---
title: "Repeated-measures ANOVA (one-way, within-subjects)"
method_id: SM.DIF.PAR.KDEP.RMANOVA
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/repeated_measures_anova.md
source: Clarus method library
---

# Repeated-measures ANOVA (one-way, within-subjects)

> A classical statistical method in the Clarus library (Difference family).
> Clarus selects, assumption-checks and runs this method on your data with a
> deterministic rule engine and real numerical libraries (scipy / statsmodels);
> it never generates numbers, citations or results.

**Also known as:** within-subjects ANOVA; one-way repeated-measures ANOVA; RM-ANOVA.

## Hypotheses

- **Null (H0):** mu_1 = mu_2 = ... = mu_k (population means equal across all conditions)
- **Alternative (H1):** at least one condition mean of {dependent} differs from another

## When to use it

Use this method when your goal is to:
- compare 3plus related means
- compare within subject conditions over time

## Data it expects

- **dependent:** 1 continuous
- **independent:** 1 within-subject factor / 3+ levels
- **pairing:** repeated_within_subject

## Assumptions Clarus checks

- **normality** (gate: shapiro_wilk; severity: warning; on violation: reroute)
- **sphericity** (gate: mauchly; severity: error; on violation: correct)

## Effect size reported

- **partial eta squared** (Cohen (1973); Lakens (2013))

## Honest limitations

- Repeated-measures designs assume sphericity; when it is violated the uncorrected F is too liberal, so always read the corrected degrees of freedom.
- A significant omnibus F only says the conditions are not all equal; consult the Bonferroni pairwise comparisons to see which conditions differ.
- For data measured over time, an effect of condition is not evidence that the manipulation caused the change unless order was controlled/counterbalanced.
- Carry-over, practice, and fatigue effects can masquerade as condition effects in within-subject designs.
- Results generalize only to the sampled population, and small subject counts make estimates unstable.

## Primary sources

- Mauchly, J. W. (1940). Significance test for sphericity of a normal n-variate distribution. The Annals of Mathematical Statistics, 11(2), 204-209. https://doi.org/10.1214/aoms/1177731915
- Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95-112. https://doi.org/10.1007/BF02289823
- Huynh, H., & Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1(1), 69-82. https://doi.org/10.2307/1164736
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage. Ch.15 (Repeated-measures designs).
- Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863

## How to cite this

To cite this Clarus method page (the page itself — for the method's own primary sources, see above):

**Plain text**

Clarus, "Repeated-measures ANOVA (one-way, within-subjects)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/repeated_measures_anova.md

**APA**

Clarus. (2026). Repeated-measures ANOVA (one-way, within-subjects) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/repeated_measures_anova.md

**BibTeX**

```bibtex
@misc{clarus-repeated-measures-anova,
  author       = {Clarus},
  title        = {Repeated-measures ANOVA (one-way, within-subjects)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/repeated_measures_anova.md}
}
```

_No DOI is minted for Clarus method pages yet; this citation uses the canonical URL, version and date. Cite the primary sources above for the method's scientific provenance._

---

METHOD SM.DIF.PAR.KDEP.RMANOVA · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library