Repeated Measures ANOVA

Analyze within-subject changes over time or conditions while controlling for individual differences.

Repeated Measures ANOVA Overview & Key Advantages

Repeated Measures ANOVA tests whether means differ significantly across repeated measurements on the same subjects over time or conditions. It partitions variance into between-subjects and within-subjects components, increasing statistical power by removing individual differences from the error term.

Advantages:

• • Higher statistical power than between-subjects
• • Controls individual differences effectively
• • Fewer subjects needed for same power
• • Tracks change over time efficiently
• • Reduces error variance significantly

Critical Assumptions:

• • Sphericity (equal variances/covariances)
• • Normality within each condition
• • Independence of subjects
• • No systematic missing data
• • Compound symmetry preferred

Variance Partitioning & F Statistic

Total variability is split into between-subjects variation and within-subjects variation; the latter is further split into the effect of conditions and residual error, which forms the denominator of the F-test.

Sum of squares partition

SStotal

= total sum of squares

SSbetween

= between-subjects sum of squares

SSwithin

= within-subjects sum of squares

SScond

= conditions (treatment) sum of squares

SSerror

= within-subjects error sum of squares

F statistic for the condition effect

MScond

= conditions mean square

MSerror

= within-subjects error mean square

When sphericity is violated, degrees of freedom are adjusted using Greenhouse-Geisser or Huynh-Feldt epsilon.

Reading the Repeated-Measures Profile Plot

Example Result & Signal Interpretation

Suppose a study across 4 time points yields F(3,15)=6.42,p=0.005, and Mauchly's test is non-significant (p=0.42), so sphericity holds.

Significant Result

• • p ≤ 0.05: means differ across time/conditions
• • Sphericity met: use standard F-test
• • Follow up with pairwise comparisons

Sphericity Violated

• • Mauchly's p ≤ 0.05: apply correction
• • Use Greenhouse-Geisser adjusted df
• • Consider MANOVA or mixed-model approach

sixsigmacenter.com Implementation Guide

This platform provides comprehensive Repeated Measures ANOVA analysis with sphericity testing, automatic corrections, and alternative approaches when assumptions are violated.

Analysis Features:

• • Mauchly's test for sphericity
• • Greenhouse-Geisser correction
• • Huynh-Feldt correction
• • Lower-bound correction
• • Post-hoc pairwise comparisons

Sphericity Corrections:

• • Greenhouse-Geisser: Conservative, always valid
• • Huynh-Feldt: Less conservative, ε > 0.75
• • Lower-bound: Most conservative (df = 1)
• • Multivariate: No sphericity assumption

Alternative Approaches:

• • Mixed-effects models: Handle missing data, unequal intervals
• • MANOVA approach: No sphericity assumption required
• • Profile analysis: Specific patterns over time
• • Friedman test: Non-parametric alternative

Example Data Layout for Repeated Measures ANOVA

Repeated measures data with subjects as rows and time points as columns. Each subject measured under multiple conditions or time points. Sample Size Recommendation: Minimum 6-10 subjects with 3+ repeated measures for adequate power in detecting within-subject effects.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.