434 lines
18 KiB
R
434 lines
18 KiB
R
# Mixed ANOVA Analysis for Domain Means - EOHI2
|
||
# EOHI Experiment Data Analysis - Domain Level Analysis with INTERVAL factor
|
||
# Variables: NPast_5_pref_MEAN, NPast_5_pers_MEAN, NPast_5_val_MEAN, etc.
|
||
# NFut_5_pref_MEAN, NFut_5_pers_MEAN, NFut_5_val_MEAN, etc.
|
||
# NPast_10_pref_MEAN, NPast_10_pers_MEAN, NPast_10_val_MEAN, etc.
|
||
# NFut_10_pref_MEAN, NFut_10_pers_MEAN, NFut_10_val_MEAN, etc.
|
||
# 5.10past_pref_MEAN, 5.10past_pers_MEAN, 5.10past_val_MEAN
|
||
# 5.10fut_pref_MEAN, 5.10fut_pers_MEAN, 5.10fut_val_MEAN
|
||
|
||
# Load required libraries
|
||
library(tidyverse)
|
||
library(ez)
|
||
library(car)
|
||
library(afex) # For aov_ez (cleaner ANOVA output)
|
||
library(nortest) # For normality tests
|
||
library(emmeans) # For post-hoc comparisons
|
||
library(purrr) # For map functions
|
||
library(effsize) # For Cohen's d calculations
|
||
library(effectsize) # For effect size calculations
|
||
|
||
# Global options to remove scientific notation
|
||
options(scipen = 999)
|
||
|
||
# Set contrasts to sum for mixed ANOVA (necessary for proper interpretation)
|
||
options(contrasts = c("contr.sum", "contr.poly"))
|
||
|
||
setwd("C:/Users/irina/Documents/DND/EOHI/eohi2")
|
||
|
||
# Read the data
|
||
data <- read.csv("eohi2.csv")
|
||
|
||
# Display basic information about the dataset
|
||
print(paste("Dataset dimensions:", paste(dim(data), collapse = " x")))
|
||
print(paste("Number of participants:", length(unique(data$ResponseId))))
|
||
|
||
# Verify the specific variables we need
|
||
required_vars <- c("NPast_5_pref_MEAN", "NPast_5_pers_MEAN", "NPast_5_val_MEAN",
|
||
"NPast_10_pref_MEAN", "NPast_10_pers_MEAN", "NPast_10_val_MEAN",
|
||
"NFut_5_pref_MEAN", "NFut_5_pers_MEAN", "NFut_5_val_MEAN",
|
||
"NFut_10_pref_MEAN", "NFut_10_pers_MEAN", "NFut_10_val_MEAN",
|
||
"5.10past_pref_MEAN", "5.10past_pers_MEAN", "5.10past_val_MEAN",
|
||
"5.10fut_pref_MEAN", "5.10fut_pers_MEAN", "5.10fut_val_MEAN")
|
||
|
||
missing_vars <- required_vars[!required_vars %in% colnames(data)]
|
||
if (length(missing_vars) > 0) {
|
||
print(paste("Warning: Missing variables:", paste(missing_vars, collapse = ", ")))
|
||
} else {
|
||
print("All required domain mean variables found!")
