One-Way RM-ANOVA (3+ measurements)

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Repeat / Within

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

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Tests whether means of a continuous DV differ across three or more RELATED measurements (same subjects measured multiple times).

Removes between-subject variance — much more powerful than between-groups ANOVA at the same n. Reports the omnibus F, η²p effect size, Mauchly sphericity test, and Greenhouse-Geisser / Huynh-Feldt corrections automatically applied when sphericity rejects. Pairwise post-hoc with Bonferroni or Holm correction. Switch to linear mixed-effects for missing-data tolerance or non-spherical correlation structures.

Worked example

Does reaction time change across three training sessions?

24 participants were each measured at Session 1, 2 and 3 (within-subjects); a repeated-measures ANOVA with a sphericity check.

Result

Reaction time changed significantly across the three sessions, F(2, 46) = 24.39, p < .001 — a large effect, with times falling from Session 1 to Session 3.

How you'd report it (APA)

A repeated-measures ANOVA showed a significant effect of session on reaction time, F(2, 46) = 24.39, p < .001.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Multiple time points (longitudinal within-subjects)
    Depression scores measured in 50 patients at baseline, 3 months, 6 months, and 12 months after starting treatment.
  • Multiple conditions (within-subjects experiment)
    Reaction time measured under 3 lighting conditions (dim, normal, bright) for the same 40 participants.
  • Multiple related measurements (same scale)
    Students' anxiety scores measured across 3 domains (social, academic, health) using the same Likert scale.

When NOT to — use instead

Hypotheses

H₀: μ₁ = μ₂ = … = μₖ — all k condition means are equal in the population (the same subjects are measured at each level).
Hₐ: at least one μᵢ ≠ μⱼ — the population means at the k levels are NOT all equal.

Parameter tested: set of population condition means {μ₁, …, μₖ}

Assumptions (and what to do if they fail)

No significant outliers within any condition / levelmedium

Check: Inspect the per-condition boxplot; flag points beyond the whiskers.

If violated: Outliers within a condition can inflate within-condition variance and distort the F-test.

Dependent variable is approximately normally distributed at each level of the within-subjects factormedium

Check: Run Shapiro-Wilk on each condition; inspect per-condition Q-Q plots.

If violated: Severely non-normal data threatens the F-test's nominal Type I error rate, especially with small n.

Sphericity — variances of all pairwise differences between levels are equal (Mauchly's test)medium

Check: Mauchly's test; non-significant (p > .05) → sphericity met.

If violated: When sphericity is violated, the standard F-test inflates the Type I error rate.

Ready to run a One-Way RM-ANOVA (3+ measurements) on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

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