 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.760251575 -0.004081952 0.010433537 0.003139048 -0.002249502 0.006750027
Step7 Step8 Step9 Step10 Step11 Step12
0.006005804 0.002087329 -0.014821024 -0.019052724 -0.015871234 -0.041449618
Step13 Step14 Step15 Step16 Step17 Step18
-0.059539334 -0.049239621 -0.043660179 -0.072092211 -0.069763954 -0.057911575
Random Effects:
$subject
(Intercept)
2 0.133493523
3 -0.089255505
4 -0.292488130
5 -0.412203426
7 -0.092821268
8 0.394583850
10 1.115495062
11 0.436833169
13 -0.196860275
14 -0.019002968
15 -0.209721780
16 0.146724719
17 -0.138276478
18 -0.009218011
19 -0.265866345
20 -0.246121905
22 -0.216634483
23 -0.038659749
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.1221600 -0.3364183 0.2445792 -0.1955896 -0.3375715 -0.1649986
=============================================================
--- Mixed - SD - Block 4 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.91232 0.053666 17 289 5.283 3.563e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -0.010572 0.0336 289 -0.315 1.0000
Step1 - Step3 0.017260 0.0336 289 0.514 1.0000
Step1 - Step4 0.018979 0.0336 289 0.565 1.0000
Step1 - Step5 0.018681 0.0336 289 0.556 1.0000
Step1 - Step6 0.045146 0.0336 289 1.344 0.9971
Step1 - Step7 0.024826 0.0336 289 0.739 1.0000
Step1 - Step8 0.060440 0.0336 289 1.799 0.9424
Step1 - Step9 0.062160 0.0336 289 1.850 0.9271
Step1 - Step10 0.074862 0.0336 289 2.228 0.7331
Step1 - Step11 0.086740 0.0336 289 2.582 0.4706
Step1 - Step12 0.107573 0.0336 289 3.202 0.1254
Step1 - Step13 0.144386 0.0336 289 4.298 0.0031
Step1 - Step14 0.122415 0.0336 289 3.644 0.0338
Step1 - Step15 0.111555 0.0336 289 3.321 0.0906
Step1 - Step16 0.154417 0.0336 289 4.596 0.0009
Step1 - Step17 0.144269 0.0336 289 4.294 0.0031
Step1 - Step18 0.135487 0.0336 289 4.033 0.0086
Step2 - Step3 0.027833 0.0336 289 0.828 1.0000
Step2 - Step4 0.029551 0.0336 289 0.880 1.0000
Step2 - Step5 0.029254 0.0336 289 0.871 1.0000
Step2 - Step6 0.055718 0.0336 289 1.658 0.9725
Step2 - Step7 0.035398 0.0336 289 1.054 0.9999
Step2 - Step8 0.071012 0.0336 289 2.114 0.8062
Step2 - Step9 0.072732 0.0336 289 2.165 0.7748
Step2 - Step10 0.085434 0.0336 289 2.543 0.4997
Step2 - Step11 0.097312 0.0336 289 2.897 0.2613
Step2 - Step12 0.118146 0.0336 289 3.517 0.0506
Step2 - Step13 0.154958 0.0336 289 4.612 0.0008
Step2 - Step14 0.132987 0.0336 289 3.958 0.0113
Step2 - Step15 0.122127 0.0336 289 3.635 0.0347
Step2 - Step16 0.164989 0.0336 289 4.911 0.0002
Step2 - Step17 0.154842 0.0336 289 4.609 0.0008
Step2 - Step18 0.146060 0.0336 289 4.348 0.0025
Step3 - Step4 0.001719 0.0336 289 0.051 1.0000
Step3 - Step5 0.001421 0.0336 289 0.042 1.0000
Step3 - Step6 0.027886 0.0336 289 0.830 1.0000
Step3 - Step7 0.007566 0.0336 289 0.225 1.0000
Step3 - Step8 0.043179 0.0336 289 1.285 0.9983
Step3 - Step9 0.044899 0.0336 289 1.336 0.9973
Step3 - Step10 0.057601 0.0336 289 1.715 0.9625
Step3 - Step11 0.069479 0.0336 289 2.068 0.8321
Step3 - Step12 0.090313 0.0336 289 2.688 0.3935
Step3 - Step13 0.127125 0.0336 289 3.784 0.0211
Step3 - Step14 0.105154 0.0336 289 3.130 0.1511
Step3 - Step15 0.094295 0.0336 289 2.807 0.3147
Step3 - Step16 0.137157 0.0336 289 4.083 0.0071
Step3 - Step17 0.127009 0.0336 289 3.780 0.0213
Step3 - Step18 0.118227 0.0336 289 3.519 0.0503
Step4 - Step5 -0.000298 0.0336 289 -0.009 1.0000
Step4 - Step6 0.026167 0.0336 289 0.779 1.0000
Step4 - Step7 0.005847 0.0336 289 0.174 1.0000
Step4 - Step8 0.041461 0.0336 289 1.234 0.9990
Step4 - Step9 0.043181 0.0336 289 1.285 0.9983
Step4 - Step10 0.055883 0.0336 289 1.663 0.9718
Step4 - Step11 0.067761 0.0336 289 2.017 0.8588
Step4 - Step12 0.088594 0.0336 289 2.637 0.4300
Step4 - Step13 0.125407 0.0336 289 3.733 0.0251
Step4 - Step14 0.103436 0.0336 289 3.079 0.1717
Step4 - Step15 0.092576 0.0336 289 2.756 0.3476
Step4 - Step16 0.135438 0.0336 289 4.031 0.0087
Step4 - Step17 0.125290 0.0336 289 3.729 0.0254
Step4 - Step18 0.116508 0.0336 289 3.468 0.0588
Step5 - Step6 0.026465 0.0336 289 0.788 1.0000
Step5 - Step7 0.006145 0.0336 289 0.183 1.0000
Step5 - Step8 0.041758 0.0336 289 1.243 0.9989
Step5 - Step9 0.043479 0.0336 289 1.294 0.9982
Step5 - Step10 0.056180 0.0336 289 1.672 0.9703
Step5 - Step11 0.068058 0.0336 289 2.026 0.8544
Step5 - Step12 0.088892 0.0336 289 2.646 0.4236
Step5 - Step13 0.125704 0.0336 289 3.742 0.0244
Step5 - Step14 0.103734 0.0336 289 3.088 0.1680
Step5 - Step15 0.092874 0.0336 289 2.764 0.3418
Step5 - Step16 0.135736 0.0336 289 4.040 0.0084
Step5 - Step17 0.125588 0.0336 289 3.738 0.0247
Step5 - Step18 0.116806 0.0336 289 3.477 0.0573
Step6 - Step7 -0.020320 0.0336 289 -0.605 1.0000
Step6 - Step8 0.015294 0.0336 289 0.455 1.0000
Step6 - Step9 0.017014 0.0336 289 0.506 1.0000
Step6 - Step10 0.029716 0.0336 289 0.885 1.0000
Step6 - Step11 0.041594 0.0336 289 1.238 0.9989
Step6 - Step12 0.062427 0.0336 289 1.858 0.9245
Step6 - Step13 0.099240 0.0336 289 2.954 0.2303
Step6 - Step14 0.077269 0.0336 289 2.300 0.6827
Step6 - Step15 0.066409 0.0336 289 1.977 0.8779
Step6 - Step16 0.109271 0.0336 289 3.253 0.1095
Step6 - Step17 0.099123 0.0336 289 2.950 0.2321
Step6 - Step18 0.090341 0.0336 289 2.689 0.3929
Step7 - Step8 0.035613 0.0336 289 1.060 0.9999
Step7 - Step9 0.037334 0.0336 289 1.111 0.9997
Step7 - Step10 0.050035 0.0336 289 1.489 0.9908
Step7 - Step11 0.061913 0.0336 289 1.843 0.9295
Step7 - Step12 0.082747 0.0336 289 2.463 0.5605
Step7 - Step13 0.119559 0.0336 289 3.559 0.0444
Step7 - Step14 0.097589 0.0336 289 2.905 0.2567
Step7 - Step15 0.086729 0.0336 289 2.582 0.4708
Step7 - Step16 0.129591 0.0336 289 3.857 0.0163
Step7 - Step17 0.119443 0.0336 289 3.555 0.0449
Step7 - Step18 0.110661 0.0336 289 3.294 0.0977
Step8 - Step9 0.001720 0.0336 289 0.051 1.0000
Step8 - Step10 0.014422 0.0336 289 0.429 1.0000
Step8 - Step11 0.026300 0.0336 289 0.783 1.0000
Step8 - Step12 0.047134 0.0336 289 1.403 0.9953
Step8 - Step13 0.083946 0.0336 289 2.499 0.5333
Step8 - Step14 0.061975 0.0336 289 1.845 0.9289
Step8 - Step15 0.051116 0.0336 289 1.521 0.9885
Step8 - Step16 0.093977 0.0336 289 2.797 0.3206
Step8 - Step17 0.083830 0.0336 289 2.495 0.5360
Step8 - Step18 0.075048 0.0336 289 2.234 0.7293
Step9 - Step10 0.012702 0.0336 289 0.378 1.0000
Step9 - Step11 0.024580 0.0336 289 0.732 1.0000
Step9 - Step12 0.045413 0.0336 289 1.352 0.9969
Step9 - Step13 0.082226 0.0336 289 2.447 0.5724
Step9 - Step14 0.060255 0.0336 289 1.794 0.9439
Step9 - Step15 0.049395 0.0336 289 1.470 0.9920
Step9 - Step16 0.092257 0.0336 289 2.746 0.3539
Step9 - Step17 0.082110 0.0336 289 2.444 0.5750
Step9 - Step18 0.073328 0.0336 289 2.183 0.7635
Step10 - Step11 0.011878 0.0336 289 0.354 1.0000
Step10 - Step12 0.032712 0.0336 289 0.974 1.0000
Step10 - Step13 0.069524 0.0336 289 2.069 0.8314
Step10 - Step14 0.047553 0.0336 289 1.415 0.9948
Step10 - Step15 0.036694 0.0336 289 1.092 0.9998
Step10 - Step16 0.079555 0.0336 289 2.368 0.6326
Step10 - Step17 0.069408 0.0336 289 2.066 0.8333
Step10 - Step18 0.060626 0.0336 289 1.805 0.9409
Step11 - Step12 0.020834 0.0336 289 0.620 1.0000
Step11 - Step13 0.057646 0.0336 289 1.716 0.9622
Step11 - Step14 0.035675 0.0336 289 1.062 0.9999
Step11 - Step15 0.024816 0.0336 289 0.739 1.0000
Step11 - Step16 0.067677 0.0336 289 2.014 0.8600
Step11 - Step17 0.057530 0.0336 289 1.712 0.9629
Step11 - Step18 0.048748 0.0336 289 1.451 0.9931
Step12 - Step13 0.036812 0.0336 289 1.096 0.9998
Step12 - Step14 0.014841 0.0336 289 0.442 1.0000
Step12 - Step15 0.003982 0.0336 289 0.119 1.0000
Step12 - Step16 0.046844 0.0336 289 1.394 0.9956
Step12 - Step17 0.036696 0.0336 289 1.092 0.9998
Step12 - Step18 0.027914 0.0336 289 0.831 1.0000
Step13 - Step14 -0.021971 0.0336 289 -0.654 1.0000
Step13 - Step15 -0.032830 0.0336 289 -0.977 1.0000
Step13 - Step16 0.010031 0.0336 289 0.299 1.0000
Step13 - Step17 -0.000116 0.0336 289 -0.003 1.0000
Step13 - Step18 -0.008898 0.0336 289 -0.265 1.0000
Step14 - Step15 -0.010860 0.0336 289 -0.323 1.0000
Step14 - Step16 0.032002 0.0336 289 0.953 1.0000
Step14 - Step17 0.021855 0.0336 289 0.651 1.0000
Step14 - Step18 0.013073 0.0336 289 0.389 1.0000
Step15 - Step16 0.042862 0.0336 289 1.276 0.9985
Step15 - Step17 0.032714 0.0336 289 0.974 1.0000
Step15 - Step18 0.023932 0.0336 289 0.712 1.0000
Step16 - Step17 -0.010148 0.0336 289 -0.302 1.0000
Step16 - Step18 -0.018930 0.0336 289 -0.563 1.0000
Step17 - Step18 -0.008782 0.0336 289 -0.261 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
0.84729822 0.01057221 -0.01726047 -0.01897903 -0.01868129 -0.04514604
Step7 Step8 Step9 Step10 Step11 Step12
-0.02482628 -0.06043960 -0.06215989 -0.07486165 -0.08673962 -0.10757336
Step13 Step14 Step15 Step16 Step17 Step18
-0.14438567 -0.12241483 -0.11155518 -0.15441707 -0.14426947 -0.13548749
Random Effects:
$subject
(Intercept)
2 0.23686269
3 0.14056269
4 -0.25091267
5 -0.35722401
7 -0.26037530
8 0.47784901
10 1.01008640
11 0.45755492
13 -0.25056942
14 -0.06607123
15 -0.20351636
16 0.04212556
17 -0.11054393
18 -0.01857692
19 -0.36030068
20 -0.24815343
22 -0.32189577
23 0.08309845
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
-2.1070941 -0.9853128 -0.9498442 -1.6010645 -0.7385196 -0.6184307
=============================================================
--- Mixed - SD - Block 4 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 1.7068 0.1004 17 289 4.7411 6.822e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.007507 0.0485 289 0.155 1.0000
Step1 - Step3 0.011289 0.0485 289 0.233 1.0000
Step1 - Step4 0.023877 0.0485 289 0.492 1.0000
Step1 - Step5 0.035562 0.0485 289 0.733 1.0000
Step1 - Step6 0.021569 0.0485 289 0.445 1.0000
Step1 - Step7 0.029218 0.0485 289 0.602 1.0000
Step1 - Step8 0.027924 0.0485 289 0.576 1.0000
Step1 - Step9 0.053863 0.0485 289 1.110 0.9997
Step1 - Step10 0.077944 0.0485 289 1.607 0.9798
Step1 - Step11 0.066793 0.0485 289 1.377 0.9962
Step1 - Step12 0.135987 0.0485 289 2.803 0.3168
Step1 - Step13 0.183665 0.0485 289 3.786 0.0209
Step1 - Step14 0.166552 0.0485 289 3.434 0.0652
Step1 - Step15 0.135800 0.0485 289 2.800 0.3192
Step1 - Step16 0.201231 0.0485 289 4.148 0.0055
Step1 - Step17 0.215160 0.0485 289 4.436 0.0017
Step1 - Step18 0.164141 0.0485 289 3.384 0.0756
Step2 - Step3 0.003783 0.0485 289 0.078 1.0000
Step2 - Step4 0.016370 0.0485 289 0.337 1.0000
Step2 - Step5 0.028055 0.0485 289 0.578 1.0000
Step2 - Step6 0.014062 0.0485 289 0.290 1.0000
Step2 - Step7 0.021712 0.0485 289 0.448 1.0000
Step2 - Step8 0.020417 0.0485 289 0.421 1.0000
Step2 - Step9 0.046356 0.0485 289 0.956 1.0000
Step2 - Step10 0.070437 0.0485 289 1.452 0.9930
Step2 - Step11 0.059286 0.0485 289 1.222 0.9991
Step2 - Step12 0.128480 0.0485 289 2.649 0.4216
Step2 - Step13 0.176159 0.0485 289 3.632 0.0351
Step2 - Step14 0.159046 0.0485 289 3.279 0.1019
Step2 - Step15 0.128294 0.0485 289 2.645 0.4244
Step2 - Step16 0.193725 0.0485 289 3.994 0.0100
Step2 - Step17 0.207653 0.0485 289 4.281 0.0033
Step2 - Step18 0.156634 0.0485 289 3.229 0.1166
Step3 - Step4 0.012588 0.0485 289 0.260 1.0000
Step3 - Step5 0.024272 0.0485 289 0.500 1.0000
Step3 - Step6 0.010280 0.0485 289 0.212 1.0000
Step3 - Step7 0.017929 0.0485 289 0.370 1.0000
Step3 - Step8 0.016635 0.0485 289 0.343 1.0000
Step3 - Step9 0.042573 0.0485 289 0.878 1.0000
Step3 - Step10 0.066654 0.0485 289 1.374 0.9963
Step3 - Step11 0.055503 0.0485 289 1.144 0.9996
Step3 - Step12 0.124698 0.0485 289 2.571 0.4789
Step3 - Step13 0.172376 0.0485 289 3.554 0.0451
Step3 - Step14 0.155263 0.0485 289 3.201 0.1258
Step3 - Step15 0.124511 0.0485 289 2.567 0.4818
Step3 - Step16 0.189942 0.0485 289 3.916 0.0132
Step3 - Step17 0.203870 0.0485 289 4.203 0.0045
Step3 - Step18 0.152851 0.0485 289 3.151 0.1432
Step4 - Step5 0.011684 0.0485 289 0.241 1.0000
