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RM-ANOVA

Repeated-Measures ANOVA — Memory Scores at Three Time Points

Within-subjects ANOVA for participants measured at Baseline, Week 4, and Week 8. SS decomposition.

📊 F(2,14) significant, η² large
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🔁 9 · Repeated-Measures ANOVA

Memory Scores at Three Time Points
RM-ANOVA
Research Question: Do memory scores change across three time points (Baseline, Week 4, Week 8) for the same 5 participants?
SubjectBaselineWeek 4Week 8Row Mean
14686.0
25797.0
33575.0
468108.0
52464.0
T̄ⱼ4.06.08.06.0 (Grand)
SS Decomposition
S S T i m e = n ∑ j ( T ¯ j − x ¯ . . ) 2 = 5 [ ( 4 − 6 ) 2 + ( 6 − 6 ) 2 + ( 8 − 6 ) 2 ] = 5 [ 4 + 0 + 4 ] = 40 S S S u b j e c t s = k ∑ i ( P ¯ i − x ¯ . . ) 2 = 3 [ ( 6 − 6 ) 2 + ( 7 − 6 ) 2 + ( 5 − 6 ) 2 + ( 8 − 6 ) 2 + ( 4 − 6 ) 2 ] = 3 [ 0 + 1 + 1 + 4 + 4 ] = 30 S S E r r o r = S S T o t a l − S S T i m e − S S S u b j e c t s S S T o t a l = ∑ ( x i j − x ¯ . . ) 2 = 70 , S S E r r o r = 70 − 40 − 30 = 0
F = M S T i m e M S E r r o r = 40 / 2 0 / 8 → ∞ (perfect linear trend — theoretical) η p a r t i a l 2 = S S T i m e S S T i m e + S S E r r o r = 40 40 + 0 = 1.000
📌 This example shows a perfect linear trend. In practice, use MindStat to compute exact F, df, p with Greenhouse-Geisser/Huynh-Feldt corrections when Mauchly's sphericity test is violated.
APA-7 (template)
A one-way repeated-measures ANOVA indicated a significant effect of time on memory scores, F(2, 8) = XX.XX, p < .001, η²_p = .XX. Pairwise comparisons with Bonferroni correction revealed significant increases from T1 to T2 (p = .XXX) and T2 to T3 (p = .XXX).

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