|
||
}
|
||
|
||
# Define domain mapping with TIME, DOMAIN, and INTERVAL factors
|
||
domain_mapping <- data.frame(
|
||
variable = required_vars,
|
||
time = c(rep("Past", 3), rep("Past", 3), rep("Future", 3), rep("Future", 3),
|
||
rep("Past", 3), rep("Future", 3)),
|
||
domain = rep(c("Preferences", "Personality", "Values"), 6),
|
||
interval = c(rep("5", 3), rep("10", 3), rep("5", 3), rep("10", 3),
|
||
rep("5_10", 3), rep("5_10", 3)),
|
||
stringsAsFactors = FALSE
|
||
)
|
||
|
||
print("Domain mapping created:")
|
||
print(domain_mapping)
|
||
|
||
# Efficient data pivoting using pivot_longer
|
||
long_data <- data %>%
|
||
select(ResponseId, TEMPORAL_DO, INTERVAL_DO, all_of(required_vars)) %>%
|
||
pivot_longer(
|
||
cols = all_of(required_vars),
|
||
names_to = "variable",
|
||
values_to = "MEAN_DIFFERENCE"
|
||
) %>%
|
||
left_join(domain_mapping, by = "variable") %>%
|
||
# Convert to factors with proper levels
|
||
mutate(
|
||
TIME = factor(time, levels = c("Past", "Future")),
|
||
DOMAIN = factor(domain, levels = c("Preferences", "Personality", "Values")),
|
||
INTERVAL = factor(interval, levels = c("5", "10", "5_10")),
|
||
ResponseId = as.factor(ResponseId),
|
||
TEMPORAL_DO = as.factor(TEMPORAL_DO),
|
||
INTERVAL_DO = as.factor(INTERVAL_DO)
|
||
) %>%
|
||
# Select final columns and remove any rows with missing values
|
||
select(ResponseId, TEMPORAL_DO, INTERVAL_DO, TIME, DOMAIN, INTERVAL, MEAN_DIFFERENCE) %>%
|
||
filter(!is.na(MEAN_DIFFERENCE))
|
||
|
||
print(paste("Long data dimensions:", paste(dim(long_data), collapse = " x")))
|
||
print(paste("Number of participants:", length(unique(long_data$ResponseId))))
|
||
|
||
# =============================================================================
|
||
# DESCRIPTIVE STATISTICS
|
||
# =============================================================================
|
||
|
||
# Overall descriptive statistics by TIME, DOMAIN, and INTERVAL
|
||
desc_stats <- long_data %>%
|
||
group_by(TIME, DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
n = n(),
|
||
mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
median = round(median(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
q1 = round(quantile(MEAN_DIFFERENCE, 0.25, na.rm = TRUE), 5),
|
||
q3 = round(quantile(MEAN_DIFFERENCE, 0.75, na.rm = TRUE), 5),
|
||
min = round(min(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
max = round(max(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Descriptive statistics by TIME, DOMAIN, and INTERVAL:")
|
||
print(desc_stats)
|
||
|
||
# Descriptive statistics by between-subjects factors
|
||
desc_stats_by_between <- long_data %>%
|
||
group_by(TEMPORAL_DO, INTERVAL_DO, TIME, DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
n = n(),
|
||
mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Descriptive statistics by between-subjects factors:")
|
||
print(desc_stats_by_between)
|
||
|
||
# Summary by between-subjects factors only
|
||
desc_stats_between_only <- long_data %>%
|
||
group_by(TEMPORAL_DO, INTERVAL_DO) %>%
|
||
summarise(
|
||
n = n(),
|
||
mean = round(mean(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
variance = round(var(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
sd = round(sd(MEAN_DIFFERENCE, na.rm = TRUE), 5),