Step4 - Step6 -0.002308 0.0485 289 -0.048 1.0000
Step4 - Step7 0.005341 0.0485 289 0.110 1.0000
Step4 - Step8 0.004047 0.0485 289 0.083 1.0000
Step4 - Step9 0.029986 0.0485 289 0.618 1.0000
Step4 - Step10 0.054066 0.0485 289 1.115 0.9997
Step4 - Step11 0.042916 0.0485 289 0.885 1.0000
Step4 - Step12 0.112110 0.0485 289 2.311 0.6746
Step4 - Step13 0.159788 0.0485 289 3.294 0.0976
Step4 - Step14 0.142675 0.0485 289 2.941 0.2369
Step4 - Step15 0.111923 0.0485 289 2.307 0.6774
Step4 - Step16 0.177354 0.0485 289 3.656 0.0324
Step4 - Step17 0.191283 0.0485 289 3.943 0.0120
Step4 - Step18 0.140264 0.0485 289 2.892 0.2641
Step5 - Step6 -0.013992 0.0485 289 -0.288 1.0000
Step5 - Step7 -0.006343 0.0485 289 -0.131 1.0000
Step5 - Step8 -0.007638 0.0485 289 -0.157 1.0000
Step5 - Step9 0.018301 0.0485 289 0.377 1.0000
Step5 - Step10 0.042382 0.0485 289 0.874 1.0000
Step5 - Step11 0.031231 0.0485 289 0.644 1.0000
Step5 - Step12 0.100425 0.0485 289 2.070 0.8309
Step5 - Step13 0.148104 0.0485 289 3.053 0.1827
Step5 - Step14 0.130991 0.0485 289 2.700 0.3850
Step5 - Step15 0.100239 0.0485 289 2.066 0.8330
Step5 - Step16 0.165670 0.0485 289 3.415 0.0689
Step5 - Step17 0.179598 0.0485 289 3.702 0.0278
Step5 - Step18 0.128579 0.0485 289 2.651 0.4201
Step6 - Step7 0.007649 0.0485 289 0.158 1.0000
Step6 - Step8 0.006355 0.0485 289 0.131 1.0000
Step6 - Step9 0.032294 0.0485 289 0.666 1.0000
Step6 - Step10 0.056375 0.0485 289 1.162 0.9995
Step6 - Step11 0.045224 0.0485 289 0.932 1.0000
Step6 - Step12 0.114418 0.0485 289 2.359 0.6395
Step6 - Step13 0.162096 0.0485 289 3.342 0.0853
Step6 - Step14 0.144983 0.0485 289 2.989 0.2127
Step6 - Step15 0.114231 0.0485 289 2.355 0.6423
Step6 - Step16 0.179662 0.0485 289 3.704 0.0277
Step6 - Step17 0.193591 0.0485 289 3.991 0.0101
Step6 - Step18 0.142572 0.0485 289 2.939 0.2380
Step7 - Step8 -0.001295 0.0485 289 -0.027 1.0000
Step7 - Step9 0.024644 0.0485 289 0.508 1.0000
Step7 - Step10 0.048725 0.0485 289 1.004 0.9999
Step7 - Step11 0.037574 0.0485 289 0.775 1.0000
Step7 - Step12 0.106768 0.0485 289 2.201 0.7514
Step7 - Step13 0.154447 0.0485 289 3.184 0.1315
Step7 - Step14 0.137334 0.0485 289 2.831 0.2996
Step7 - Step15 0.106582 0.0485 289 2.197 0.7539
Step7 - Step16 0.172013 0.0485 289 3.546 0.0462
Step7 - Step17 0.185941 0.0485 289 3.833 0.0178
Step7 - Step18 0.134922 0.0485 289 2.781 0.3307
Step8 - Step9 0.025939 0.0485 289 0.535 1.0000
Step8 - Step10 0.050020 0.0485 289 1.031 0.9999
Step8 - Step11 0.038869 0.0485 289 0.801 1.0000
Step8 - Step12 0.108063 0.0485 289 2.228 0.7335
Step8 - Step13 0.155742 0.0485 289 3.211 0.1225
Step8 - Step14 0.138628 0.0485 289 2.858 0.2835
Step8 - Step15 0.107876 0.0485 289 2.224 0.7361
Step8 - Step16 0.173307 0.0485 289 3.573 0.0425
Step8 - Step17 0.187236 0.0485 289 3.860 0.0162
Step8 - Step18 0.136217 0.0485 289 2.808 0.3138
Step9 - Step10 0.024081 0.0485 289 0.496 1.0000
Step9 - Step11 0.012930 0.0485 289 0.267 1.0000
Step9 - Step12 0.082124 0.0485 289 1.693 0.9666
Step9 - Step13 0.129803 0.0485 289 2.676 0.4022
Step9 - Step14 0.112689 0.0485 289 2.323 0.6658
Step9 - Step15 0.081937 0.0485 289 1.689 0.9673
Step9 - Step16 0.147369 0.0485 289 3.038 0.1895
Step9 - Step17 0.161297 0.0485 289 3.325 0.0894
Step9 - Step18 0.110278 0.0485 289 2.273 0.7017
Step10 - Step11 -0.011151 0.0485 289 -0.230 1.0000
Step10 - Step12 0.058043 0.0485 289 1.197 0.9993
Step10 - Step13 0.105722 0.0485 289 2.179 0.7655
Step10 - Step14 0.088609 0.0485 289 1.827 0.9345
Step10 - Step15 0.057857 0.0485 289 1.193 0.9993
Step10 - Step16 0.123288 0.0485 289 2.542 0.5008
Step10 - Step17 0.137216 0.0485 289 2.829 0.3010
Step10 - Step18 0.086197 0.0485 289 1.777 0.9483
Step11 - Step12 0.069194 0.0485 289 1.426 0.9943
Step11 - Step13 0.116873 0.0485 289 2.409 0.6014
Step11 - Step14 0.099760 0.0485 289 2.057 0.8383
Step11 - Step15 0.069008 0.0485 289 1.423 0.9945
Step11 - Step16 0.134439 0.0485 289 2.772 0.3372
Step11 - Step17 0.148367 0.0485 289 3.059 0.1803
Step11 - Step18 0.097348 0.0485 289 2.007 0.8637
Step12 - Step13 0.047678 0.0485 289 0.983 1.0000
Step12 - Step14 0.030565 0.0485 289 0.630 1.0000
Step12 - Step15 -0.000187 0.0485 289 -0.004 1.0000
Step12 - Step16 0.065244 0.0485 289 1.345 0.9971
Step12 - Step17 0.079173 0.0485 289 1.632 0.9765
Step12 - Step18 0.028154 0.0485 289 0.580 1.0000
Step13 - Step14 -0.017113 0.0485 289 -0.353 1.0000
Step13 - Step15 -0.047865 0.0485 289 -0.987 0.9999
Step13 - Step16 0.017566 0.0485 289 0.362 1.0000
Step13 - Step17 0.031494 0.0485 289 0.649 1.0000
Step13 - Step18 -0.019525 0.0485 289 -0.403 1.0000
Step14 - Step15 -0.030752 0.0485 289 -0.634 1.0000
Step14 - Step16 0.034679 0.0485 289 0.715 1.0000
Step14 - Step17 0.048608 0.0485 289 1.002 0.9999
Step14 - Step18 -0.002411 0.0485 289 -0.050 1.0000
Step15 - Step16 0.065431 0.0485 289 1.349 0.9970
Step15 - Step17 0.079360 0.0485 289 1.636 0.9759
Step15 - Step18 0.028340 0.0485 289 0.584 1.0000
Step16 - Step17 0.013928 0.0485 289 0.287 1.0000
Step16 - Step18 -0.037091 0.0485 289 -0.765 1.0000
Step17 - Step18 -0.051019 0.0485 289 -1.052 0.9999
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.546187223 -0.007506652 -0.011289454 -0.023877137 -0.035561495 -0.021569017
Step7 Step8 Step9 Step10 Step11 Step12
-0.029218490 -0.027923969 -0.053862753 -0.077943517 -0.066792657 -0.135986973
Step13 Step14 Step15 Step16 Step17 Step18
-0.183665476 -0.166552178 -0.135800239 -0.201231423 -0.215159900 -0.164140685
Random Effects:
$subject
(Intercept)
2 -0.20444388
3 0.16793208
4 -0.52273921
5 -0.76710749
7 0.19331618
8 0.93172801
10 1.83374291
11 0.75301851
13 -0.33530390
14 -0.01222930
15 -0.38026005
16 0.01250088
17 -0.37972232
18 0.29008591
19 -0.67066623
20 -0.53197340
22 -0.68132186
23 0.30344316
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.2470682 0.6430676 -0.1631906 -0.1460216 0.3377222 -0.2740907
=============================================================
--- Mixed - SD - Block 5 - Axis X ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.065754 0.0038679 17 289 1.1268 0.3271
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -6.42e-04 0.0195 289 -0.033 1.0000
Step1 - Step3 -7.62e-03 0.0195 289 -0.390 1.0000
Step1 - Step4 7.08e-03 0.0195 289 0.363 1.0000
Step1 - Step5 8.37e-03 0.0195 289 0.428 1.0000
Step1 - Step6 -1.51e-02 0.0195 289 -0.775 1.0000
Step1 - Step7 9.12e-03 0.0195 289 0.467 1.0000
Step1 - Step8 1.58e-02 0.0195 289 0.807 1.0000
Step1 - Step9 1.69e-02 0.0195 289 0.866 1.0000
Step1 - Step10 1.18e-02 0.0195 289 0.603 1.0000
Step1 - Step11 1.26e-02 0.0195 289 0.648 1.0000
Step1 - Step12 2.44e-02 0.0195 289 1.250 0.9988
Step1 - Step13 2.52e-02 0.0195 289 1.290 0.9982
Step1 - Step14 2.53e-02 0.0195 289 1.295 0.9982
Step1 - Step15 3.04e-02 0.0195 289 1.556 0.9854
Step1 - Step16 3.04e-02 0.0195 289 1.559 0.9852
Step1 - Step17 3.69e-02 0.0195 289 1.890 0.9133
Step1 - Step18 3.37e-02 0.0195 289 1.725 0.9603
Step2 - Step3 -6.98e-03 0.0195 289 -0.357 1.0000
Step2 - Step4 7.73e-03 0.0195 289 0.396 1.0000
Step2 - Step5 9.01e-03 0.0195 289 0.461 1.0000
Step2 - Step6 -1.45e-02 0.0195 289 -0.742 1.0000
Step2 - Step7 9.76e-03 0.0195 289 0.500 1.0000
Step2 - Step8 1.64e-02 0.0195 289 0.840 1.0000
Step2 - Step9 1.76e-02 0.0195 289 0.899 1.0000
Step2 - Step10 1.24e-02 0.0195 289 0.636 1.0000
Step2 - Step11 1.33e-02 0.0195 289 0.680 1.0000
Step2 - Step12 2.51e-02 0.0195 289 1.283 0.9983
Step2 - Step13 2.58e-02 0.0195 289 1.323 0.9976
Step2 - Step14 2.59e-02 0.0195 289 1.328 0.9975
Step2 - Step15 3.10e-02 0.0195 289 1.589 0.9819
Step2 - Step16 3.11e-02 0.0195 289 1.591 0.9817
Step2 - Step17 3.76e-02 0.0195 289 1.923 0.9008
Step2 - Step18 3.43e-02 0.0195 289 1.758 0.9530
Step3 - Step4 1.47e-02 0.0195 289 0.753 1.0000
Step3 - Step5 1.60e-02 0.0195 289 0.819 1.0000
Step3 - Step6 -7.52e-03 0.0195 289 -0.385 1.0000
Step3 - Step7 1.67e-02 0.0195 289 0.857 1.0000
Step3 - Step8 2.34e-02 0.0195 289 1.198 0.9993
Step3 - Step9 2.45e-02 0.0195 289 1.256 0.9987
Step3 - Step10 1.94e-02 0.0195 289 0.994 0.9999
Step3 - Step11 2.03e-02 0.0195 289 1.038 0.9999
Step3 - Step12 3.20e-02 0.0195 289 1.641 0.9753
Step3 - Step13 3.28e-02 0.0195 289 1.681 0.9689
Step3 - Step14 3.29e-02 0.0195 289 1.685 0.9681
Step3 - Step15 3.80e-02 0.0195 289 1.947 0.8911
Step3 - Step16 3.81e-02 0.0195 289 1.949 0.8902
Step3 - Step17 4.45e-02 0.0195 289 2.281 0.6967
Step3 - Step18 4.13e-02 0.0195 289 2.115 0.8053
Step4 - Step5 1.28e-03 0.0195 289 0.066 1.0000
Step4 - Step6 -2.22e-02 0.0195 289 -1.138 0.9996
Step4 - Step7 2.03e-03 0.0195 289 0.104 1.0000
Step4 - Step8 8.68e-03 0.0195 289 0.445 1.0000
Step4 - Step9 9.82e-03 0.0195 289 0.503 1.0000
Step4 - Step10 4.70e-03 0.0195 289 0.241 1.0000
Step4 - Step11 5.56e-03 0.0195 289 0.285 1.0000
Step4 - Step12 1.73e-02 0.0195 289 0.888 1.0000
Step4 - Step13 1.81e-02 0.0195 289 0.928 1.0000
Step4 - Step14 1.82e-02 0.0195 289 0.932 1.0000
Step4 - Step15 2.33e-02 0.0195 289 1.194 0.9993
Step4 - Step16 2.34e-02 0.0195 289 1.196 0.9993
Step4 - Step17 2.98e-02 0.0195 289 1.527 0.9880
Step4 - Step18 2.66e-02 0.0195 289 1.362 0.9966
Step5 - Step6 -2.35e-02 0.0195 289 -1.204 0.9993
Step5 - Step7 7.52e-04 0.0195 289 0.039 1.0000
Step5 - Step8 7.40e-03 0.0195 289 0.379 1.0000
Step5 - Step9 8.54e-03 0.0195 289 0.438 1.0000
Step5 - Step10 3.42e-03 0.0195 289 0.175 1.0000
Step5 - Step11 4.28e-03 0.0195 289 0.219 1.0000
Step5 - Step12 1.61e-02 0.0195 289 0.822 1.0000
Step5 - Step13 1.68e-02 0.0195 289 0.862 1.0000
Step5 - Step14 1.69e-02 0.0195 289 0.866 1.0000
Step5 - Step15 2.20e-02 0.0195 289 1.128 0.9997
Step5 - Step16 2.21e-02 0.0195 289 1.130 0.9997
Step5 - Step17 2.85e-02 0.0195 289 1.462 0.9925
Step5 - Step18 2.53e-02 0.0195 289 1.297 0.9981
Step6 - Step7 2.43e-02 0.0195 289 1.242 0.9989
Step6 - Step8 3.09e-02 0.0195 289 1.583 0.9827
Step6 - Step9 3.21e-02 0.0195 289 1.641 0.9752
Step6 - Step10 2.69e-02 0.0195 289 1.379 0.9961
Step6 - Step11 2.78e-02 0.0195 289 1.423 0.9945
Step6 - Step12 3.96e-02 0.0195 289 2.026 0.8544
Step6 - Step13 4.03e-02 0.0195 289 2.066 0.8335
Step6 - Step14 4.04e-02 0.0195 289 2.070 0.8310
Step6 - Step15 4.55e-02 0.0195 289 2.332 0.6595
Step6 - Step16 4.56e-02 0.0195 289 2.334 0.6580
Step6 - Step17 5.21e-02 0.0195 289 2.666 0.4095
Step6 - Step18 4.88e-02 0.0195 289 2.500 0.5322
Step7 - Step8 6.65e-03 0.0195 289 0.341 1.0000
Step7 - Step9 7.79e-03 0.0195 289 0.399 1.0000
Step7 - Step10 2.67e-03 0.0195 289 0.136 1.0000
Step7 - Step11 3.53e-03 0.0195 289 0.181 1.0000
Step7 - Step12 1.53e-02 0.0195 289 0.784 1.0000
Step7 - Step13 1.61e-02 0.0195 289 0.823 1.0000
Step7 - Step14 1.62e-02 0.0195 289 0.828 1.0000
Step7 - Step15 2.13e-02 0.0195 289 1.090 0.9998
Step7 - Step16 2.13e-02 0.0195 289 1.092 0.9998
Step7 - Step17 2.78e-02 0.0195 289 1.423 0.9944
Step7 - Step18 2.46e-02 0.0195 289 1.258 0.9987
Step8 - Step9 1.14e-03 0.0195 289 0.058 1.0000
Step8 - Step10 -3.99e-03 0.0195 289 -0.204 1.0000
Step8 - Step11 -3.12e-03 0.0195 289 -0.160 1.0000
Step8 - Step12 8.65e-03 0.0195 289 0.443 1.0000
Step8 - Step13 9.43e-03 0.0195 289 0.483 1.0000
Step8 - Step14 9.52e-03 0.0195 289 0.487 1.0000
Step8 - Step15 1.46e-02 0.0195 289 0.749 1.0000
Step8 - Step16 1.47e-02 0.0195 289 0.751 1.0000
Step8 - Step17 2.11e-02 0.0195 289 1.083 0.9998
Step8 - Step18 1.79e-02 0.0195 289 0.918 1.0000
Step9 - Step10 -5.13e-03 0.0195 289 -0.263 1.0000
Step9 - Step11 -4.26e-03 0.0195 289 -0.218 1.0000
Step9 - Step12 7.51e-03 0.0195 289 0.385 1.0000
Step9 - Step13 8.29e-03 0.0195 289 0.424 1.0000
Step9 - Step14 8.38e-03 0.0195 289 0.429 1.0000
Step9 - Step15 1.35e-02 0.0195 289 0.691 1.0000
Step9 - Step16 1.35e-02 0.0195 289 0.693 1.0000
Step9 - Step17 2.00e-02 0.0195 289 1.024 0.9999
Step9 - Step18 1.68e-02 0.0195 289 0.859 1.0000
Step10 - Step11 8.63e-04 0.0195 289 0.044 1.0000
