---
title: "Friedman test"
method_id: SM.DIF.NPA.KDEP.FRIED
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/friedman.md
source: Clarus method library
---

# Friedman test

> 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:** Friedman two-way analysis of variance by ranks; Friedman rank test; non-parametric repeated-measures ANOVA.

## Hypotheses

- **Null (H0):** The k related conditions share the same distribution (equal mean ranks across conditions).
- **Alternative (H1):** At least one condition's distribution differs (mean ranks are not all equal).

## When to use it

Use this method when your goal is to:
- compare three or more related conditions
- repeated measures nonparametric
- within subjects rank difference

## Data it expects

- **dependent:** 1 ordinal or continuous (rank-able), measured under each condition
- **independent:** 1 within-subjects factor with >= 3 levels (conditions/time points)
- **pairing:** related (repeated measures / matched blocks); same subjects across all conditions

## Assumptions Clarus checks

- **related complete blocks** (severity: critical; on violation: warn_only)
- **ordinal within block comparability** (severity: critical; on violation: warn_only)
- **few within block ties** (severity: warning; on violation: warn_only)

## Effect size reported

- **kendall w** (Kendall & Babington Smith (1939); W = Q / (n*(k-1)) [W definition, NOT a magnitude-band anchor])

## Honest limitations

- A significant Friedman test tells you the conditions differ somewhere but not which pairs — read the Nemenyi post-hoc comparisons.
- This is a within-subjects (repeated-measures) test: the difference is across conditions on the same subjects, not across independent groups.
- With small n or heavy within-block ties, the chi-square p-value is an approximation; an exact Friedman test is preferable.
- A difference across conditions is not causal unless the conditions were administered under a randomized (e.g. counterbalanced) experimental design.
- Results generalize only to the sampled population.

## Primary sources

- Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. JASA, 32(200), 675-701. https://doi.org/10.1080/01621459.1937.10503522
- Kendall, M. G., & Babington Smith, B. (1939). The problem of m rankings. Annals of Mathematical Statistics, 10(3), 275-287. https://doi.org/10.1214/aoms/1177732186
- Nemenyi, P. (1963). Distribution-free multiple comparisons (Doctoral dissertation, Princeton University).
- Demsar, J. (2006). Statistical comparisons of classifiers over multiple data sets. JMLR, 7, 1-30.
- Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.), Ch.5.
- Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences (2nd ed.), Ch.7.
- Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited. Trends in Sport Sciences, 1(21), 19-25.

## 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, "Friedman test", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/friedman.md

**APA**

Clarus. (2026). Friedman test (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/friedman.md

**BibTeX**

```bibtex
@misc{clarus-friedman,
  author       = {Clarus},
  title        = {Friedman test},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/friedman.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.NPA.KDEP.FRIED · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library