Repeated Measure ANOVA

Author

SEOYEON CHOI

Published

November 13, 2025

Import

import pandas as pd
import numpy as np

import pingouin as pg

import matplotlib.pyplot as plt
import seaborn as sns

Data

np.random.seed(1212)
n_groups = 3
n_sub_per_group = 50
groups = ['G1', 'G2', 'G3']
times = ['T1', 'T2', 'T3'] 
data = []
subject_id = 1
for g in groups:
    for _ in range(n_sub_per_group):
        subject_effect = np.random.normal(0, 3)
        
        if g == 'G1':
            base_mean = 50
        elif g == 'G2':
            base_mean = 55
        else:  # G3
            base_mean = 60
            
        means_by_time = {
            'T1': base_mean,
            'T2': base_mean + 5,
            'T3': base_mean + 8
        }
        
        for t in times:
            score = np.random.normal(means_by_time[t] + subject_effect, 5)
            data.append([subject_id, g, t, score])
        
        subject_id += 1
df = pd.DataFrame(data, columns=['subject', 'group', 'time', 'score'])
df.head()
subject group time score
0 1 G1 T1 55.325018
1 1 G1 T2 58.587960
2 1 G1 T3 51.686803
3 2 G1 T1 51.155675
4 2 G1 T2 46.891737 
df.groupby(['group', 'time'])['score'].mean()
group  time
G1     T1      49.059198
       T2      54.496584
       T3      57.815065
G2     T1      54.890146
       T2      60.616516
       T3      62.853200
G3     T1      62.157166
       T2      63.992115
       T3      67.534879
Name: score, dtype: float64

Repeated Measure ANOVA

anova = pg.mixed_anova(
    data=df,
    dv='score',
    within='time',
    between='group',
    subject='subject'
)
anova
Source SS DF1 DF2 MS F p-unc np2 eps
0 group 8708.950374 2 147 4354.475187 96.426159 1.770075e-27 0.567459 NaN
1 time 4111.110365 2 294 2055.555183 78.371474 5.242077e-28 0.347744 0.990805
2 Interaction 276.972914 4 294 69.243228 2.640014 3.406025e-02 0.034673 NaN

Results

  1. Between-subject effect: group
  • F(2,147)=96.43, p < .0001
  • The mean differences among the three groups were statistically significant.
  • np2 - 0.567 -> Large effect
  • The mean baselines of three groups are different.
  • The Groups have effective to the Score.
  1. Within-subject effect: time (Repeated measure factor)
  • F(2,294)=78.37, p < .0001
  • The mean scores changed significantly over time.
  • p = 5.24e-28 -> significant
  • np2 = 0.348
  • eps = 1 -> sphericity satisfation
  1. Interaction effect: group × time

  • F(4,294)=2.64, p = 0.034 -> significant

  • p = 0.034 -> significant

  • np2 = 0.035 -> small effect

  • This indicates that the pattern of change over time differs across groups.

  • In the mixed ANOVA, the main effect of group was significant (F(2,147) = 96.43, p < .001, η² = .57), indicating substantial differences among the three groups.

  • The main effect of time was also significant (F(2,294) = 78.37, p < .001, η² = .35), showing that scores changed meaningfully across the three time points.

  • Additionally, the group × time interaction was significant (F(4,294) = 2.64, p = .034), suggesting that the pattern of change over time differed across groups.

Figure

plt.figure(figsize=(12,8))
sns.pointplot(data=df, x='time', y='score', hue='group', dodge=True)
plt.title('Group × Time (Repeated Measures)')
plt.xlabel('Time')
plt.ylabel('Score')
plt.tight_layout()
plt.show()