Step10 - Step12 1.26e-02 0.0195 289 0.647 1.0000
Step10 - Step13 1.34e-02 0.0195 289 0.687 1.0000
Step10 - Step14 1.35e-02 0.0195 289 0.691 1.0000
Step10 - Step15 1.86e-02 0.0195 289 0.953 1.0000
Step10 - Step16 1.87e-02 0.0195 289 0.955 1.0000
Step10 - Step17 2.51e-02 0.0195 289 1.287 0.9983
Step10 - Step18 2.19e-02 0.0195 289 1.122 0.9997
Step11 - Step12 1.18e-02 0.0195 289 0.603 1.0000
Step11 - Step13 1.26e-02 0.0195 289 0.643 1.0000
Step11 - Step14 1.26e-02 0.0195 289 0.647 1.0000
Step11 - Step15 1.77e-02 0.0195 289 0.909 1.0000
Step11 - Step16 1.78e-02 0.0195 289 0.911 1.0000
Step11 - Step17 2.43e-02 0.0195 289 1.243 0.9989
Step11 - Step18 2.10e-02 0.0195 289 1.077 0.9998
Step12 - Step13 7.79e-04 0.0195 289 0.040 1.0000
Step12 - Step14 8.65e-04 0.0195 289 0.044 1.0000
Step12 - Step15 5.98e-03 0.0195 289 0.306 1.0000
Step12 - Step16 6.02e-03 0.0195 289 0.308 1.0000
Step12 - Step17 1.25e-02 0.0195 289 0.640 1.0000
Step12 - Step18 9.27e-03 0.0195 289 0.475 1.0000
Step13 - Step14 8.60e-05 0.0195 289 0.004 1.0000
Step13 - Step15 5.20e-03 0.0195 289 0.266 1.0000
Step13 - Step16 5.24e-03 0.0195 289 0.268 1.0000
Step13 - Step17 1.17e-02 0.0195 289 0.600 1.0000
Step13 - Step18 8.49e-03 0.0195 289 0.435 1.0000
Step14 - Step15 5.11e-03 0.0195 289 0.262 1.0000
Step14 - Step16 5.15e-03 0.0195 289 0.264 1.0000
Step14 - Step17 1.16e-02 0.0195 289 0.596 1.0000
Step14 - Step18 8.40e-03 0.0195 289 0.430 1.0000
Step15 - Step16 4.23e-05 0.0195 289 0.002 1.0000
Step15 - Step17 6.52e-03 0.0195 289 0.334 1.0000
Step15 - Step18 3.29e-03 0.0195 289 0.169 1.0000
Step16 - Step17 6.48e-03 0.0195 289 0.332 1.0000
Step16 - Step18 3.25e-03 0.0195 289 0.166 1.0000
Step17 - Step18 -3.23e-03 0.0195 289 -0.165 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
0.6416571230 0.0006422534 0.0076217536 -0.0070849041 -0.0083650595
Step6 Step7 Step8 Step9 Step10
0.0151410671 -0.0091173718 -0.0157683118 -0.0169096281 -0.0117825693
Step11 Step12 Step13 Step14 Step15
-0.0126458434 -0.0244196584 -0.0251987634 -0.0252847810 -0.0303950162
Step16 Step17 Step18
-0.0304373015 -0.0369146344 -0.0336866821
Random Effects:
$subject
(Intercept)
2 0.04809144
3 -0.07132608
4 -0.11918782
5 -0.29774643
7 -0.24606343
8 0.46188258
10 0.62466687
11 0.04343660
13 -0.05255563
14 0.01584357
15 0.18357038
16 -0.09157103
17 -0.11897484
18 -0.07984503
19 -0.25669845
20 -0.14841635
22 -0.13052233
23 0.23541597
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
1.1699274 2.0613735 1.4959752 1.3834955 1.4460097 0.3626504
=============================================================
--- Mixed - SD - Block 5 - Axis Y ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.69634 0.040961 17 289 1.261 0.217
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 0.00040 0.0601 289 0.007 1.0000
Step1 - Step3 -0.05436 0.0601 289 -0.905 1.0000
Step1 - Step4 -0.02137 0.0601 289 -0.356 1.0000
Step1 - Step5 -0.02281 0.0601 289 -0.380 1.0000
Step1 - Step6 -0.09259 0.0601 289 -1.541 0.9868
Step1 - Step7 -0.03412 0.0601 289 -0.568 1.0000
Step1 - Step8 -0.02781 0.0601 289 -0.463 1.0000
Step1 - Step9 0.00560 0.0601 289 0.093 1.0000
Step1 - Step10 0.00878 0.0601 289 0.146 1.0000
Step1 - Step11 -0.01623 0.0601 289 -0.270 1.0000
Step1 - Step12 0.01316 0.0601 289 0.219 1.0000
Step1 - Step13 -0.02955 0.0601 289 -0.492 1.0000
Step1 - Step14 0.02652 0.0601 289 0.441 1.0000
Step1 - Step15 0.05532 0.0601 289 0.921 1.0000
Step1 - Step16 0.02211 0.0601 289 0.368 1.0000
Step1 - Step17 0.10540 0.0601 289 1.754 0.9538
Step1 - Step18 0.08659 0.0601 289 1.441 0.9936
Step2 - Step3 -0.05476 0.0601 289 -0.912 1.0000
Step2 - Step4 -0.02177 0.0601 289 -0.362 1.0000
Step2 - Step5 -0.02321 0.0601 289 -0.386 1.0000
Step2 - Step6 -0.09299 0.0601 289 -1.548 0.9862
Step2 - Step7 -0.03452 0.0601 289 -0.575 1.0000
Step2 - Step8 -0.02821 0.0601 289 -0.470 1.0000
Step2 - Step9 0.00520 0.0601 289 0.087 1.0000
Step2 - Step10 0.00838 0.0601 289 0.139 1.0000
Step2 - Step11 -0.01663 0.0601 289 -0.277 1.0000
Step2 - Step12 0.01276 0.0601 289 0.212 1.0000
Step2 - Step13 -0.02994 0.0601 289 -0.498 1.0000
Step2 - Step14 0.02612 0.0601 289 0.435 1.0000
Step2 - Step15 0.05492 0.0601 289 0.914 1.0000
Step2 - Step16 0.02171 0.0601 289 0.361 1.0000
Step2 - Step17 0.10500 0.0601 289 1.748 0.9553
Step2 - Step18 0.08619 0.0601 289 1.435 0.9939
Step3 - Step4 0.03300 0.0601 289 0.549 1.0000
Step3 - Step5 0.03155 0.0601 289 0.525 1.0000
Step3 - Step6 -0.03823 0.0601 289 -0.636 1.0000
Step3 - Step7 0.02024 0.0601 289 0.337 1.0000
Step3 - Step8 0.02656 0.0601 289 0.442 1.0000
Step3 - Step9 0.05997 0.0601 289 0.998 0.9999
Step3 - Step10 0.06314 0.0601 289 1.051 0.9999
Step3 - Step11 0.03814 0.0601 289 0.635 1.0000
Step3 - Step12 0.06752 0.0601 289 1.124 0.9997
Step3 - Step13 0.02482 0.0601 289 0.413 1.0000
Step3 - Step14 0.08088 0.0601 289 1.346 0.9971
Step3 - Step15 0.10968 0.0601 289 1.826 0.9348
Step3 - Step16 0.07647 0.0601 289 1.273 0.9985
Step3 - Step17 0.15976 0.0601 289 2.659 0.4140
Step3 - Step18 0.14095 0.0601 289 2.346 0.6488
Step4 - Step5 -0.00144 0.0601 289 -0.024 1.0000
Step4 - Step6 -0.07123 0.0601 289 -1.186 0.9994
Step4 - Step7 -0.01276 0.0601 289 -0.212 1.0000
Step4 - Step8 -0.00644 0.0601 289 -0.107 1.0000
Step4 - Step9 0.02697 0.0601 289 0.449 1.0000
Step4 - Step10 0.03015 0.0601 289 0.502 1.0000
Step4 - Step11 0.00514 0.0601 289 0.086 1.0000
Step4 - Step12 0.03453 0.0601 289 0.575 1.0000
Step4 - Step13 -0.00818 0.0601 289 -0.136 1.0000
Step4 - Step14 0.04789 0.0601 289 0.797 1.0000
Step4 - Step15 0.07669 0.0601 289 1.276 0.9984
Step4 - Step16 0.04348 0.0601 289 0.724 1.0000
Step4 - Step17 0.12677 0.0601 289 2.110 0.8083
Step4 - Step18 0.10796 0.0601 289 1.797 0.9430
Step5 - Step6 -0.06978 0.0601 289 -1.162 0.9995
Step5 - Step7 -0.01132 0.0601 289 -0.188 1.0000
Step5 - Step8 -0.00500 0.0601 289 -0.083 1.0000
Step5 - Step9 0.02841 0.0601 289 0.473 1.0000
Step5 - Step10 0.03159 0.0601 289 0.526 1.0000
Step5 - Step11 0.00658 0.0601 289 0.110 1.0000
Step5 - Step12 0.03597 0.0601 289 0.599 1.0000
Step5 - Step13 -0.00674 0.0601 289 -0.112 1.0000
Step5 - Step14 0.04933 0.0601 289 0.821 1.0000
Step5 - Step15 0.07813 0.0601 289 1.300 0.9981
Step5 - Step16 0.04492 0.0601 289 0.748 1.0000
Step5 - Step17 0.12821 0.0601 289 2.134 0.7940
Step5 - Step18 0.10940 0.0601 289 1.821 0.9362
Step6 - Step7 0.05847 0.0601 289 0.973 1.0000
Step6 - Step8 0.06479 0.0601 289 1.078 0.9998
Step6 - Step9 0.09820 0.0601 289 1.635 0.9761
Step6 - Step10 0.10137 0.0601 289 1.687 0.9676
Step6 - Step11 0.07637 0.0601 289 1.271 0.9985
Step6 - Step12 0.10575 0.0601 289 1.760 0.9524
Step6 - Step13 0.06305 0.0601 289 1.049 0.9999
Step6 - Step14 0.11911 0.0601 289 1.983 0.8752
Step6 - Step15 0.14791 0.0601 289 2.462 0.5613
Step6 - Step16 0.11471 0.0601 289 1.909 0.9062
Step6 - Step17 0.19799 0.0601 289 3.296 0.0972
Step6 - Step18 0.17918 0.0601 289 2.983 0.2158
Step7 - Step8 0.00632 0.0601 289 0.105 1.0000
Step7 - Step9 0.03973 0.0601 289 0.661 1.0000
Step7 - Step10 0.04290 0.0601 289 0.714 1.0000
Step7 - Step11 0.01790 0.0601 289 0.298 1.0000
Step7 - Step12 0.04729 0.0601 289 0.787 1.0000
Step7 - Step13 0.00458 0.0601 289 0.076 1.0000
Step7 - Step14 0.06064 0.0601 289 1.009 0.9999
Step7 - Step15 0.08944 0.0601 289 1.489 0.9909
Step7 - Step16 0.05624 0.0601 289 0.936 1.0000
Step7 - Step17 0.13952 0.0601 289 2.322 0.6664
Step7 - Step18 0.12071 0.0601 289 2.009 0.8625
Step8 - Step9 0.03341 0.0601 289 0.556 1.0000
Step8 - Step10 0.03659 0.0601 289 0.609 1.0000
Step8 - Step11 0.01158 0.0601 289 0.193 1.0000
Step8 - Step12 0.04097 0.0601 289 0.682 1.0000
Step8 - Step13 -0.00174 0.0601 289 -0.029 1.0000
Step8 - Step14 0.05433 0.0601 289 0.904 1.0000
Step8 - Step15 0.08313 0.0601 289 1.384 0.9960
Step8 - Step16 0.04992 0.0601 289 0.831 1.0000
Step8 - Step17 0.13321 0.0601 289 2.217 0.7406
Step8 - Step18 0.11440 0.0601 289 1.904 0.9081
Step9 - Step10 0.00318 0.0601 289 0.053 1.0000
Step9 - Step11 -0.02183 0.0601 289 -0.363 1.0000
Step9 - Step12 0.00756 0.0601 289 0.126 1.0000
Step9 - Step13 -0.03515 0.0601 289 -0.585 1.0000
Step9 - Step14 0.02092 0.0601 289 0.348 1.0000
Step9 - Step15 0.04972 0.0601 289 0.828 1.0000
Step9 - Step16 0.01651 0.0601 289 0.275 1.0000
Step9 - Step17 0.09980 0.0601 289 1.661 0.9721
Step9 - Step18 0.08099 0.0601 289 1.348 0.9970
Step10 - Step11 -0.02501 0.0601 289 -0.416 1.0000
Step10 - Step12 0.00438 0.0601 289 0.073 1.0000
Step10 - Step13 -0.03832 0.0601 289 -0.638 1.0000
Step10 - Step14 0.01774 0.0601 289 0.295 1.0000
Step10 - Step15 0.04654 0.0601 289 0.775 1.0000
Step10 - Step16 0.01333 0.0601 289 0.222 1.0000
Step10 - Step17 0.09662 0.0601 289 1.608 0.9797
Step10 - Step18 0.07781 0.0601 289 1.295 0.9981
Step11 - Step12 0.02939 0.0601 289 0.489 1.0000
Step11 - Step13 -0.01332 0.0601 289 -0.222 1.0000
Step11 - Step14 0.04275 0.0601 289 0.712 1.0000
Step11 - Step15 0.07155 0.0601 289 1.191 0.9993
Step11 - Step16 0.03834 0.0601 289 0.638 1.0000
Step11 - Step17 0.12163 0.0601 289 2.025 0.8550
Step11 - Step18 0.10282 0.0601 289 1.711 0.9631
Step12 - Step13 -0.04271 0.0601 289 -0.711 1.0000
Step12 - Step14 0.01336 0.0601 289 0.222 1.0000
Step12 - Step15 0.04216 0.0601 289 0.702 1.0000
Step12 - Step16 0.00895 0.0601 289 0.149 1.0000
Step12 - Step17 0.09224 0.0601 289 1.535 0.9873
Step12 - Step18 0.07343 0.0601 289 1.222 0.9991
Step13 - Step14 0.05606 0.0601 289 0.933 1.0000
Step13 - Step15 0.08486 0.0601 289 1.413 0.9949
Step13 - Step16 0.05166 0.0601 289 0.860 1.0000
Step13 - Step17 0.13494 0.0601 289 2.246 0.7208
Step13 - Step18 0.11614 0.0601 289 1.933 0.8967
Step14 - Step15 0.02880 0.0601 289 0.479 1.0000
Step14 - Step16 -0.00441 0.0601 289 -0.073 1.0000
Step14 - Step17 0.07888 0.0601 289 1.313 0.9978
Step14 - Step18 0.06007 0.0601 289 1.000 0.9999
Step15 - Step16 -0.03321 0.0601 289 -0.553 1.0000
Step15 - Step17 0.05008 0.0601 289 0.834 1.0000
Step15 - Step18 0.03127 0.0601 289 0.521 1.0000
Step16 - Step17 0.08329 0.0601 289 1.386 0.9959
Step16 - Step18 0.06448 0.0601 289 1.073 0.9998
Step17 - Step18 -0.01881 0.0601 289 -0.313 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5
0.7164847082 -0.0003997668 0.0543621459 0.0213668393 0.0228089934
Step6 Step7 Step8 Step9 Step10
0.0925934920 0.0341243851 0.0278068363 -0.0056034314 -0.0087796362
Step11 Step12 Step13 Step14 Step15
0.0162264815 -0.0131610538 0.0295452020 -0.0265188585 -0.0553189413
Step16 Step17 Step18
-0.0221122733 -0.1053993706 -0.0865899610
Random Effects:
$subject
(Intercept)
2 0.231870708
3 0.031041493
4 -0.202542504
5 -0.382931103
7 -0.145524181
8 0.267665349
10 0.444212727
11 -0.193619476
13 -0.110748426
14 -0.095764829
15 0.009626768
16 -0.038985325
17 -0.118293557
18 -0.168432315
19 -0.375329567
20 -0.362454336
22 -0.280901193
23 1.491109765
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.53586800 0.64293419 0.09449059 0.43919461 0.43030755 -0.15644541
=============================================================
--- Mixed - SD - Block 5 - Axis Z ---
ANOVA:
Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.13543 0.0079664 17 289 0.5164 0.9442
Pairwise Comparisons:
contrast estimate SE df t.ratio p.value
Step1 - Step2 -9.59e-03 0.0414 289 -0.232 1.0000
Step1 - Step3 -2.16e-02 0.0414 289 -0.521 1.0000
Step1 - Step4 1.55e-03 0.0414 289 0.038 1.0000
Step1 - Step5 1.06e-02 0.0414 289 0.255 1.0000
Step1 - Step6 -1.09e-02 0.0414 289 -0.264 1.0000
Step1 - Step7 7.29e-03 0.0414 289 0.176 1.0000
Step1 - Step8 7.48e-03 0.0414 289 0.181 1.0000
Step1 - Step9 2.71e-02 0.0414 289 0.655 1.0000
Step1 - Step10 1.76e-02 0.0414 289 0.424 1.0000
Step1 - Step11 -7.29e-03 0.0414 289 -0.176 1.0000
Step1 - Step12 2.69e-02 0.0414 289 0.649 1.0000
Step1 - Step13 2.42e-02 0.0414 289 0.585 1.0000
Step1 - Step14 4.57e-02 0.0414 289 1.104 0.9998
