Compare means across three or more time points or conditions measured on the same participants.
Repeated Measures ANOVA (Within-Subjects ANOVA) is the extension of the paired t-test to three or more time points or conditions. Because the same participants are measured multiple times, individual differences are partialled out of the error term, giving the test much greater statistical power than a between-subjects design. It is widely used in longitudinal studies, intervention research with multiple follow-up assessments, and within-subjects experimental designs.
A key assumption is sphericity — that the variances of the differences between all pairs of conditions are equal. StatRyx applies Mauchly's test for sphericity automatically. When violated, it applies the Greenhouse-Geisser correction to the degrees of freedom to maintain the correct Type I error rate.
StatRyx produces the full within-subjects ANOVA table, partial eta-squared, Bonferroni-corrected pairwise post-hoc comparisons, and a profile plot across time points — all in APA 7 format.
The key assumption is sphericity: the variances of the differences between every pair of time points should be equal. Mauchly's test checks it; when it is violated, the Greenhouse–Geisser correction lowers the degrees of freedom so the p-value stays accurate (that is why corrected results have decimal df such as F(1.74, 86.8)). After a significant overall effect, pairwise comparisons with a Bonferroni or Holm correction show which time points differ.
| Source | SS | df | MS | F | p | partial η² |
|---|---|---|---|---|---|---|
| Time (GG corrected) | 842.6 | 1.74 | 484.2 | 14.32 | < .001 | .22 |
| Error | 2938.4 | 86.8 | 33.8 |
A one-way repeated measures ANOVA showed a significant effect of time on depression scores, F(1.74, 86.8) = 14.32, p < .001, partial η² = .22. The Greenhouse-Geisser correction was applied (ε = .87). Bonferroni post-hoc tests revealed significant decreases from baseline to 3 months (p < .001) and from 3 to 6 months (p = .023).
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
Sphericity assumes the variances of differences between all pairs of conditions are equal. Violations inflate the F-ratio, increasing Type I error. Mauchly's test checks this; the GG correction fixes it.
For a medium effect (partial η² = .06) across 3 time points at 80% power, approximately 28 participants suffice — far fewer than a between-subjects design.
State whether sphericity held and which correction you used, then F with its (corrected) df, p and partial η²: "Mauchly's test indicated a violation of sphericity, so Greenhouse–Geisser corrected values are reported, F(1.74, 86.8) = 14.32, p < .001, partial η² = .22." Follow with the pairwise comparisons.
Classical repeated measures ANOVA needs complete data, so participants with any missing time point are dropped (listwise deletion). If many are missing, a linear mixed model uses all available observations and is usually the better choice.
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