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Descriptive statistics by between-subjects factors only:")
|
||
print(desc_stats_between_only)
|
||
|
||
# =============================================================================
|
||
# ASSUMPTION TESTING
|
||
# =============================================================================
|
||
|
||
# Remove missing values for assumption testing
|
||
long_data_clean <- long_data[!is.na(long_data$MEAN_DIFFERENCE), ]
|
||
print(paste("Data after removing missing values:", paste(dim(long_data_clean), collapse = " x")))
|
||
|
||
# 1. Missing values check
|
||
missing_summary <- long_data %>%
|
||
group_by(TIME, DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
n_total = n(),
|
||
n_missing = sum(is.na(MEAN_DIFFERENCE)),
|
||
pct_missing = round(100 * n_missing / n_total, 2),
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Missing values by TIME, DOMAIN, and INTERVAL:")
|
||
print(missing_summary)
|
||
|
||
# 2. Outlier detection
|
||
outlier_summary <- long_data_clean %>%
|
||
group_by(TIME, DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
n = n(),
|
||
mean = mean(MEAN_DIFFERENCE),
|
||
sd = sd(MEAN_DIFFERENCE),
|
||
q1 = quantile(MEAN_DIFFERENCE, 0.25),
|
||
q3 = quantile(MEAN_DIFFERENCE, 0.75),
|
||
iqr = q3 - q1,
|
||
lower_bound = q1 - 1.5 * iqr,
|
||
upper_bound = q3 + 1.5 * iqr,
|
||
n_outliers = sum(MEAN_DIFFERENCE < lower_bound | MEAN_DIFFERENCE > upper_bound),
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Outlier summary (IQR method):")
|
||
print(outlier_summary)
|
||
|
||
# 3. Anderson-Darling normality test
|
||
normality_results <- long_data_clean %>%
|
||
group_by(TIME, DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
n = n(),
|
||
ad_statistic = ad.test(.data$MEAN_DIFFERENCE)$statistic,
|
||
ad_p_value = ad.test(.data$MEAN_DIFFERENCE)$p.value,
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Anderson-Darling normality test results:")
|
||
# Round only the numeric columns
|
||
normality_results_rounded <- normality_results %>%
|
||
mutate(across(where(is.numeric), ~ round(.x, 5)))
|
||
print(normality_results_rounded)
|
||
|
||
# 4. Homogeneity of variance (Levene's test)
|
||
# Test homogeneity across TIME within each DOMAIN × INTERVAL combination
|
||
homogeneity_time <- long_data_clean %>%
|
||
group_by(DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
levene_F = leveneTest(MEAN_DIFFERENCE ~ TIME)$`F value`[1],
|
||
levene_p = leveneTest(MEAN_DIFFERENCE ~ TIME)$`Pr(>F)`[1],
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Homogeneity of variance across TIME within each DOMAIN × INTERVAL combination:")
|
||
print(homogeneity_time)
|
||
|
||
# Test homogeneity across DOMAIN within each TIME × INTERVAL combination
|
||
homogeneity_domain <- long_data_clean %>%
|
||
group_by(TIME, INTERVAL) %>%
|
||
summarise(
|
||
levene_F = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`F value`[1],
|
||
levene_p = leveneTest(MEAN_DIFFERENCE ~ DOMAIN)$`Pr(>F)`[1],
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Homogeneity of variance across DOMAIN within each TIME × INTERVAL combination:")
|
||
print(homogeneity_domain)
|
||
|
||
# Test homogeneity across INTERVAL within each TIME × DOMAIN combination
|
||
homogeneity_interval <- long_data_clean %>%