Step1 - Step15 3.15e-02 0.0414 289 0.762 1.0000
Step1 - Step16 1.75e-02 0.0414 289 0.423 1.0000
Step1 - Step17 5.36e-02 0.0414 289 1.295 0.9982
Step1 - Step18 4.30e-02 0.0414 289 1.038 0.9999
Step2 - Step3 -1.20e-02 0.0414 289 -0.290 1.0000
Step2 - Step4 1.11e-02 0.0414 289 0.269 1.0000
Step2 - Step5 2.01e-02 0.0414 289 0.487 1.0000
Step2 - Step6 -1.32e-03 0.0414 289 -0.032 1.0000
Step2 - Step7 1.69e-02 0.0414 289 0.408 1.0000
Step2 - Step8 1.71e-02 0.0414 289 0.412 1.0000
Step2 - Step9 3.67e-02 0.0414 289 0.886 1.0000
Step2 - Step10 2.71e-02 0.0414 289 0.656 1.0000
Step2 - Step11 2.29e-03 0.0414 289 0.055 1.0000
Step2 - Step12 3.65e-02 0.0414 289 0.881 1.0000
Step2 - Step13 3.38e-02 0.0414 289 0.817 1.0000
Step2 - Step14 5.53e-02 0.0414 289 1.336 0.9973
Step2 - Step15 4.11e-02 0.0414 289 0.993 0.9999
Step2 - Step16 2.71e-02 0.0414 289 0.654 1.0000
Step2 - Step17 6.32e-02 0.0414 289 1.526 0.9881
Step2 - Step18 5.25e-02 0.0414 289 1.269 0.9986
Step3 - Step4 2.31e-02 0.0414 289 0.559 1.0000
Step3 - Step5 3.21e-02 0.0414 289 0.776 1.0000
Step3 - Step6 1.07e-02 0.0414 289 0.258 1.0000
Step3 - Step7 2.89e-02 0.0414 289 0.697 1.0000
Step3 - Step8 2.91e-02 0.0414 289 0.702 1.0000
Step3 - Step9 4.87e-02 0.0414 289 1.176 0.9994
Step3 - Step10 3.91e-02 0.0414 289 0.945 1.0000
Step3 - Step11 1.43e-02 0.0414 289 0.345 1.0000
Step3 - Step12 4.85e-02 0.0414 289 1.171 0.9995
Step3 - Step13 4.58e-02 0.0414 289 1.106 0.9998
Step3 - Step14 6.73e-02 0.0414 289 1.625 0.9775
Step3 - Step15 5.31e-02 0.0414 289 1.283 0.9984
Step3 - Step16 3.91e-02 0.0414 289 0.944 1.0000
Step3 - Step17 7.52e-02 0.0414 289 1.816 0.9377
Step3 - Step18 6.45e-02 0.0414 289 1.559 0.9852
Step4 - Step5 9.00e-03 0.0414 289 0.218 1.0000
Step4 - Step6 -1.25e-02 0.0414 289 -0.301 1.0000
Step4 - Step7 5.74e-03 0.0414 289 0.139 1.0000
Step4 - Step8 5.93e-03 0.0414 289 0.143 1.0000
Step4 - Step9 2.55e-02 0.0414 289 0.617 1.0000
Step4 - Step10 1.60e-02 0.0414 289 0.387 1.0000
Step4 - Step11 -8.85e-03 0.0414 289 -0.214 1.0000
Step4 - Step12 2.53e-02 0.0414 289 0.612 1.0000
Step4 - Step13 2.27e-02 0.0414 289 0.548 1.0000
Step4 - Step14 4.42e-02 0.0414 289 1.066 0.9998
Step4 - Step15 3.00e-02 0.0414 289 0.724 1.0000
Step4 - Step16 1.59e-02 0.0414 289 0.385 1.0000
Step4 - Step17 5.20e-02 0.0414 289 1.257 0.9987
Step4 - Step18 4.14e-02 0.0414 289 1.000 0.9999
Step5 - Step6 -2.15e-02 0.0414 289 -0.519 1.0000
Step5 - Step7 -3.27e-03 0.0414 289 -0.079 1.0000
Step5 - Step8 -3.08e-03 0.0414 289 -0.074 1.0000
Step5 - Step9 1.65e-02 0.0414 289 0.400 1.0000
Step5 - Step10 7.00e-03 0.0414 289 0.169 1.0000
Step5 - Step11 -1.79e-02 0.0414 289 -0.431 1.0000
Step5 - Step12 1.63e-02 0.0414 289 0.394 1.0000
Step5 - Step13 1.37e-02 0.0414 289 0.330 1.0000
Step5 - Step14 3.51e-02 0.0414 289 0.849 1.0000
Step5 - Step15 2.10e-02 0.0414 289 0.507 1.0000
Step5 - Step16 6.94e-03 0.0414 289 0.168 1.0000
Step5 - Step17 4.30e-02 0.0414 289 1.040 0.9999
Step5 - Step18 3.24e-02 0.0414 289 0.783 1.0000
Step6 - Step7 1.82e-02 0.0414 289 0.440 1.0000
Step6 - Step8 1.84e-02 0.0414 289 0.444 1.0000
Step6 - Step9 3.80e-02 0.0414 289 0.918 1.0000
Step6 - Step10 2.85e-02 0.0414 289 0.688 1.0000
Step6 - Step11 3.62e-03 0.0414 289 0.087 1.0000
Step6 - Step12 3.78e-02 0.0414 289 0.913 1.0000
Step6 - Step13 3.51e-02 0.0414 289 0.849 1.0000
Step6 - Step14 5.66e-02 0.0414 289 1.368 0.9965
Step6 - Step15 4.24e-02 0.0414 289 1.025 0.9999
Step6 - Step16 2.84e-02 0.0414 289 0.686 1.0000
Step6 - Step17 6.45e-02 0.0414 289 1.558 0.9852
Step6 - Step18 5.39e-02 0.0414 289 1.301 0.9980
Step7 - Step8 1.89e-04 0.0414 289 0.005 1.0000
Step7 - Step9 1.98e-02 0.0414 289 0.479 1.0000
Step7 - Step10 1.03e-02 0.0414 289 0.248 1.0000
Step7 - Step11 -1.46e-02 0.0414 289 -0.352 1.0000
Step7 - Step12 1.96e-02 0.0414 289 0.473 1.0000
Step7 - Step13 1.69e-02 0.0414 289 0.409 1.0000
Step7 - Step14 3.84e-02 0.0414 289 0.928 1.0000
Step7 - Step15 2.42e-02 0.0414 289 0.586 1.0000
Step7 - Step16 1.02e-02 0.0414 289 0.247 1.0000
Step7 - Step17 4.63e-02 0.0414 289 1.119 0.9997
Step7 - Step18 3.57e-02 0.0414 289 0.862 1.0000
Step8 - Step9 1.96e-02 0.0414 289 0.474 1.0000
Step8 - Step10 1.01e-02 0.0414 289 0.244 1.0000
Step8 - Step11 -1.48e-02 0.0414 289 -0.357 1.0000
Step8 - Step12 1.94e-02 0.0414 289 0.469 1.0000
Step8 - Step13 1.67e-02 0.0414 289 0.405 1.0000
Step8 - Step14 3.82e-02 0.0414 289 0.923 1.0000
Step8 - Step15 2.41e-02 0.0414 289 0.581 1.0000
Step8 - Step16 1.00e-02 0.0414 289 0.242 1.0000
Step8 - Step17 4.61e-02 0.0414 289 1.114 0.9997
Step8 - Step18 3.55e-02 0.0414 289 0.857 1.0000
Step9 - Step10 -9.54e-03 0.0414 289 -0.230 1.0000
Step9 - Step11 -3.44e-02 0.0414 289 -0.831 1.0000
Step9 - Step12 -2.12e-04 0.0414 289 -0.005 1.0000
Step9 - Step13 -2.87e-03 0.0414 289 -0.069 1.0000
Step9 - Step14 1.86e-02 0.0414 289 0.449 1.0000
Step9 - Step15 4.43e-03 0.0414 289 0.107 1.0000
Step9 - Step16 -9.60e-03 0.0414 289 -0.232 1.0000
Step9 - Step17 2.65e-02 0.0414 289 0.640 1.0000
Step9 - Step18 1.59e-02 0.0414 289 0.383 1.0000
Step10 - Step11 -2.49e-02 0.0414 289 -0.600 1.0000
Step10 - Step12 9.33e-03 0.0414 289 0.225 1.0000
Step10 - Step13 6.66e-03 0.0414 289 0.161 1.0000
Step10 - Step14 2.81e-02 0.0414 289 0.680 1.0000
Step10 - Step15 1.40e-02 0.0414 289 0.337 1.0000
Step10 - Step16 -5.99e-05 0.0414 289 -0.001 1.0000
Step10 - Step17 3.60e-02 0.0414 289 0.870 1.0000
Step10 - Step18 2.54e-02 0.0414 289 0.614 1.0000
Step11 - Step12 3.42e-02 0.0414 289 0.826 1.0000
Step11 - Step13 3.15e-02 0.0414 289 0.761 1.0000
Step11 - Step14 5.30e-02 0.0414 289 1.280 0.9984
Step11 - Step15 3.88e-02 0.0414 289 0.938 1.0000
Step11 - Step16 2.48e-02 0.0414 289 0.599 1.0000
Step11 - Step17 6.09e-02 0.0414 289 1.471 0.9920
Step11 - Step18 5.03e-02 0.0414 289 1.214 0.9992
Step12 - Step13 -2.66e-03 0.0414 289 -0.064 1.0000
Step12 - Step14 1.88e-02 0.0414 289 0.455 1.0000
Step12 - Step15 4.64e-03 0.0414 289 0.112 1.0000
Step12 - Step16 -9.39e-03 0.0414 289 -0.227 1.0000
Step12 - Step17 2.67e-02 0.0414 289 0.645 1.0000
Step12 - Step18 1.61e-02 0.0414 289 0.388 1.0000
Step13 - Step14 2.15e-02 0.0414 289 0.519 1.0000
Step13 - Step15 7.30e-03 0.0414 289 0.176 1.0000
Step13 - Step16 -6.72e-03 0.0414 289 -0.162 1.0000
Step13 - Step17 2.94e-02 0.0414 289 0.709 1.0000
Step13 - Step18 1.87e-02 0.0414 289 0.453 1.0000
Step14 - Step15 -1.42e-02 0.0414 289 -0.342 1.0000
Step14 - Step16 -2.82e-02 0.0414 289 -0.681 1.0000
Step14 - Step17 7.89e-03 0.0414 289 0.191 1.0000
Step14 - Step18 -2.74e-03 0.0414 289 -0.066 1.0000
Step15 - Step16 -1.40e-02 0.0414 289 -0.339 1.0000
Step15 - Step17 2.21e-02 0.0414 289 0.533 1.0000
Step15 - Step18 1.14e-02 0.0414 289 0.276 1.0000
Step16 - Step17 3.61e-02 0.0414 289 0.872 1.0000
Step16 - Step18 2.55e-02 0.0414 289 0.615 1.0000
Step17 - Step18 -1.06e-02 0.0414 289 -0.257 1.0000
Degrees-of-freedom method: kenward-roger
P value adjustment: tukey method for comparing a family of 18 estimates
Fixed Effects:
(Intercept) Step2 Step3 Step4 Step5 Step6
1.278491439 0.009585867 0.021577171 -0.001552903 -0.010557839 0.010910687
Step7 Step8 Step9 Step10 Step11 Step12
-0.007289094 -0.007477986 -0.027099393 -0.017560955 0.007292232 -0.026887470
Step13 Step14 Step15 Step16 Step17 Step18
-0.024225566 -0.045704534 -0.031530425 -0.017501088 -0.053597721 -0.042960723
Random Effects:
$subject
(Intercept)
2 0.08381805
3 -0.06876900
4 -0.38605698
5 -0.68900389
7 -0.22135937
8 0.51895893
10 1.74313146
11 -0.08312183
13 0.31324720
14 -0.32353367
15 0.70247387
16 0.12199951
17 -0.52083593
18 -0.10028139
19 -0.57155079
20 -0.53250219
22 -0.49580635
23 0.50919235
with conditional variances for "subject"
Sample Scaled Residuals:
1 2 3 4 5 6
0.6062832 2.3399335 1.7985767 1.8151180 1.5004825 0.4211344
=============================================================4. Additional models
4.1 SD of Acceleration - changes over time
# --- Compute SD per trial and assign trial index ---
compute_sd <- function(df) {
df %>%
group_by(subject, Block, trial, phase) %>%
summarise(
sd_x = sd(CoM.acc.x, na.rm = TRUE),
sd_y = sd(CoM.acc.y, na.rm = TRUE),
sd_z = sd(CoM.acc.z, na.rm = TRUE),
.groups = "drop"
) %>%
group_by(subject, Block, phase) %>%
arrange(trial) %>%
mutate(TrialInBlock = row_number()) %>%
ungroup()
}
# --- Run LMMs for SD and extract ANOVA p-values ---
run_sd_model_analysis <- function(tagged_df, label) {
sd_df <- compute_sd(tagged_df) %>%
mutate(
Block = factor(Block),
subject = factor(subject),
phase = factor(phase)
)
get_anova <- function(axis) {
model <- lmer(as.formula(paste0("sd_", axis, " ~ TrialInBlock * Block * phase + (1 + Block | subject)")),
data = sd_df)
anova(model)
}
an_x <- get_anova("x")
an_y <- get_anova("y")
an_z <- get_anova("z")
tibble(
Dataset = label,
Axis = c("X", "Y", "Z"),
`TrialInBlock p-value` = c(an_x["TrialInBlock", "Pr(>F)"], an_y["TrialInBlock", "Pr(>F)"], an_z["TrialInBlock", "Pr(>F)"]),
`Block p-value` = c(an_x["Block", "Pr(>F)"], an_y["Block", "Pr(>F)"], an_z["Block", "Pr(>F)"]),
`Phase p-value` = c(an_x["phase", "Pr(>F)"], an_y["phase", "Pr(>F)"], an_z["phase", "Pr(>F)"]),
`TrialInBlock:Block p` = c(an_x["TrialInBlock:Block", "Pr(>F)"], an_y["TrialInBlock:Block", "Pr(>F)"], an_z["TrialInBlock:Block", "Pr(>F)"]),
`TrialInBlock:Phase p` = c(an_x["TrialInBlock:phase", "Pr(>F)"], an_y["TrialInBlock:phase", "Pr(>F)"], an_z["TrialInBlock:phase", "Pr(>F)"]),
`Block:Phase p` = c(an_x["Block:phase", "Pr(>F)"], an_y["Block:phase", "Pr(>F)"], an_z["Block:phase", "Pr(>F)"]),
`3-way p-value` = c(an_x["TrialInBlock:Block:phase", "Pr(>F)"],
an_y["TrialInBlock:Block:phase", "Pr(>F)"],
an_z["TrialInBlock:Block:phase", "Pr(>F)"])
)
}
# Use already-tagged data if available
sd_mixed_pvals <- run_sd_model_analysis(tagged_data, "Mixed")Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00251375 (tol = 0.002, component 1)print(sd_mixed_pvals)# A tibble: 3 × 9
Dataset Axis `TrialInBlock p-value` `Block p-value` `Phase p-value`
<chr> <chr> <dbl> <dbl> <dbl>
1 Mixed X 0.125 0.0000460 0
2 Mixed Y 0.0904 0.00158 0
3 Mixed Z 0.000567 0.00182 0
# ℹ 4 more variables: `TrialInBlock:Block p` <dbl>,
# `TrialInBlock:Phase p` <dbl>, `Block:Phase p` <dbl>, `3-way p-value` <dbl># --- Suppress emmeans/pbkrtest warnings globally ---
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# --- Compute SD per trial and assign trial index ---
compute_sd <- function(df) {
df %>%
group_by(subject, Block, trial, phase) %>%
summarise(
sd_x = sd(CoM.acc.x, na.rm = TRUE),
sd_y = sd(CoM.acc.y, na.rm = TRUE),
sd_z = sd(CoM.acc.z, na.rm = TRUE),
.groups = "drop"
) %>%
group_by(subject, Block, phase) %>%
arrange(trial) %>%
mutate(TrialInBlock = row_number()) %>%
ungroup()
}
# --- Extended: Run SD LMM with Full Output per Axis ---
run_sd_model_diagnostics <- function(tagged_df, label) {
sd_df <- compute_sd(tagged_df) %>%
mutate(
Block = factor(Block),
subject = factor(subject),
phase = factor(phase)
)
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
model <- lmer(
as.formula(paste0("sd_", axis, " ~ TrialInBlock * Block * phase + (1 + Block | subject)")),
data = sd_df
)
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
ANOVA = anova(model),
Emmeans = emmeans(model, ~ Block * phase),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
return(results)
}
# --- Run Extended SD Diagnostics ---
sd_mixed_diagnostics <- run_sd_model_diagnostics(tagged_data, "Mixed")NOTE: Results may be misleading due to involvement in interactionsWarning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.00251375 (tol = 0.002, component 1)NOTE: Results may be misleading due to involvement in interactions
NOTE: Results may be misleading due to involvement in interactions# --- Print Diagnostics Example (Axis X) ---
cat("\n=== SD LMM: Axis X ===\n")
