Repeated-measures ANOVA
Repeated-measures Analysis of Variance · Also known as: within-subjects ANOVA, repeated measures analysis of variance, rm-ANOVA, Tekrarlı Ölçüm ANOVA
Repeated-measures ANOVA is a parametric hypothesis test that compares three or more measurements taken from the same individuals — typically across time points or conditions — to decide whether their means differ. It extends one-way ANOVA to within-subjects designs, as treated in standard references such as Girden (1992) and Field (2013).
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When to use it
Use it to compare a single continuous outcome measured three or more times on the same individuals (longitudinal or panel data). Assumptions: each measurement is approximately normally distributed (check Shapiro-Wilk at each time point), and sphericity holds — the variances of the differences between all pairs of conditions are equal (check with Mauchly's test). A sample of at least about 20 subjects is recommended; with smaller samples or non-normal data the nonparametric Friedman test is more appropriate, and substantial missing data is better handled by a linear mixed-effects model.
Strengths & limitations
- Removes stable between-subject variability, so it has more power than a between-groups design for the same number of observations.
- Tests three or more time points or conditions in a single omnibus test, avoiding inflated error from multiple paired tests.
- Reports an interpretable effect size (partial eta-squared) and supports standard correction methods for sphericity.
- Requires the sphericity assumption; when it fails, a Greenhouse-Geisser or Huynh-Feldt correction is mandatory.
- Sensitive to non-normality at any time point, especially in small samples.
- Classic form requires complete data for every subject at every time point — missing observations force dropping cases or switching to a mixed model.
Frequently asked
How is this different from a paired t-test?
A paired t-test compares exactly two related measurements. Repeated-measures ANOVA generalises that idea to three or more time points or conditions in a single test, which avoids inflating the false-positive rate that running many paired t-tests would cause.
What is sphericity and why does it matter?
Sphericity means the variances of the differences between every pair of conditions are equal. If Mauchly's test shows it is violated, the F test becomes too liberal, so a Greenhouse-Geisser or Huynh-Feldt epsilon correction is applied to the degrees of freedom before the decision is read.
What if my data are not normal or my sample is small?
With marked non-normality or a sample below about 20, the parametric F test inflates the Type I error risk. The Friedman test is the nonparametric alternative for repeated measures, while a linear mixed-effects model is preferred when there is missing data.
How do I know which time points differ?
A significant omnibus F only says that some means differ. Follow it with Bonferroni-corrected pairwise comparisons to identify which specific conditions differ, and report partial eta-squared as the effect size.
Sources
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed., Ch. 14). SAGE. ISBN: 978-1446249185
- Girden, E. R. (1992). ANOVA: Repeated Measures. SAGE. ISBN: 978-0803942578
How to cite this page
ScholarGate. (2026, June 1). Repeated-measures Analysis of Variance. ScholarGate. https://scholargate.app/en/statistics/repeated-measures-anova
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Friedman testStatistics↔ compare
- One-way ANOVAStatistics↔ compare
- Paired t-testStatistics↔ compare
- Two-Way ANOVAStatistics↔ compare