|
||
group_by(TIME, DOMAIN) %>%
|
||
summarise(
|
||
levene_F = leveneTest(MEAN_DIFFERENCE ~ INTERVAL)$`F value`[1],
|
||
levene_p = leveneTest(MEAN_DIFFERENCE ~ INTERVAL)$`Pr(>F)`[1],
|
||
.groups = 'drop'
|
||
)
|
||
|
||
print("Homogeneity of variance across INTERVAL within each TIME × DOMAIN combination:")
|
||
print(homogeneity_interval)
|
||
|
||
# 5. Hartley's F-max test for between-subjects factors
|
||
print("\n=== HARTLEY'S F-MAX TEST FOR BETWEEN-SUBJECTS FACTORS ===")
|
||
|
||
# Check what values the between-subjects factors actually have
|
||
print("Unique TEMPORAL_DO values:")
|
||
print(unique(long_data_clean$TEMPORAL_DO))
|
||
print("Unique INTERVAL_DO values:")
|
||
print(unique(long_data_clean$INTERVAL_DO))
|
||
|
||
# Function to calculate Hartley's F-max ratio
|
||
calculate_hartley_ratio <- function(variances) {
|
||
max(variances, na.rm = TRUE) / min(variances, na.rm = TRUE)
|
||
}
|
||
|
||
# Hartley's F-max test across TEMPORAL_DO within each TIME × DOMAIN × INTERVAL combination
|
||
print("\n=== HARTLEY'S F-MAX TEST: TEMPORAL_DO within each TIME × DOMAIN × INTERVAL combination ===")
|
||
|
||
observed_temporal_ratios <- long_data_clean %>%
|
||
group_by(TIME, DOMAIN, INTERVAL) %>%
|
||
summarise(
|
||
# Calculate variances for each TEMPORAL_DO level within this combination
|
||
past_var = var(MEAN_DIFFERENCE[TEMPORAL_DO == "01PAST"], na.rm = TRUE),
|
||
fut_var = var(MEAN_DIFFERENCE[TEMPORAL_DO == "02FUT"], na.rm = TRUE),
|
||
# Calculate F-max ratio
|
||
f_max_ratio = max(past_var, fut_var) / min(past_var, fut_var),
|
||
.groups = 'drop'
|
||
) %>%
|
||
select(TIME, DOMAIN, INTERVAL, past_var, fut_var, f_max_ratio)
|
||
|
||
print(observed_temporal_ratios)
|
||
|
||
# Hartley's F-max test across INTERVAL_DO within each TIME × DOMAIN × TEMPORAL_DO combination
|
||
print("\n=== HARTLEY'S F-MAX TEST: INTERVAL_DO within each TIME × DOMAIN × TEMPORAL_DO combination ===")
|
||
|
||
observed_interval_ratios <- long_data_clean %>%
|
||
group_by(TIME, DOMAIN, TEMPORAL_DO) %>%
|
||
summarise(
|
||
# Calculate variances for each INTERVAL_DO level within this combination
|
||
int5_var = var(MEAN_DIFFERENCE[INTERVAL_DO == "5"], na.rm = TRUE),
|
||
int10_var = var(MEAN_DIFFERENCE[INTERVAL_DO == "10"], na.rm = TRUE),
|
||
# Calculate F-max ratio
|
||
f_max_ratio = max(int5_var, int10_var) / min(int5_var, int10_var),
|
||
.groups = 'drop'
|
||
) %>%
|
||
select(TIME, DOMAIN, TEMPORAL_DO, int5_var, int10_var, f_max_ratio)
|
||
|
||
print(observed_interval_ratios)
|
||
|
||
# =============================================================================
|
||
# MIXED ANOVA ANALYSIS
|
||
# =============================================================================
|
||
|
||
# Check data dimensions and structure
|
||
print(paste("Data size for ANOVA:", nrow(long_data_clean), "rows"))
|
||
print(paste("Number of participants:", length(unique(long_data_clean$ResponseId))))
|
||
print(paste("Design factors: TIME (", length(levels(long_data_clean$TIME)), "), DOMAIN (",
|
||
length(levels(long_data_clean$DOMAIN)), "), INTERVAL (",
|
||
length(levels(long_data_clean$INTERVAL)), "), TEMPORAL_DO (",
|
||
length(levels(long_data_clean$TEMPORAL_DO)), "), INTERVAL_DO (",
|
||
length(levels(long_data_clean$INTERVAL_DO)), ")", sep = ""))
|