=== SD LMM: Axis X ===print(sd_mixed_diagnostics$Mixed_X$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
TrialInBlock 0.135 0.135 1 5746.5 2.3590 0.1246
Block 1.972 0.493 4 38.6 8.5982 4.597e-05 ***
phase 249.104 249.104 1 6434.0 4345.2038 < 2.2e-16 ***
TrialInBlock:Block 1.553 0.388 4 4790.3 6.7711 1.975e-05 ***
TrialInBlock:phase 17.954 17.954 1 6434.8 313.1832 < 2.2e-16 ***
Block:phase 6.784 1.696 4 6434.0 29.5819 < 2.2e-16 ***
TrialInBlock:Block:phase 7.883 1.971 4 6434.8 34.3752 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(sd_mixed_diagnostics$Mixed_X$Emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.8589 0.0463 17.8 0.7616 0.956
2 Execution 0.7722 0.0460 18.1 0.6757 0.869
3 Execution 0.5958 0.0348 21.3 0.5235 0.668
4 Execution 0.7512 0.0372 18.0 0.6730 0.829
5 Execution 0.5829 0.0234 19.8 0.5341 0.632
1 Preparation 0.0665 0.0462 17.7 -0.0307 0.164
2 Preparation 0.1416 0.0459 18.0 0.0451 0.238
3 Preparation 0.2170 0.0346 20.9 0.1450 0.289
4 Preparation 0.1057 0.0372 18.0 0.0275 0.184
5 Preparation 0.1058 0.0233 19.8 0.0570 0.154
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(sd_mixed_diagnostics$Mixed_X$FixedEffects) (Intercept) TrialInBlock
0.8670157681 -0.0004070869
Block2 Block3
0.0559088391 -0.0360016658
Block4 Block5
-0.0267292326 -0.2966271553
phasePreparation TrialInBlock:Block2
-0.8045860884 -0.0071820838
TrialInBlock:Block3 TrialInBlock:Block4
-0.0114413892 -0.0040774891
TrialInBlock:Block5 TrialInBlock:phasePreparation
0.0010358221 0.0006132538
Block2:phasePreparation Block3:phasePreparation
-0.1321684047 -0.0065997845
Block4:phasePreparation Block5:phasePreparation
-0.0350077883 0.2389905765
TrialInBlock:Block2:phasePreparation TrialInBlock:Block3:phasePreparation
0.0148035495 0.0211674507
TrialInBlock:Block4:phasePreparation TrialInBlock:Block5:phasePreparation
0.0091604473 0.0038433568 print(sd_mixed_diagnostics$Mixed_X$RandomEffects)$subject
(Intercept) Block2 Block3 Block4 Block5
2 -0.002988795 0.14156712 0.1581594223 0.08769465 0.059652684
3 0.212609300 -0.20029327 -0.2619025889 -0.27899585 -0.250960985
4 -0.085181378 -0.05349970 -0.0210815156 -0.01082793 0.060289294
5 -0.114621143 -0.06346916 -0.0538648037 -0.09673877 -0.035267752
7 -0.082730012 0.03177071 0.0723551492 0.06539204 0.005344579
8 0.023389807 0.04016877 -0.0008738165 0.05538312 0.048245656
10 0.320251535 0.17728157 0.0556958401 0.09787794 -0.082884933
11 0.420755543 -0.04364919 -0.2389522326 -0.17238057 -0.343794765
13 -0.105300030 -0.01409427 0.0304672747 0.08532433 0.075952557
14 0.121575104 -0.04358855 -0.0843247333 -0.08775479 -0.063264006
15 -0.120445885 0.01060097 0.0514848796 0.01798462 0.187721830
16 -0.103117330 0.06730267 0.1317134148 0.17176740 0.072982024
17 -0.192825214 0.04684707 0.1279847332 0.09152784 0.153400768
18 -0.097032137 0.05689834 0.1338593646 0.13412624 0.065676588
19 -0.199767968 0.01788578 0.0733258041 0.05520932 0.084107052
20 -0.126808714 -0.00562211 0.0126196789 -0.02084153 0.061604516
22 -0.156404295 0.02848354 0.0755602517 0.05215784 0.130604689
23 0.288641611 -0.19459030 -0.2622261227 -0.24690591 -0.229409796
with conditional variances for "subject" print(head(sd_mixed_diagnostics$Mixed_X$ScaledResiduals)) 1 2 3 4 5 6
-0.2362797 -0.1681371 0.1413259 -1.0167938 0.3667212 -0.5659619 # --- Print Diagnostics Example (Axis X) ---
cat("\n=== SD LMM: Axis Y ===\n")
=== SD LMM: Axis Y ===print(sd_mixed_diagnostics$Mixed_Y$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
TrialInBlock 0.232 0.232 1 5188.0 2.8680 0.090415 .
Block 1.718 0.430 4 39.9 5.3171 0.001578 **
phase 279.561 279.561 1 6435.5 3460.2860 < 2.2e-16 ***
TrialInBlock:Block 0.663 0.166 4 5224.0 2.0511 0.084541 .
TrialInBlock:phase 20.396 20.396 1 6436.2 252.4581 < 2.2e-16 ***
Block:phase 5.904 1.476 4 6435.5 18.2685 6.184e-15 ***
TrialInBlock:Block:phase 9.118 2.279 4 6436.2 28.2133 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(sd_mixed_diagnostics$Mixed_Y$Emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 0.9118 0.0586 17.7 0.7885 1.035
2 Execution 0.8268 0.0548 18.1 0.7116 0.942
3 Execution 0.6162 0.0367 22.7 0.5402 0.692
4 Execution 0.7805 0.0422 18.1 0.6918 0.869
5 Execution 0.6118 0.0242 20.8 0.5614 0.662
1 Preparation 0.0672 0.0585 17.6 -0.0560 0.190
2 Preparation 0.1630 0.0548 18.0 0.0479 0.278
3 Preparation 0.2246 0.0364 22.1 0.1490 0.300
4 Preparation 0.1009 0.0422 18.1 0.0123 0.190
5 Preparation 0.1000 0.0242 20.7 0.0496 0.150
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(sd_mixed_diagnostics$Mixed_Y$FixedEffects) (Intercept) TrialInBlock
0.8897810297 0.0011082715
Block2 Block3
0.0822160265 -0.0101378448
Block4 Block5
-0.0282883665 -0.2550414971
phasePreparation TrialInBlock:Block2
-0.8348514013 -0.0084211023
TrialInBlock:Block3 TrialInBlock:Block4
-0.0143766421 -0.0051883951
TrialInBlock:Block5 TrialInBlock:phasePreparation
-0.0022635025 -0.0004895652
Block2:phasePreparation Block3:phasePreparation
-0.1570715557 -0.0244418559
Block4:phasePreparation Block5:phasePreparation
-0.0371109447 0.2002025356
TrialInBlock:Block2:phasePreparation TrialInBlock:Block3:phasePreparation
0.0170130632 0.0240441539
TrialInBlock:Block4:phasePreparation TrialInBlock:Block5:phasePreparation
0.0101794347 0.0066785128 print(sd_mixed_diagnostics$Mixed_Y$RandomEffects)$subject
(Intercept) Block2 Block3 Block4 Block5
2 -0.08234594 0.185087259 0.21785201 0.17962949 0.17679332
3 0.04611270 0.030726485 0.03928753 0.02114883 -0.01357963
4 -0.18744612 -0.017242124 0.08289313 0.04887136 0.15646520
5 -0.22431229 -0.007321099 0.06374761 0.02113200 0.08861165
7 -0.11122260 0.029650181 0.06720228 0.03336942 0.12308974
8 0.14526321 0.086655267 -0.05307747 0.01753172 -0.09464450
10 0.45010656 0.015506627 -0.07733778 -0.01851272 -0.22497245
11 0.50219223 0.052184107 -0.38386833 -0.19761004 -0.53817922
13 0.08345246 -0.174887857 -0.19853261 -0.17321943 -0.11352360
14 0.13354972 -0.095393264 -0.13814968 -0.12584080 -0.13187409
15 -0.12732127 -0.048888855 0.07609548 0.03206445 0.16208994
16 -0.12626597 0.073484805 0.15052722 0.13297897 0.16768904
17 -0.25109265 0.127282488 0.21870252 0.16863979 0.23151458
18 -0.09146300 0.015964763 0.13349575 0.08206185 0.06999104
19 -0.21066210 0.020881983 0.03255722 0.01429839 0.06453651
20 -0.15620016 0.052418546 0.04419543 0.01924245 0.03648449
22 -0.20574993 0.010400748 0.08228253 0.04755815 0.15636494
23 0.41340515 -0.356510062 -0.35787284 -0.30334390 -0.31685696
with conditional variances for "subject" print(head(sd_mixed_diagnostics$Mixed_Y$ScaledResiduals)) 1 2 3 4 5 6
-0.1962739 -0.2278271 0.4396876 -0.6653148 -0.1065930 -0.6182290 # --- Print Diagnostics Example (Axis X) ---
cat("\n=== SD LMM: Axis Z ===\n")
=== SD LMM: Axis Z ===print(sd_mixed_diagnostics$Mixed_Z$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
TrialInBlock 2.52 2.52 1 5510.2 11.8939 0.0005674 ***
Block 4.44 1.11 4 38.5 5.2332 0.0018246 **
phase 782.80 782.80 1 6435.6 3691.2368 < 2.2e-16 ***
TrialInBlock:Block 3.26 0.81 4 5576.1 3.8377 0.0040594 **
TrialInBlock:phase 50.32 50.32 1 6436.2 237.2811 < 2.2e-16 ***
Block:phase 16.84 4.21 4 6435.7 19.8532 2.922e-16 ***
TrialInBlock:Block:phase 26.47 6.62 4 6436.3 31.1994 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(sd_mixed_diagnostics$Mixed_Z$Emmeans)) Block phase emmean SE df lower.CL upper.CL
1 Execution 1.4196 0.0878 17.8 1.2351 1.604
2 Execution 1.3741 0.0888 18.1 1.1877 1.561
3 Execution 1.0528 0.0687 21.1 0.9100 1.196
4 Execution 1.3081 0.0666 18.2 1.1682 1.448
5 Execution 1.0221 0.0508 19.1 0.9158 1.128
1 Preparation 0.0748 0.0876 17.7 -0.1095 0.259
2 Preparation 0.2279 0.0887 18.0 0.0415 0.414
3 Preparation 0.3327 0.0684 20.7 0.1904 0.475
4 Preparation 0.1288 0.0666 18.2 -0.0111 0.269
5 Preparation 0.1267 0.0508 19.1 0.0204 0.233
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(sd_mixed_diagnostics$Mixed_Z$FixedEffects) (Intercept) TrialInBlock
1.341741268 0.003922163
Block2 Block3
0.185823520 0.149101971
Block4 Block5
0.120401517 -0.321050371
phasePreparation TrialInBlock:Block2
-1.298535171 -0.011649781
TrialInBlock:Block3 TrialInBlock:Block4
-0.025982147 -0.011679048
TrialInBlock:Block5 TrialInBlock:phasePreparation
-0.003849036 -0.002329397
Block2:phasePreparation Block3:phasePreparation
-0.307614345 -0.216104710
Block4:phasePreparation Block5:phasePreparation
-0.226894068 0.227467258
TrialInBlock:Block2:phasePreparation TrialInBlock:Block3:phasePreparation
0.025491280 0.042344641
TrialInBlock:Block4:phasePreparation TrialInBlock:Block5:phasePreparation
0.019758505 0.011175646 print(sd_mixed_diagnostics$Mixed_Z$RandomEffects)$subject
(Intercept) Block2 Block3 Block4 Block5
2 -0.30814638 0.2294529029 0.355770427 0.26626784 0.32513676
3 0.33931050 -0.2224618321 -0.274188557 -0.26835375 -0.34185102
4 -0.16498059 -0.1098020214 -0.044309010 -0.03275700 0.12512196
5 -0.32110439 -0.0249757532 0.007379763 -0.01210276 -0.01133951
7 -0.01433727 0.0191648020 0.113187192 0.10448933 -0.01003884
8 0.23908248 0.1732785798 -0.045565883 0.04541524 -0.04813707
10 0.48215997 0.1960701192 0.173182408 0.10486479 0.03346474
11 0.86180585 0.0216850999 -0.638736567 -0.45985346 -0.84410570
13 0.12409308 -0.2496958168 -0.280339405 -0.22561690 0.01598564
14 -0.03086219 -0.0048061321 0.090539945 0.05475269 -0.03247776
15 -0.13856395 -0.1082509979 -0.045030319 -0.06627008 0.31934134
16 -0.08506709 0.2409337594 0.259708867 0.22973424 0.19159645
17 -0.45334855 0.0935573501 0.313503133 0.24907473 0.31135975
18 -0.08421651 0.0808597662 0.349342671 0.25776675 0.04866049
19 -0.31123439 -0.0307044060 -0.024431129 -0.02492679 0.03281403
20 -0.25232766 0.0136265854 0.020800977 0.01380094 0.07789839
22 -0.39354146 -0.0009274911 0.047353663 0.03946954 0.19078152
23 0.51127856 -0.3170045144 -0.378168178 -0.27575534 -0.38421115
with conditional variances for "subject" print(head(sd_mixed_diagnostics$Mixed_Z$ScaledResiduals)) 1 2 3 4 5 6
0.405538236 0.082510827 -0.253608734 -1.000084912 0.003132928 -0.709006436 4.2 LMM step level
# Extract Step-Level RMS with ±3 Line Buffer Around Markers
extract_step_rms <- function(df, label) {
buffer <- 3
step_markers <- c(14, 15, 16, 17)
step_data <- df %>%
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)
# Extract ±3 rows around each marker
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)
})
# Compute RMS over buffered region
window_data %>%
group_by(subject, Block, 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 = gsub("rms_", "", Axis),
Dataset = label,
Step = factor(Step), # ✅ Now a factor
subject = factor(subject),
Block = factor(Block)
)
}
# --- Run Step-Level LMMs and Extract ANOVA p-values ---
run_step_model <- function(df, label) {
get_anova <- function(axis_label) {
model <- lmer(RMS ~ Step * Block + (1 | subject), data = filter(df, Axis == axis_label))
anova(model)
}
ax <- get_anova("x")
ay <- get_anova("y")
az <- get_anova("z")
tibble(
Dataset = label,
Axis = c("X", "Y", "Z"),
`Step p-value` = c(ax["Step", "Pr(>F)"], ay["Step", "Pr(>F)"], az["Step", "Pr(>F)"]),
`Block p-value` = c(ax["Block", "Pr(>F)"], ay["Block", "Pr(>F)"], az["Block", "Pr(>F)"]),
`Interaction p-value` = c(ax["Step:Block", "Pr(>F)"], ay["Step:Block", "Pr(>F)"], az["Step:Block", "Pr(>F)"])
)
}
# --- Execute Updated Step-Level RMS Analysis ---
step_rms_data <- extract_step_rms(tagged_data, "Mixed")
step_model_results <- run_step_model(step_rms_data, "Mixed")fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsMissing cells for: Step7:Block1, Step8:Block1, Step9:Block1, Step10:Block1, Step11:Block1, Step12:Block1, Step13:Block1, Step14:Block1, Step15:Block1, Step16:Block1, Step17:Block1, Step18:Block1, Step13:Block2, Step14:Block2, Step15:Block2, Step16:Block2, Step17:Block2, Step18:Block2.
