Repeated Measures ANOVA

Repeated Measures ANOVA compares means of three or more measurements taken on the same subjects — for example, measuring patient weight at baseline, 3 months, 6 months, and 12 months on the same individuals.

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Step 1 — Provide your measurements

The Data Input panel uses a different shape than independent ANOVA — instead of independent groups, you define time points / measures (one column per measurement occasion):

• Add Measure to add another time point
• Remove Measure to drop one
• Update the name and values of each measure

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Step 2 — Load your data

Three options:

• Manual entry for each measure

• Sample data — pick from four built-in clinical scenarios:

  • Blood Pressure Monitoring (Systolic BP, Diastolic BP)
  • Cognitive Training (4 Sessions) (Memory Score, Reaction Time)
  • Pain Management (3 Visits) (VAS Pain, ROM Degrees)
  • Glycemic Control (5 Visits)

  The Sample Data Generator can also download the chosen scenario as an Excel file.

• Excel upload with full handling of complex layouts:

  • Format selection — choose between stacked vs. separate data layout
  • Column selection — for each detected column, decide whether to include it
  • Missing data handling — the module reports rows excluded due to missing values

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Step 3 — Calculate

Click Calculate Repeated Measures ANOVA.

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Step 4 — Read the results

The Repeated Measures ANOVA Results panel shows:

• F-value, p-value, and Eta-squared (η²) with effect-size interpretation
• Mauchly's Test of Sphericity — shows W statistic, chi-square statistic, and sphericity p-value
• Sphericity corrections — Greenhouse-Geisser (GG ε) and Huynh-Feldt (HF ε) epsilons. Shown only when sphericity is violated (Mauchly's test p < 0.05).
• ANOVA Summary Table — Source / SS / df / MS rows for Between Measures, Error, and Total

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Step 5 — Visualisations

A RepeatedAnovaCharts panel provides a line/profile plot showing how the mean of each measure changes across time points and a comparison of the measures' distributions.

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Step 6 — Discuss with the chatbot

A UniversalChatBot is available below.

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Statistical methods used

Test statistic

Component	Formula
Grand mean	x̄ = (Σ x̄ⱼ) / k (k = number of measures)
SS_between	n × Σⱼ (x̄ⱼ − x̄)²
SS_subjects	k × Σᵢ (x̄ᵢ· − x̄)²
SS_total	Σⱼ Σᵢ (xⱼᵢ − x̄)²
SS_error	SS_total − SS_between − SS_subjects
df_between	k − 1
df_error	(k − 1) × (n − 1)
F-statistic	MS_between / MS_error

Hypothesis statement

• H₀: μ₁ = μ₂ = ... = μₖ (all measure means are equal)
• H₁: At least one μⱼ differs
• Significance level: α = 0.05

Effect size — Eta-squared (η²)

Computed as η² = SS_between / (SS_between + SS_error). Same Cohen convention:

η² value	Label
< 0.06	Small effect
0.06 – 0.14	Medium effect
≥ 0.14	Large effect

Sphericity — Mauchly's Test

Element	Method
Mauchly's W	W = det(C) / (trace(C)/p)ᵖ where C is the covariance matrix of pairwise differences
Chi-square	χ² = −(n − 1 − (2k+5)/6) × ln(W)
p-value	From the chi-square distribution

If sphericity is violated (p < 0.05), corrections are shown:

Correction	When to use
Greenhouse-Geisser (GG ε)	Preferred when ε < 0.75 (severe violation)
Huynh-Feldt (HF ε)	Preferred when ε ≥ 0.75 (mild violation)

Excel data layouts supported

Layout	Structure
Stacked (long)	One row per observation with subject, time point, and value columns
Separate (wide)	One row per subject with each measure in its own column

Error handling

Condition	Error message
Fewer than 2 measures	"At least two measures are required"
Unequal subjects per measure	"All measures must have the same number of subjects"
Fewer than 3 subjects	"At least 3 subjects are required"