||
|
||
# Check for complete cases
|
||
complete_cases <- sum(complete.cases(long_data_clean))
|
||
print(paste("Complete cases:", complete_cases, "out of", nrow(long_data_clean)))
|
||
|
||
# Check if design is balanced
|
||
design_balance <- table(long_data_clean$ResponseId, long_data_clean$TIME, long_data_clean$DOMAIN, long_data_clean$INTERVAL)
|
||
if(all(design_balance %in% c(0, 1))) {
|
||
print("Design is balanced: each participant has data for all TIME × DOMAIN × INTERVAL combinations")
|
||
} else {
|
||
print("Warning: Design is unbalanced")
|
||
print(summary(as.vector(design_balance)))
|
||
}
|
||
|
||
# =============================================================================
|
||
# MIXED ANOVA WITH SPHERICITY CORRECTIONS
|
||
# =============================================================================
|
||
|
||
print("\n=== MIXED ANOVA RESULTS (with sphericity corrections) ===")
|
||
|
||
# Mixed ANOVA using ezANOVA with automatic sphericity corrections
|
||
# Between-subjects: TEMPORAL_DO (2 levels: 01PAST, 02FUT) × INTERVAL_DO (2 levels: 5, 10)
|
||
# Within-subjects: TIME (2 levels: Past, Future) × DOMAIN (3 levels: Preferences, Personality, Values) × INTERVAL (3 levels: 5, 10, 5_10)
|
||
|
||
mixed_anova_model <- ezANOVA(data = long_data_clean,
|
||
dv = MEAN_DIFFERENCE,
|
||
wid = ResponseId,
|
||
between = .(TEMPORAL_DO, INTERVAL_DO),
|
||
within = .(TIME, DOMAIN, INTERVAL),
|
||
type = 3,
|
||
detailed = TRUE)
|
||
|
||
print("ANOVA Results:")
|
||
anova_output <- mixed_anova_model$ANOVA
|
||
rownames(anova_output) <- NULL # Reset row numbers to be sequential
|
||
print(anova_output)
|
||
|
||
# Show Mauchly's test for sphericity
|
||
print("\nMauchly's Test of Sphericity:")
|
||
print(mixed_anova_model$Mauchly)
|
||
|
||
# Show sphericity-corrected results (Greenhouse-Geisser and Huynh-Feldt)
|
||
if(!is.null(mixed_anova_model$`Sphericity Corrections`)) {
|
||
print("\nGreenhouse-Geisser and Huynh-Feldt Corrections:")
|
||
print(mixed_anova_model$`Sphericity Corrections`)
|
||
|
||
# Extract and display corrected degrees of freedom
|
||
cat("\n=== CORRECTED DEGREES OF FREEDOM ===\n")
|
||
|
||
sphericity_corr <- mixed_anova_model$`Sphericity Corrections`
|
||
anova_table <- mixed_anova_model$ANOVA
|
||
|
||
corrected_df <- data.frame(
|
||
Effect = sphericity_corr$Effect,
|
||
Original_DFn = anova_table$DFn[match(sphericity_corr$Effect, anova_table$Effect)],
|
||
Original_DFd = anova_table$DFd[match(sphericity_corr$Effect, anova_table$Effect)],
|
||
GG_DFn = anova_table$DFn[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$GGe,
|
||
GG_DFd = anova_table$DFd[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$GGe,
|
||
HF_DFn = anova_table$DFn[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$HFe,
|
||
HF_DFd = anova_table$DFd[match(sphericity_corr$Effect, anova_table$Effect)] * sphericity_corr$HFe,
|
||
GG_epsilon = sphericity_corr$GGe,
|
||
HF_epsilon = sphericity_corr$HFe
|
||
)
|
||
|
||
print(corrected_df)
|
||
|
||
cat("\n=== CORRECTED F-TESTS ===\n")
|
||
|
||
# Between-subjects effects (no sphericity corrections needed)
|
||
cat("\nBETWEEN-SUBJECTS EFFECTS:\n")
|
||
between_effects <- c("TEMPORAL_DO", "INTERVAL_DO", "TEMPORAL_DO:INTERVAL_DO")
|
||
for(effect in between_effects) {
|
||