Interpret type III hypotheses with care.fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsMissing cells for: Step7:Block1, Step8:Block1, Step9:Block1, Step10:Block1, Step11:Block1, Step12:Block1, Step13:Block1, Step14:Block1, Step15:Block1, Step16:Block1, Step17:Block1, Step18:Block1, Step13:Block2, Step14:Block2, Step15:Block2, Step16:Block2, Step17:Block2, Step18:Block2.
Interpret type III hypotheses with care.fixed-effect model matrix is rank deficient so dropping 18 columns / coefficientsMissing cells for: Step7:Block1, Step8:Block1, Step9:Block1, Step10:Block1, Step11:Block1, Step12:Block1, Step13:Block1, Step14:Block1, Step15:Block1, Step16:Block1, Step17:Block1, Step18:Block1, Step13:Block2, Step14:Block2, Step15:Block2, Step16:Block2, Step17:Block2, Step18:Block2.
Interpret type III hypotheses with care.# --- Output ---
print(step_model_results)# A tibble: 3 × 5
Dataset Axis `Step p-value` `Block p-value` `Interaction p-value`
<chr> <chr> <dbl> <dbl> <dbl>
1 Mixed X 0.0125 5.77e-36 1.00
2 Mixed Y 0.00339 7.44e-15 1.00
3 Mixed Z 0.0537 2.89e-28 1.00# -------- Suppress Emmeans Warnings Globally --------
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# --- Extract Step-Level RMS with ±3 Row Buffer Around Markers ---
extract_step_rms <- function(df, label) {
buffer <- 3
step_markers <- c(14, 15, 16, 17)
step_data <- df %>%
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)
})
window_data %>%
group_by(subject, Block, 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 = gsub("rms_", "", Axis),
Dataset = label,
Step = as.numeric(Step),
subject = factor(subject),
Block = factor(Block)
)
}
# --- Run Step-Level LMMs with Full Diagnostics ---
run_step_model_diagnostics <- function(df, label) {
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
data_sub <- df %>% filter(Axis == axis)
model <- lmer(RMS ~ Step * Block + (1 | subject), data = data_sub)
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
ANOVA = anova(model),
Emmeans = emmeans(model, ~ Step * Block),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
return(results)
}
# --- Run Analysis and Extract Diagnostics ---
step_rms_data <- extract_step_rms(tagged_data, "Mixed")
step_model_diag_results <- run_step_model_diagnostics(step_rms_data, "Mixed")
# --- Print Diagnostics Example for Axis X ---
cat("\n=== STEP-LEVEL RMS LMM: Axis X ===\n")
=== STEP-LEVEL RMS LMM: Axis X ===print(step_model_diag_results$Mixed_X$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.23877 0.23877 1 1269 6.9077 0.008686 **
Block 2.41418 0.60355 4 1269 17.4610 5.874e-14 ***
Step:Block 0.31355 0.07839 4 1269 2.2678 0.059955 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(step_model_diag_results$Mixed_X$Emmeans)) Step Block emmean SE df lower.CL upper.CL
8.5 1 0.926 0.0896 43.8 0.745 1.106
8.5 2 0.780 0.0720 18.3 0.629 0.931
8.5 3 0.655 0.0713 17.6 0.505 0.805
8.5 4 0.759 0.0713 17.6 0.609 0.909
8.5 5 0.654 0.0713 17.6 0.504 0.804
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(step_model_diag_results$Mixed_X$FixedEffects) (Intercept) Step Block2 Block3 Block4 Block5
0.915119362 0.001237707 -0.001022194 -0.210534955 -0.100201149 -0.229933792
Step:Block2 Step:Block3 Step:Block4 Step:Block5
-0.017027599 -0.007057896 -0.007769410 -0.004876759 print(step_model_diag_results$Mixed_X$RandomEffects)$subject
(Intercept)
2 0.11002898
3 0.03724100
4 -0.24933085
5 -0.34342046
7 -0.15999779
8 0.31398331
10 0.81534049
11 0.52169432
13 -0.18853320
14 0.03463009
15 -0.06972254
16 -0.06112373
17 -0.18563684
18 -0.03037388
19 -0.28291659
20 -0.24510198
22 -0.14256874
23 0.12580842
with conditional variances for "subject" print(head(step_model_diag_results$Mixed_X$ScaledResiduals)) 1 2 3 4 5 6
-2.407074 -2.365733 -2.359757 -2.366414 -2.201504 -2.278840 # --- Print Diagnostics Example for Axis Y ---
cat("\n=== STEP-LEVEL RMS LMM: Axis Y ===\n")
=== STEP-LEVEL RMS LMM: Axis Y ===print(step_model_diag_results$Mixed_Y$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.44036 0.44036 1 1269 6.1963 0.01293 *
Block 2.38367 0.59592 4 1269 8.3853 1.123e-06 ***
Step:Block 0.36458 0.09115 4 1269 1.2825 0.27483
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(step_model_diag_results$Mixed_Y$Emmeans)) Step Block emmean SE df lower.CL upper.CL
8.5 1 0.920 0.1120 67.1 0.697 1.143
8.5 2 0.852 0.0814 19.2 0.682 1.022
8.5 3 0.676 0.0801 17.9 0.507 0.844
8.5 4 0.812 0.0801 17.9 0.644 0.980
8.5 5 0.750 0.0801 17.9 0.582 0.918
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(step_model_diag_results$Mixed_Y$FixedEffects) (Intercept) Step Block2 Block3 Block4 Block5
0.935720192 -0.001859348 0.011416990 -0.219819184 -0.009199095 -0.098823885
Step:Block2 Step:Block3 Step:Block4 Step:Block5
-0.009354914 -0.002880084 -0.011599384 -0.008347937 print(step_model_diag_results$Mixed_Y$RandomEffects)$subject
(Intercept)
2 0.215930304
3 0.181924219
4 -0.295210899
5 -0.351153879
7 -0.199510787
8 0.404200990
10 0.767464280
11 0.428233663
13 -0.188243262
14 0.005818085
15 -0.130100848
16 -0.078256254
17 -0.160586355
18 -0.075812111
19 -0.347035341
20 -0.274834330
22 -0.351687924
23 0.448860452
with conditional variances for "subject" print(head(step_model_diag_results$Mixed_Y$ScaledResiduals)) 1 2 3 4 5 6
-2.024183 -2.162425 -2.129534 -2.122559 -2.028701 -1.911946 # --- Print Diagnostics Example for Axis Z ---
cat("\n=== STEP-LEVEL RMS LMM: Axis Z ===\n")
=== STEP-LEVEL RMS LMM: Axis Z ===print(step_model_diag_results$Mixed_Z$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.5721 0.57209 1 1269 3.6005 0.05799 .
Block 9.0610 2.26524 4 1269 14.2565 2.181e-11 ***
Step:Block 1.4199 0.35499 4 1269 2.2341 0.06333 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(step_model_diag_results$Mixed_Z$Emmeans)) Step Block emmean SE df lower.CL upper.CL
8.5 1 1.94 0.201 39.4 1.54 2.35
8.5 2 1.72 0.166 18.1 1.37 2.06
8.5 3 1.44 0.164 17.5 1.09 1.78
8.5 4 1.65 0.164 17.5 1.30 2.00
8.5 5 1.43 0.164 17.5 1.09 1.78
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(step_model_diag_results$Mixed_Z$FixedEffects) (Intercept) Step Block2 Block3 Block4 Block5
1.907241742 0.004300091 -0.062824207 -0.428918866 -0.072468609 -0.387961951
Step:Block2 Step:Block3 Step:Block4 Step:Block5
-0.019328358 -0.009085057 -0.026036291 -0.014328949 print(step_model_diag_results$Mixed_Z$RandomEffects)$subject
(Intercept)
2 -0.09776719
3 0.29920593
4 -0.65956180
5 -0.81472718
7 0.13898391
8 0.55945688
10 1.96205535
11 0.83171422
13 -0.13930132
14 -0.26992210
15 -0.04939117
16 0.15528059
17 -0.64051400
18 0.33940562
19 -0.73185992
20 -0.59496903
22 -0.59578675
23 0.30769796
with conditional variances for "subject" print(head(step_model_diag_results$Mixed_Z$ScaledResiduals)) 1 2 3 4 5 6
-1.707922 -1.851905 -2.013106 -2.023894 -2.268428 -2.198652 #4.3 Model: Does Sequence Length Influence RMS?
# --- Compute RMS with Sequence Length per Trial ---
compute_step_rms_with_sequence_length <- function(df, label) {
df %>%
filter(phase == "Execution", Marker.Text %in% c(14, 15, 16, 17)) %>%
group_by(subject, Block, trial) %>%
mutate(SequenceLength = n()) %>%
group_by(subject, Block, trial, Marker.Text, SequenceLength) %>%
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 = gsub("rms_", "", Axis),
Dataset = label,
subject = factor(subject),
SequenceLength = factor(SequenceLength)
)
}
# --- LMM per Axis for Sequence Length Effect ---
run_sequence_length_model <- function(df, label) {
get_anova <- function(axis_label) {
model <- lmer(RMS ~ SequenceLength + (1 | subject), data = filter(df, Axis == axis_label))
anova(model)
}
ax <- get_anova("x")
ay <- get_anova("y")
az <- get_anova("z")
tibble(
Dataset = label,
Axis = c("X", "Y", "Z"),
`SequenceLength p-value` = c(ax["SequenceLength", "Pr(>F)"],
ay["SequenceLength", "Pr(>F)"],
az["SequenceLength", "Pr(>F)"])
)
}
# --- Run Sequence Length Analysis on Mixed Data ---
step_rms_seq_mixed <- compute_step_rms_with_sequence_length(tagged_data, "Mixed")
seq_length_pvals <- run_sequence_length_model(step_rms_seq_mixed, "Mixed")
# --- Display Results ---
print(seq_length_pvals)# A tibble: 3 × 3
Dataset Axis `SequenceLength p-value`
<chr> <chr> <dbl>
1 Mixed X 0.00000000547
2 Mixed Y 0.0000863
3 Mixed Z 0.000000826 # --- Suppress lmerTest/pbkrtest warnings globally ---
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# --- Compute RMS with Sequence Length per Trial ---
compute_step_rms_with_sequence_length <- function(df, label) {
df %>%
filter(phase == "Execution", Marker.Text %in% c(14, 15, 16, 17)) %>%
group_by(subject, Block, trial) %>%
mutate(SequenceLength = n()) %>%
group_by(subject, Block, trial, Marker.Text, SequenceLength) %>%
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 = gsub("rms_", "", Axis),
Dataset = label,
subject = factor(subject),
SequenceLength = factor(SequenceLength)
)
}
# --- Extended: LMM per Axis for Sequence Length Effect + Diagnostics ---
run_sequence_length_model_diagnostics <- function(df, label) {
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
model <- lmer(RMS ~ SequenceLength + (1 | subject), data = filter(df, Axis == axis))
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
ANOVA = anova(model),
Emmeans = emmeans(model, ~ SequenceLength),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
return(results)
}
# --- Run Model and Extract Diagnostics ---
step_rms_seq_mixed <- compute_step_rms_with_sequence_length(tagged_data, "Mixed")
seq_length_diag <- run_sequence_length_model_diagnostics(step_rms_seq_mixed, "Mixed")
# --- Display Diagnostics for Axis X ---
cat("\n=== SEQUENCE LENGTH RMS MODEL: Axis X ===\n")
=== SEQUENCE LENGTH RMS MODEL: Axis X ===print(seq_length_diag$Mixed_X$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
SequenceLength 12.509 2.5017 5 12832 9.4326 5.467e-09 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(seq_length_diag$Mixed_X$Emmeans)) SequenceLength emmean SE df lower.CL upper.CL
4 0.7637 0.1930 1641.3 0.386 1.141
5 0.8554 0.1360 445.2 0.588 1.123
6 0.6433 0.0600 17.4 0.517 0.770
11 -0.0672 0.1920 1626.5 -0.444 0.309
12 0.6300 0.0601 17.4 0.504 0.757
18 0.5853 0.0601 17.5 0.459 0.712
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(seq_length_diag$Mixed_X$FixedEffects) (Intercept) SequenceLength5 SequenceLength6 SequenceLength11
0.76370009 0.09171029 -0.12044732 -0.83088215
SequenceLength12 SequenceLength18
-0.13366738 -0.17843204 print(seq_length_diag$Mixed_X$RandomEffects)$subject
(Intercept)
2 0.02489508
3 0.08326921
4 -0.21935031
5 -0.28237119
7 -0.15103986
8 0.26310369
10 0.67778730
11 0.41232158
13 -0.18595566
14 0.06469506
15 -0.01953860
16 -0.03857193
17 -0.18366675
18 -0.06357062
19 -0.25103141
20 -0.19254560
22 -0.11384027
23 0.17541029
with conditional variances for "subject" print(head(seq_length_diag$Mixed_X$ScaledResiduals)) 1 2 3 4 5 6
-0.6827629 -0.8548025 0.0423730 -0.1269665 -0.7462673 -0.5825483 # --- Display Diagnostics for Axis Y ---
cat("\n=== SEQUENCE LENGTH RMS MODEL: Axis Y ===\n")
=== SEQUENCE LENGTH RMS MODEL: Axis Y ===print(seq_length_diag$Mixed_Y$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
SequenceLength 8.5664 1.7133 5 12832 5.2197 8.629e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(seq_length_diag$Mixed_Y$Emmeans)) SequenceLength emmean SE df lower.CL upper.CL
4 0.661 0.2140 1654.1 0.241 1.081
5 0.462 0.1510 448.7 0.165 0.759
6 0.661 0.0666 17.4 0.520 0.801
11 0.275 0.2140 1639.3 -0.144 0.694
12 0.669 0.0667 17.4 0.529 0.810
18 0.615 0.0667 17.5 0.475 0.756
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(seq_length_diag$Mixed_Y$FixedEffects) (Intercept) SequenceLength5 SequenceLength6 SequenceLength11
0.6613243056 -0.1994382630 -0.0007259362 -0.3866337575
SequenceLength12 SequenceLength18
0.0081033492 -0.0460787019 print(seq_length_diag$Mixed_Y$RandomEffects)$subject
(Intercept)
2 0.16437097
3 0.16331899
4 -0.27385113
5 -0.29253679
7 -0.15742241
8 0.34376582
10 0.70260269
11 0.37257745
13 -0.18343453
14 0.08767554
15 -0.12664871
16 -0.04886466
17 -0.14491544
18 -0.04644085
19 -0.27856427
20 -0.21896539
22 -0.28502361
23 0.22235631
with conditional variances for "subject" print(head(seq_length_diag$Mixed_Y$ScaledResiduals)) 1 2 3 4 5 6
-0.9029029 -1.3907004 -0.9201271 -1.0519783 -1.3013022 -1.2657374 # --- Display Diagnostics for Axis Z ---
cat("\n=== SEQUENCE LENGTH RMS MODEL: Axis Z ===\n")
=== SEQUENCE LENGTH RMS MODEL: Axis Z ===print(seq_length_diag$Mixed_Z$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
SequenceLength 38.542 7.7084 5 12832 7.2702 8.257e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(seq_length_diag$Mixed_Z$Emmeans)) SequenceLength emmean SE df lower.CL upper.CL
4 1.6260 0.390 1124.9 0.861 2.391
5 1.2101 0.279 310.6 0.662 1.758
6 1.4232 0.135 17.3 1.139 1.707
11 0.0696 0.389 1114.3 -0.693 0.832
12 1.3848 0.135 17.3 1.101 1.669
18 1.3171 0.135 17.4 1.033 1.601
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(seq_length_diag$Mixed_Z$FixedEffects) (Intercept) SequenceLength5 SequenceLength6 SequenceLength11
1.6259910 -0.4159359 -0.2028338 -1.5564279
SequenceLength12 SequenceLength18
-0.2411451 -0.3089131 print(seq_length_diag$Mixed_Z$RandomEffects)$subject
(Intercept)
2 -0.14574863
3 0.29801432
4 -0.60504327
5 -0.72630042
7 0.17801680
8 0.52524867
10 1.41134086
11 0.69413886
13 -0.10292345
14 -0.32161570
15 0.03962644
16 0.19739584
17 -0.61375376
18 0.33765739
19 -0.63553399
20 -0.48683277
22 -0.46516627
23 0.42147909
with conditional variances for "subject" print(head(seq_length_diag$Mixed_Z$ScaledResiduals)) 1 2 3 4 5 6
-0.73126265 -0.36255661 -0.95756250 -0.10941782 0.18974358 -0.08769942 #4.4 Model: Does Sequence Length Influence SD?
