Statistical model reference
Repeated Measures ANOVA
Review when to use this method, its data requirements, implementation patterns, and interpretation guidance.
Description
A specialized form of ANOVA designed for analyzing data when the same subjects are measured multiple times. It accounts for the correlation between repeated measurements on the same individuals, making it essential for longitudinal studies, time series experiments, or any design where measurements are taken from the same subjects across different conditions or time points.
Use Cases
- longitudinal studies
- within-subjects designs
- pre-post intervention analysis
- time series experiments
Requirements
- Sample Size: small, medium, large
- Missing Data: none, random, systematic
- Data Distribution: normal
- Relationship Type: linear
Variable Types
Dependent Variables
- continuous
Independent Variables
- categorical
- time
Implementation
import pingouin as pg
# Using pingouin for repeated measures ANOVA
rm_anova = pg.rm_anova(data=df, dv='score', within='time', subject='subject_id')
print(rm_anova)
# Post-hoc pairwise comparisons
posthoc = pg.pairwise_ttests(data=df, dv='score', within='time', subject='subject_id', padjust='bonf')library(afex)
# Using afex package for repeated measures ANOVA
model <- aov_ez(
id = "subject_id",
dv = "score",
within = c("time", "condition"),
data = df
)
# Model summary
summary(model)
# Post-hoc tests with emmeans
library(emmeans)
emm <- emmeans(model, ~ time)
pairs(emm, adjust = "bonferroni")GLM time1 time2 time3
/WSFACTOR=time 3 Polynomial
/METHOD=SSTYPE(3)
/PRINT=DESCRIPTIVE ETASQ
/CRITERIA=ALPHA(.05)
/WSDESIGN=time.PROC GLM DATA=dataset;
CLASS subject_id;
MODEL time1 time2 time3 = / NOUNI;
REPEATED time 3 / PRINTE SUMMARY;
RUN;anova score subject_id / time#subject_id, repeated(time)
margins time
pwcompare time, mcompare(bonferroni)Synthetic Data Example
A longitudinal dataset suitable for Repeated Measures ANOVA analysis with three time points
R Code for Data Generation and Analysis
# Generate synthetic data for Repeated Measures ANOVA
set.seed(123)
library(tidyverse)
# Parameters
n_subjects <- 30
time_points <- 3
baseline_mean <- 50
treatment_effect <- 5
subject_variability <- 3
error_sd <- 2
# Create data frame
df <- expand.grid(
subject_id = factor(1:n_subjects),
time = factor(1:time_points, labels = c("Baseline", "Midpoint", "Post"))
) %>%
mutate(
# Subject-specific random intercept
subject_effect = rep(rnorm(n_subjects, 0, subject_variability), each = time_points),
# Time effect
time_effect = case_when(
time == "Baseline" ~ 0,
time == "Midpoint" ~ treatment_effect * 0.6,
time == "Post" ~ treatment_effect
),
# Generate scores with random error
score = baseline_mean + subject_effect + time_effect + rnorm(n_subjects * time_points, 0, error_sd)
)
# Descriptive statistics
df %>%
group_by(time) %>%
summarise(
mean = mean(score),
sd = sd(score),
min = min(score),
max = max(score)
)
# Visualization
ggplot(df, aes(x = time, y = score, group = subject_id)) +
geom_line(alpha = 0.3) +
geom_point() +
stat_summary(aes(group = 1), fun = mean, geom = "line", color = "red", size = 1.5) +
labs(title = "Repeated Measures Data with Individual Trajectories",
subtitle = "Red line shows group mean at each time point")
# Fit repeated measures ANOVA
library(afex)
model <- aov_ez(
id = "subject_id",
dv = "score",
within = "time",
data = df
)
# Model summary
summary(model)
# Post-hoc tests
library(emmeans)
emm <- emmeans(model, ~ time)
pairs(emm, adjust = "bonferroni")
Copy this code into your R environment to generate synthetic data and perform analysis with this model.
Expected Analysis Results
Console Output
> # Model summary
> summary(model)
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
Effect df MSE F ges p.value
1 time 2, 58 4.123 28.76 0.498 <.001
---
Sphericity correction method: GG
> # Post-hoc tests
> pairs(emm, adjust = "bonferroni")
contrast estimate SE df t.ratio p.value
Baseline - Midpoint -3.12 0.42 58 -7.429 <.0001
Baseline - Post -5.01 0.45 58 -11.125 <.0001
Midpoint - Post -1.89 0.38 58 -4.973 0.0001
Results are averaged over the levels of: subject_id
P value adjustment: bonferroni method for 3 tests
These results are from running the R code on synthetic data. Your actual results may vary depending on your data.
Interpretation Guide
Need help interpreting the results of your Repeated Measures ANOVA analysis? Our comprehensive interpretation guide explains:
- How to read and understand model outputs
- Interpreting coefficients and effect sizes correctly
- Understanding diagnostic plots and visualizations
- Common pitfalls and how to avoid them
- Making valid conclusions from your analysis