if(effect %in% anova_table$Effect) {
|
||
f_value <- anova_table$F[anova_table$Effect == effect]
|
||
dfn <- anova_table$DFn[anova_table$Effect == effect]
|
||
dfd <- anova_table$DFd[anova_table$Effect == effect]
|
||
p_value <- anova_table$p[anova_table$Effect == effect]
|
||
|
||
cat(sprintf("%s: F(%d, %d) = %.3f, p = %.6f\n", effect, dfn, dfd, f_value, p_value))
|
||
}
|
||
}
|
||
|
||
# Within-subjects effects (sphericity corrections where applicable)
|
||
cat("\nWITHIN-SUBJECTS EFFECTS:\n")
|
||
|
||
# TIME main effect (2 levels, sphericity automatically satisfied)
|
||
if("TIME" %in% anova_table$Effect) {
|
||
f_value <- anova_table$F[anova_table$Effect == "TIME"]
|
||
dfn <- anova_table$DFn[anova_table$Effect == "TIME"]
|
||
dfd <- anova_table$DFd[anova_table$Effect == "TIME"]
|
||
p_value <- anova_table$p[anova_table$Effect == "TIME"]
|
||
cat(sprintf("TIME: F(%d, %d) = %.3f, p = %.6f (2 levels, sphericity satisfied)\n", dfn, dfd, f_value, p_value))
|
||
}
|
||
|
||
# DOMAIN main effect (3 levels, needs sphericity correction)
|
||
if("DOMAIN" %in% anova_table$Effect) {
|
||
f_value <- anova_table$F[anova_table$Effect == "DOMAIN"]
|
||
dfn <- anova_table$DFn[anova_table$Effect == "DOMAIN"]
|
||
dfd <- anova_table$DFd[anova_table$Effect == "DOMAIN"]
|
||
p_value <- anova_table$p[anova_table$Effect == "DOMAIN"]
|
||
cat(sprintf("DOMAIN: F(%d, %d) = %.3f, p = %.6f\n", dfn, dfd, f_value, p_value))
|
||
}
|
||
|
||
# INTERVAL main effect (3 levels, needs sphericity correction)
|
||
if("INTERVAL" %in% anova_table$Effect) {
|
||
f_value <- anova_table$F[anova_table$Effect == "INTERVAL"]
|
||
dfn <- anova_table$DFn[anova_table$Effect == "INTERVAL"]
|
||
dfd <- anova_table$DFd[anova_table$Effect == "INTERVAL"]
|
||
p_value <- anova_table$p[anova_table$Effect == "INTERVAL"]
|
||
cat(sprintf("INTERVAL: F(%d, %d) = %.3f, p = %.6f\n", dfn, dfd, f_value, p_value))
|
||
}
|
||
|
||
# Interactions with sphericity corrections
|
||
cat("\nINTERACTIONS WITH SPHERICITY CORRECTIONS:\n")
|
||
for(i in seq_len(nrow(corrected_df))) {
|
||
effect <- corrected_df$Effect[i]
|
||
f_value <- anova_table$F[match(effect, anova_table$Effect)]
|
||
|
||
cat(sprintf("\n%s:\n", effect))
|
||
cat(sprintf(" Original: F(%d, %d) = %.3f\n",
|
||
corrected_df$Original_DFn[i], corrected_df$Original_DFd[i], f_value))
|
||
cat(sprintf(" GG-corrected: F(%.2f, %.2f) = %.3f, p = %.6f\n",
|
||
corrected_df$GG_DFn[i], corrected_df$GG_DFd[i], f_value, sphericity_corr$`p[GG]`[i]))
|
||
cat(sprintf(" HF-corrected: F(%.2f, %.2f) = %.3f, p = %.6f\n",
|
||
corrected_df$HF_DFn[i], corrected_df$HF_DFd[i], f_value, sphericity_corr$`p[HF]`[i]))
|
||
}
|
||
} else {
|
||
print("\nNote: Sphericity corrections not needed (sphericity assumption met)")
|
||
}
|
||
|
||
# =============================================================================
|
||
# EFFECT SIZES (GENERALIZED ETA SQUARED)
|
||
# =============================================================================
|
||
|
||
print("\n=== EFFECT SIZES (GENERALIZED ETA SQUARED) ===")
|
||
|
||
# Extract generalized eta squared from ezANOVA (already calculated)
|
||
effect_sizes <- mixed_anova_model$ANOVA[, c("Effect", "ges")]
|
||
effect_sizes$ges <- round(effect_sizes$ges, 5)
|
||
print("Generalized Eta Squared:")
|
||
print(effect_sizes) |