# --- Compute SD with Sequence Length per Trial ---
compute_step_sd_with_sequence_length <- function(df, label) {
df %>%
filter(phase == "Execution", Marker.Text %in% c(14, 15, 16, 17)) %>%
group_by(subject, Block, trial) %>%
mutate(SequenceLength = n()) %>%
group_by(subject, Block, trial, Marker.Text, SequenceLength) %>%
summarise(
sd_x = sd(CoM.acc.x, na.rm = TRUE),
sd_y = sd(CoM.acc.y, na.rm = TRUE),
sd_z = sd(CoM.acc.z, na.rm = TRUE),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("sd_"), names_to = "Axis", values_to = "SD") %>%
mutate(
Axis = gsub("sd_", "", Axis),
Dataset = label,
subject = factor(subject),
SequenceLength = factor(SequenceLength)
)
}
# --- LMM per Axis for Sequence Length Effect on SD ---
run_sequence_length_sd_model <- function(df, label) {
get_anova <- function(axis_label) {
model <- lmer(SD ~ SequenceLength + (1 | subject), data = filter(df, Axis == axis_label))
anova(model)
}
ax <- get_anova("x")
ay <- get_anova("y")
az <- get_anova("z")
tibble(
Dataset = label,
Axis = c("X", "Y", "Z"),
`SequenceLength p-value` = c(ax["SequenceLength", "Pr(>F)"],
ay["SequenceLength", "Pr(>F)"],
az["SequenceLength", "Pr(>F)"])
)
}
# --- Run Sequence Length SD Analysis on Mixed Data ---
step_sd_seq_mixed <- compute_step_sd_with_sequence_length(tagged_data, "Mixed")
seq_length_sd_pvals <- run_sequence_length_sd_model(step_sd_seq_mixed, "Mixed")
# --- Display SD Model Results ---
print(seq_length_sd_pvals)# A tibble: 3 × 3
Dataset Axis `SequenceLength p-value`
<chr> <chr> <dbl>
1 Mixed X 0.000210
2 Mixed Y 0.0214
3 Mixed Z 0.0000533# --- Suppress emmeans/pbkrtest warnings globally ---
emmeans::emm_options(
lmerTest.limit = Inf,
pbkrtest.limit = Inf
)
# --- Compute SD with Sequence Length per Trial ---
compute_step_sd_with_sequence_length <- function(df, label) {
df %>%
filter(phase == "Execution", Marker.Text %in% c(14, 15, 16, 17)) %>%
group_by(subject, Block, trial) %>%
mutate(SequenceLength = n()) %>%
group_by(subject, Block, trial, Marker.Text, SequenceLength) %>%
summarise(
sd_x = sd(CoM.acc.x, na.rm = TRUE),
sd_y = sd(CoM.acc.y, na.rm = TRUE),
sd_z = sd(CoM.acc.z, na.rm = TRUE),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("sd_"), names_to = "Axis", values_to = "SD") %>%
mutate(
Axis = gsub("sd_", "", Axis),
Dataset = label,
subject = factor(subject),
SequenceLength = factor(SequenceLength)
)
}
# --- Extended: LMM per Axis for Sequence Length Effect on SD ---
run_sequence_length_sd_model_diagnostics <- function(df, label) {
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
model <- lmer(SD ~ SequenceLength + (1 | subject), data = filter(df, Axis == axis))
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
ANOVA = anova(model),
Emmeans = emmeans(model, ~ SequenceLength),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
return(results)
}
# --- Run Model and Extract Diagnostics ---
step_sd_seq_mixed <- compute_step_sd_with_sequence_length(tagged_data, "Mixed")
seq_length_sd_diag <- run_sequence_length_sd_model_diagnostics(step_sd_seq_mixed, "Mixed")
# --- Display Diagnostics for Axis X ---
cat("\n=== SEQUENCE LENGTH SD MODEL: Axis X ===\n")
=== SEQUENCE LENGTH SD MODEL: Axis X ===print(seq_length_sd_diag$Mixed_X$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
SequenceLength 5.1399 1.285 4 10494 5.479 0.0002103 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(seq_length_sd_diag$Mixed_X$Emmeans)) SequenceLength emmean SE df lower.CL upper.CL
5 0.865 0.1910 2419.6 0.491 1.239
6 0.526 0.0530 18.0 0.415 0.637
11 -0.079 0.1790 1985.8 -0.431 0.273
12 0.547 0.0526 17.4 0.436 0.658
18 0.522 0.0526 17.5 0.411 0.633
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(seq_length_sd_diag$Mixed_X$FixedEffects) (Intercept) SequenceLength6 SequenceLength11 SequenceLength12
0.8647651 -0.3388310 -0.9437831 -0.3178414
SequenceLength18
-0.3424989 print(seq_length_sd_diag$Mixed_X$RandomEffects)$subject
(Intercept)
2 0.05357079
3 0.05179505
4 -0.17197087
5 -0.23596647
7 -0.09540464
8 0.16549144
10 0.63696777
11 0.33174416
13 -0.13389309
14 0.15327494
15 -0.09959260
16 -0.02519785
17 -0.12802594
18 -0.05634306
19 -0.20015367
20 -0.16863686
22 -0.17314635
23 0.09548725
with conditional variances for "subject" print(head(seq_length_sd_diag$Mixed_X$ScaledResiduals)) 1 3 5 7 9 11
-0.8944736 -1.0235233 -1.1320258 -0.8847848 -0.8272984 -1.0565356 # --- Display Diagnostics for Axis Y ---
cat("\n=== SEQUENCE LENGTH SD MODEL: Axis Y ===\n")
=== SEQUENCE LENGTH SD MODEL: Axis Y ===print(seq_length_sd_diag$Mixed_Y$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
SequenceLength 3.436 0.859 4 10494 2.8777 0.02143 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(seq_length_sd_diag$Mixed_Y$Emmeans)) SequenceLength emmean SE df lower.CL upper.CL
5 0.374 0.2150 2605.1 -0.0469 0.796
6 0.554 0.0583 18.1 0.4319 0.677
11 0.224 0.2020 2144.8 -0.1721 0.620
12 0.576 0.0578 17.4 0.4541 0.698
18 0.543 0.0579 17.5 0.4207 0.664
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(seq_length_sd_diag$Mixed_Y$FixedEffects) (Intercept) SequenceLength6 SequenceLength11 SequenceLength12
0.3743739 0.1801059 -0.1502666 0.2014899
SequenceLength18
0.1681699 print(seq_length_sd_diag$Mixed_Y$RandomEffects)$subject
(Intercept)
2 0.10951141
3 0.12664285
4 -0.19684764
5 -0.25913656
7 -0.06860125
8 0.26833537
10 0.61703214
11 0.32411261
13 -0.14357021
14 0.12144695
15 -0.12156601
16 -0.05942662
17 -0.11835536
18 -0.08892038
19 -0.26722993
20 -0.19137652
22 -0.26257925
23 0.21052840
with conditional variances for "subject" print(head(seq_length_sd_diag$Mixed_Y$ScaledResiduals)) 1 3 5 7 9 11
-0.4348516 -1.0671381 -1.1047401 -1.0053693 -0.2228061 -0.3297785 # --- Display Diagnostics for Axis Z ---
cat("\n=== SEQUENCE LENGTH SD MODEL: Axis Z ===\n")
=== SEQUENCE LENGTH SD MODEL: Axis Z ===print(seq_length_sd_diag$Mixed_Z$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
SequenceLength 22.772 5.6931 4 10494 6.2253 5.333e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(seq_length_sd_diag$Mixed_Z$Emmeans)) SequenceLength emmean SE df lower.CL upper.CL
5 1.2085 0.3740 3203.6 0.475 1.942
6 0.8894 0.0950 18.2 0.690 1.089
11 0.0981 0.3520 2666.3 -0.591 0.788
12 0.9910 0.0940 17.5 0.793 1.189
18 0.9749 0.0941 17.6 0.777 1.173
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(seq_length_sd_diag$Mixed_Z$FixedEffects) (Intercept) SequenceLength6 SequenceLength11 SequenceLength12
1.2085449 -0.3191928 -1.1104780 -0.2175467
SequenceLength18
-0.2336458 print(seq_length_sd_diag$Mixed_Z$RandomEffects)$subject
(Intercept)
2 -5.668181e-03
3 2.204648e-01
4 -3.089863e-01
5 -4.538521e-01
7 9.664095e-02
8 5.206798e-01
10 9.713584e-01
11 5.823385e-01
13 -9.885303e-02
14 -1.358140e-01
15 -2.836437e-02
16 -4.906112e-03
17 -3.613736e-01
18 -4.733085e-05
19 -3.992486e-01
20 -3.788382e-01
22 -4.349800e-01
23 2.194495e-01
with conditional variances for "subject" print(head(seq_length_sd_diag$Mixed_Z$ScaledResiduals)) 1 3 5 7 9 11
-0.77140783 -0.84919395 0.04769161 -0.89023568 1.36427252 -0.80744817 #5 top 50% vs bottom 50%
# --- Tag Top vs Bottom Performers ---
tag_performance_group <- function(df) {
top_ids <- c(17, 7, 23, 16, 10, 14, 13, 2, 8)
df %>%
mutate(
PerformanceGroup = ifelse(subject %in% top_ids, "Top", "Bottom"),
PerformanceGroup = factor(PerformanceGroup, levels = c("Top", "Bottom"))
)
}
# --- Compute Step-Level RMS with Buffer + Performance Group ---
compute_step_rms_grouped <- function(df) {
buffer <- 3
step_markers <- c(14, 15, 16, 17)
step_data <- df %>%
filter(phase == "Execution", Marker.Text %in% step_markers) %>%
assign_steps_by_block() %>%
arrange(subject, Block, trial, ms) %>%
group_by(subject, Block, trial) %>%
mutate(row_id = row_number()) %>%
ungroup()
step_indices <- step_data %>%
select(subject, Block, trial, row_id, Step)
window_data <- map_dfr(1:nrow(step_indices), function(i) {
step <- step_indices[i, ]
rows <- (step$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$Step)
})
window_data %>%
group_by(subject, Block, Step) %>%
summarise(
rms_x = sqrt(mean(CoM.acc.x^2, na.rm = TRUE)),
rms_y = sqrt(mean(CoM.acc.y^2, na.rm = TRUE)),
rms_z = sqrt(mean(CoM.acc.z^2, na.rm = TRUE)),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("rms_"), names_to = "Axis", values_to = "RMS") %>%
mutate(
Axis = gsub("rms_", "", Axis),
Step = as.numeric(Step),
subject = factor(subject),
Block = factor(Block)
) %>%
tag_performance_group()
}
# --- Run LMM to Compare Top vs Bottom ---
run_group_comparison_model <- function(df, label) {
axes <- c("x", "y", "z")
results <- list()
for (axis in axes) {
model <- lmer(
RMS ~ Step * Block * PerformanceGroup + (1 | subject),
data = filter(df, Axis == axis)
)
key <- paste0(label, "_", toupper(axis))
results[[key]] <- list(
ANOVA = anova(model),
Emmeans = emmeans(model, ~ Step * Block * PerformanceGroup),
FixedEffects = fixef(model),
RandomEffects = ranef(model),
ScaledResiduals = resid(model, scaled = TRUE),
Model = model
)
}
return(results)
}
# --- Compute and Run ---
step_rms_grouped <- compute_step_rms_grouped(tagged_data)
top_bottom_results <- run_group_comparison_model(step_rms_grouped, "StepRMS_PerfGroup")
# --- Inspect X-Axis Results ---
cat("\n=== TOP vs BOTTOM PERFORMER ANALYSIS: Axis X ===\n")
=== TOP vs BOTTOM PERFORMER ANALYSIS: Axis X ===print(top_bottom_results$StepRMS_PerfGroup_X$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.23877 0.23877 1 1260.00 7.0907 0.007847 **
Block 2.41418 0.60355 4 1260.00 17.9236 2.521e-14 ***
PerformanceGroup 0.04629 0.04629 1 16.82 1.3745 0.257371
Step:Block 0.31355 0.07839 4 1260.00 2.3279 0.054362 .
Step:PerformanceGroup 0.00013 0.00013 1 1260.00 0.0040 0.949598
Block:PerformanceGroup 0.20777 0.05194 4 1260.00 1.5426 0.187512
Step:Block:PerformanceGroup 0.03661 0.00915 4 1260.00 0.2718 0.896234
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(top_bottom_results$StepRMS_PerfGroup_X$Emmeans)) Step Block PerformanceGroup emmean SE df lower.CL upper.CL
8.5 1 Top 0.993 0.1250 41.6 0.742 1.245
8.5 2 Top 0.847 0.0998 17.2 0.636 1.057
8.5 3 Top 0.713 0.0988 16.6 0.504 0.921
8.5 4 Top 0.898 0.0988 16.6 0.689 1.107
8.5 5 Top 0.741 0.0988 16.6 0.532 0.950
8.5 1 Bottom 0.858 0.1250 41.6 0.607 1.109
8.5 2 Bottom 0.713 0.0998 17.2 0.503 0.924
8.5 3 Bottom 0.598 0.0988 16.6 0.389 0.807
8.5 4 Bottom 0.620 0.0988 16.6 0.412 0.829
8.5 5 Bottom 0.567 0.0988 16.6 0.359 0.776
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(top_bottom_results$StepRMS_PerfGroup_X$FixedEffects) (Intercept) Step
1.0232570767 -0.0035240667
Block2 Block3
-0.0573792029 -0.2653315214
Block4 Block5
-0.0915947287 -0.2567999848
PerformanceGroupBottom Step:Block2
-0.2162754294 -0.0105202952
Step:Block3 Step:Block4
-0.0018176046 -0.0003923818
Step:Block5 Step:PerformanceGroupBottom
0.0005326844 0.0095235474
Block2:PerformanceGroupBottom Block3:PerformanceGroupBottom
0.1127140176 0.1095931338
Block4:PerformanceGroupBottom Block5:PerformanceGroupBottom
-0.0172128406 0.0537323855
Step:Block2:PerformanceGroupBottom Step:Block3:PerformanceGroupBottom
-0.0130146071 -0.0104805832
Step:Block4:PerformanceGroupBottom Step:Block5:PerformanceGroupBottom
-0.0147540559 -0.0108188871 print(top_bottom_results$StepRMS_PerfGroup_X$RandomEffects)$subject
(Intercept)
2 0.02063865
3 0.12662081
4 -0.15993058
5 -0.25401347
7 -0.24936885
8 0.22457842
10 0.72589981
11 0.61103956
13 -0.27790222
14 -0.05475486
15 0.01966492
16 -0.15050185
17 -0.27500607
18 0.05901077
19 -0.19351392
20 -0.15570200
22 -0.05317609
23 0.03641696
with conditional variances for "subject" print(head(top_bottom_results$StepRMS_PerfGroup_X$ScaledResiduals)) 1 2 3 4 5 6
-2.514963 -2.447129 -2.415125 -2.395921 -2.202891 -2.255295 cat("\n=== TOP vs BOTTOM PERFORMER ANALYSIS: Axis Y ===\n")
=== TOP vs BOTTOM PERFORMER ANALYSIS: Axis Y ===print(top_bottom_results$StepRMS_PerfGroup_Y$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.44036 0.44036 1 1260.00 6.4295 0.0113442 *
Block 2.38367 0.59592 4 1260.00 8.7008 6.291e-07 ***
PerformanceGroup 0.31771 0.31771 1 17.48 4.6388 0.0454853 *
Step:Block 0.36458 0.09115 4 1260.00 1.3308 0.2563668
Step:PerformanceGroup 0.07288 0.07288 1 1260.00 1.0641 0.3024866
Block:PerformanceGroup 1.34674 0.33669 4 1260.00 4.9158 0.0006191 ***
Step:Block:PerformanceGroup 0.30489 0.07622 4 1260.00 1.1129 0.3488521
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(top_bottom_results$StepRMS_PerfGroup_Y$Emmeans)) Step Block PerformanceGroup emmean SE df lower.CL upper.CL
8.5 1 Top 1.081 0.152 69.5 0.779 1.384
8.5 2 Top 0.936 0.108 18.2 0.709 1.163
8.5 3 Top 0.754 0.106 17.0 0.530 0.978
8.5 4 Top 0.940 0.106 17.0 0.716 1.164
8.5 5 Top 0.969 0.106 17.0 0.745 1.193
8.5 1 Bottom 0.759 0.152 69.5 0.456 1.061
8.5 2 Bottom 0.768 0.108 18.2 0.541 0.995
8.5 3 Bottom 0.597 0.106 17.0 0.373 0.821
8.5 4 Bottom 0.685 0.106 17.0 0.460 0.909
8.5 5 Bottom 0.531 0.106 17.0 0.307 0.755
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(top_bottom_results$StepRMS_PerfGroup_Y$FixedEffects) (Intercept) Step
1.106875568 -0.003007596
Block2 Block3
0.010226216 -0.310633623
Block4 Block5
-0.050906970 -0.006449728
PerformanceGroupBottom Step:Block2
-0.342310751 -0.018299576
Step:Block3 Step:Block4
-0.001928342 -0.010668633
Step:Block5 Step:PerformanceGroupBottom
-0.012418844 0.002296496
Block2:PerformanceGroupBottom Block3:PerformanceGroupBottom
0.002381548 0.181628879
Block4:PerformanceGroupBottom Block5:PerformanceGroupBottom
0.083415750 -0.184748314
Step:Block2:PerformanceGroupBottom Step:Block3:PerformanceGroupBottom
0.017889324 -0.001903484
Step:Block4:PerformanceGroupBottom Step:Block5:PerformanceGroupBottom
-0.001861503 0.008141814 print(top_bottom_results$StepRMS_PerfGroup_Y$RandomEffects)$subject
(Intercept)
2 0.080783799
3 0.316720216
4 -0.159994548
5 -0.215888243
7 -0.334291290
8 0.268888618
10 0.631831875
11 0.562812662
13 -0.323033692
14 -0.129143313
15 0.004970042
16 -0.213143582
17 -0.295401150
18 0.059210951
19 -0.211773333
20 -0.139635931
22 -0.216421817
23 0.313508736
with conditional variances for "subject" print(head(top_bottom_results$StepRMS_PerfGroup_Y$ScaledResiduals)) 1 2 3 4 5 6
-2.195117 -2.331548 -2.293657 -2.282164 -2.182169 -2.058850 cat("\n=== TOP vs BOTTOM PERFORMER ANALYSIS: Axis Z ===\n")
=== TOP vs BOTTOM PERFORMER ANALYSIS: Axis Z ===print(top_bottom_results$StepRMS_PerfGroup_Z$ANOVA)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Step 0.5721 0.57209 1 1260.00 3.7189 0.05403 .
Block 9.0610 2.26524 4 1260.00 14.7251 9.211e-12 ***
PerformanceGroup 0.2571 0.25706 1 16.71 1.6710 0.21371
Step:Block 1.4199 0.35499 4 1260.00 2.3076 0.05620 .
Step:PerformanceGroup 0.0209 0.02091 1 1260.00 0.1359 0.71242
Block:PerformanceGroup 1.5166 0.37915 4 1260.00 2.4646 0.04343 *
Step:Block:PerformanceGroup 0.8110 0.20275 4 1260.00 1.3180 0.26117
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1print(summary(top_bottom_results$StepRMS_PerfGroup_Z$Emmeans)) Step Block PerformanceGroup emmean SE df lower.CL upper.CL
8.5 1 Top 2.04 0.278 37.6 1.477 2.60
8.5 2 Top 1.80 0.228 17.1 1.320 2.28
8.5 3 Top 1.66 0.226 16.5 1.178 2.13
8.5 4 Top 1.92 0.226 16.5 1.437 2.39
8.5 5 Top 1.73 0.226 16.5 1.252 2.21
8.5 1 Bottom 1.85 0.278 37.6 1.284 2.41
8.5 2 Bottom 1.63 0.228 17.1 1.151 2.11
8.5 3 Bottom 1.22 0.226 16.5 0.741 1.70
8.5 4 Bottom 1.39 0.226 16.5 0.907 1.86
8.5 5 Bottom 1.14 0.226 16.5 0.660 1.62
Degrees-of-freedom method: kenward-roger
Confidence level used: 0.95 print(top_bottom_results$StepRMS_PerfGroup_Z$FixedEffects) (Intercept) Step
1.9798197650 0.0070763960
Block2 Block3
0.0622920952 -0.3092209024
Block4 Block5
0.0929333079 -0.1240243787
PerformanceGroupBottom Step:Block2
-0.1451560468 -0.0353677728
Step:Block3 Step:Block4
-0.0087974049 -0.0256342517
Step:Block5 Step:PerformanceGroupBottom
-0.0218997384 -0.0055526106
Block2:PerformanceGroupBottom Block3:PerformanceGroupBottom
-0.2502326036 -0.2393959275
Block4:PerformanceGroupBottom Block5:PerformanceGroupBottom
-0.3308038330 -0.5278751442
Step:Block2:PerformanceGroupBottom Step:Block3:PerformanceGroupBottom
0.0320788302 -0.0005753052
Step:Block4:PerformanceGroupBottom Step:Block5:PerformanceGroupBottom
-0.0008040793 0.0151415792 print(top_bottom_results$StepRMS_PerfGroup_Z$RandomEffects)$subject
(Intercept)
2 -0.31728819
3 0.51870711
4 -0.43996627
5 -0.59511638
7 -0.08056039
8 0.33987120
10 1.74233164
11 1.05116300
13 -0.35881823
14 -0.48942616
15 0.17014432
16 -0.06426532
17 -0.85998160
18 0.55890285
19 -0.51225727
20 -0.37537986
22 -0.37619749
23 0.08813705
with conditional variances for "subject" print(head(top_bottom_results$StepRMS_PerfGroup_Z$ScaledResiduals)) 1 2 3 4 5 6
-1.368196 -1.521605 -1.692512 -1.710554 -1.966153 -1.902318 #5.1 step lvl rms
# --- Summarize Data for Plotting by Block ---
plot_summary_by_block <- step_rms_grouped %>%
group_by(Block, Step, Axis, PerformanceGroup) %>%
summarise(
MeanRMS = mean(RMS, na.rm = TRUE),
SERMS = sd(RMS, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)
# --- Plot Function per Block and Axis ---
plot_rms_by_step_group_blocked <- function(summary_data, axis_label) {
blocks <- unique(summary_data$Block)
plots <- lapply(blocks, function(blk) {
df_blk <- filter(summary_data, Block == blk, Axis == axis_label)
ggplot(df_blk, aes(x = Step, y = MeanRMS, color = PerformanceGroup)) +
geom_line(size = 1.2) +
geom_point(size = 2) +
geom_errorbar(aes(ymin = MeanRMS - SERMS, ymax = MeanRMS + SERMS), width = 0.2) +
labs(
title = paste("Block", blk, "- RMS (Axis", toupper(axis_label), ") by Step & Performance Group"),
x = "Step",
y = "Mean RMS Acceleration",
color = "Group"
) +
theme_minimal(base_size = 13)
})
return(plots)
}
# --- Plot for Axis X (returns list of ggplot objects, one per block) ---
plots_x <- plot_rms_by_step_group_blocked(plot_summary_by_block, "x")
plots_y <- plot_rms_by_step_group_blocked(plot_summary_by_block, "y")
plots_z <- plot_rms_by_step_group_blocked(plot_summary_by_block, "z")
# --- Display (e.g., first plot) ---
print(plots_x[[1]]) # Change index to view Block 2, 3, etc.
print(plots_x[[2]])
print(plots_x[[3]])
print(plots_x[[4]])
print(plots_x[[5]])
print(plots_y[[1]]) # Change index to view Block 2, 3, etc.
print(plots_y[[2]])
print(plots_y[[3]])
print(plots_y[[4]])
print(plots_y[[5]])
print(plots_z[[1]]) # Change index to view Block 2, 3, etc.
print(plots_z[[2]])
print(plots_z[[3]])
print(plots_z[[4]])
print(plots_z[[5]])
#5.2 Block avg RMS
# --- Assign Top/Bottom Groups ---
top_subjects <- c(17, 7, 23, 16, 10, 14, 13, 2, 8)
tagged_data <- tagged_data %>%
mutate(
PerformanceGroup = ifelse(subject %in% top_subjects, "Top", "Bottom"),
subject = factor(subject),
Block = factor(Block),
phase = factor(phase)
)
# --- Compute RMS per Block, Phase, and Subject ---
block_rms_summary <- tagged_data %>%
group_by(subject, Block, phase, PerformanceGroup) %>%
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 = gsub("rms_", "", Axis))
# --- LMM: Does Performance Group Affect RMS? ---
library(lmerTest)
run_group_block_rms_model <- function(axis) {
lmer(RMS ~ PerformanceGroup * Block * phase + (1 | subject),
data = filter(block_rms_summary, Axis == axis))
}
model_x <- run_group_block_rms_model("x")
model_y <- run_group_block_rms_model("y")
model_z <- run_group_block_rms_model("z")
anova(model_x)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
PerformanceGroup 0.0665 0.0665 1 16 2.7902 0.11429
Block 0.2654 0.0664 4 144 2.7851 0.02885 *
phase 11.7375 11.7375 1 144 492.6213 < 2.2e-16 ***
PerformanceGroup:Block 0.0634 0.0159 4 144 0.6654 0.61703
PerformanceGroup:phase 0.1430 0.1430 1 144 5.9999 0.01551 *
Block:phase 1.0974 0.2744 4 144 11.5147 3.874e-08 ***
PerformanceGroup:Block:phase 0.0123 0.0031 4 144 0.1290 0.97165
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model_y)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
PerformanceGroup 0.1166 0.1166 1 16 2.7670 0.115689
Block 0.3670 0.0918 4 144 2.1781 0.074368 .
phase 13.3322 13.3322 1 144 316.4564 < 2.2e-16 ***
PerformanceGroup:Block 0.0473 0.0118 4 144 0.2804 0.890276
PerformanceGroup:phase 0.4641 0.4641 1 144 11.0158 0.001144 **
Block:phase 1.2060 0.3015 4 144 7.1564 2.77e-05 ***
PerformanceGroup:Block:phase 0.0937 0.0234 4 144 0.5563 0.694730
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model_z)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
PerformanceGroup 0.247 0.247 1 16 2.7790 0.114960
Block 1.034 0.258 4 144 2.9125 0.023595 *
phase 36.376 36.376 1 144 409.9435 < 2.2e-16 ***
PerformanceGroup:Block 0.300 0.075 4 144 0.8446 0.499088
PerformanceGroup:phase 0.717 0.717 1 144 8.0850 0.005113 **
Block:phase 2.847 0.712 4 144 8.0198 7.259e-06 ***
PerformanceGroup:Block:phase 0.070 0.018 4 144 0.1985 0.938791
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- Plot Group Differences by Axis, Phase, and Block ---
plot_block_summary <- block_rms_summary %>%
group_by(PerformanceGroup, Block, phase, Axis) %>%
summarise(
MeanRMS = mean(RMS, na.rm = TRUE),
SERMS = sd(RMS, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)
ggplot(plot_block_summary, aes(x = Block, y = MeanRMS, fill = PerformanceGroup)) +
geom_bar(stat = "identity", position = position_dodge(width = 0.8)) +
geom_errorbar(aes(ymin = MeanRMS - SERMS, ymax = MeanRMS + SERMS),
width = 0.2, position = position_dodge(0.8)) +
facet_grid(phase ~ Axis) +
labs(
title = "Block-Level RMS by Group, Phase, and Axis",
x = "Block", y = "Mean RMS"
) +
theme_minimal(base_size = 14)
#Block avg sd
# --- Assign Top/Bottom Groups ---
top_subjects <- c(17, 7, 23, 16, 10, 14, 13, 2, 8)
tagged_data <- tagged_data %>%
mutate(
PerformanceGroup = ifelse(subject %in% top_subjects, "Top", "Bottom"),
subject = factor(subject),
Block = factor(Block),
phase = factor(phase)
)
# --- Compute SD per Block, Phase, and Subject ---
block_sd_summary <- tagged_data %>%
group_by(subject, Block, phase, PerformanceGroup) %>%
summarise(
sd_x = sd(CoM.acc.x, na.rm = TRUE),
sd_y = sd(CoM.acc.y, na.rm = TRUE),
sd_z = sd(CoM.acc.z, na.rm = TRUE),
.groups = "drop"
) %>%
pivot_longer(cols = starts_with("sd_"), names_to = "Axis", values_to = "SD") %>%
mutate(Axis = gsub("sd_", "", Axis))
# --- LMM: Does Performance Group Affect SD? ---
library(lmerTest)
run_group_block_sd_model <- function(axis) {
lmer(SD ~ PerformanceGroup * Block * phase + (1 | subject),
data = filter(block_sd_summary, Axis == axis))
}
model_x_sd <- run_group_block_sd_model("x")
model_y_sd <- run_group_block_sd_model("y")
model_z_sd <- run_group_block_sd_model("z")
anova(model_x_sd)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
PerformanceGroup 0.0664 0.0664 1 16 2.7875 0.11445
Block 0.2658 0.0665 4 144 2.7895 0.02865 *
phase 11.7419 11.7419 1 144 492.8999 < 2.2e-16 ***
PerformanceGroup:Block 0.0635 0.0159 4 144 0.6666 0.61620
PerformanceGroup:phase 0.1429 0.1429 1 144 5.9998 0.01551 *
Block:phase 1.0974 0.2743 4 144 11.5164 3.864e-08 ***
PerformanceGroup:Block:phase 0.0124 0.0031 4 144 0.1296 0.97141
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model_y_sd)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
PerformanceGroup 0.1165 0.1165 1 16 2.7656 0.115775
Block 0.3670 0.0918 4 144 2.1778 0.074397 .
phase 13.3371 13.3371 1 144 316.5745 < 2.2e-16 ***
PerformanceGroup:Block 0.0474 0.0119 4 144 0.2813 0.889703
PerformanceGroup:phase 0.4638 0.4638 1 144 11.0084 0.001149 **
Block:phase 1.2063 0.3016 4 144 7.1582 2.762e-05 ***
PerformanceGroup:Block:phase 0.0939 0.0235 4 144 0.5571 0.694137
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(model_z_sd)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
PerformanceGroup 0.246 0.246 1 16 2.7764 0.115116
Block 1.033 0.258 4 144 2.9113 0.023638 *
phase 36.347 36.347 1 144 409.6106 < 2.2e-16 ***
PerformanceGroup:Block 0.299 0.075 4 144 0.8433 0.499915
PerformanceGroup:phase 0.716 0.716 1 144 8.0702 0.005153 **
Block:phase 2.848 0.712 4 144 8.0237 7.216e-06 ***
PerformanceGroup:Block:phase 0.070 0.018 4 144 0.1981 0.939039
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# --- Plot Group Differences for SD by Axis, Phase, and Block ---
plot_block_sd <- block_sd_summary %>%
group_by(PerformanceGroup, Block, phase, Axis) %>%
summarise(
MeanSD = mean(SD, na.rm = TRUE),
SESD = sd(SD, na.rm = TRUE) / sqrt(n()),
.groups = "drop"
)
ggplot(plot_block_sd, aes(x = Block, y = MeanSD, fill = PerformanceGroup)) +
geom_bar(stat = "identity", position = position_dodge(width = 0.8)) +
geom_errorbar(aes(ymin = MeanSD - SESD, ymax = MeanSD + SESD),
width = 0.2, position = position_dodge(0.8)) +
facet_grid(phase ~ Axis) +
labs(
title = "Block-Level SD by Group, Phase, and Axis",
x = "Block", y = "Mean SD"
) +
theme_minimal(base_size = 14)