---
title: "Kruskal-Wallis H test"
method_id: SM.DIF.NPA.KIND.KW
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/kruskal_wallis.md
source: Clarus method library
---

# Kruskal-Wallis H 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:** Kruskal-Wallis one-way ANOVA on ranks; Kruskal-Wallis H; nonparametric one-way ANOVA.

## Hypotheses

- **Null (H0):** The k populations have identical distributions of {dependent} (equal mean ranks); F_1 = F_2 = ... = F_k
- **Alternative (H1):** At least one group's distribution of {dependent} is stochastically shifted relative to another (not all mean ranks are equal)

## When to use it

Use this method when your goal is to:
- compare three or more independent groups
- compare independent groups when normality doubtful
- compare distributions of ordinal or skewed outcome

## Data it expects

- **dependent:** 1 continuous or ordinal
- **independent:** 1 nominal/3+ levels
- **pairing:** independent

## Assumptions Clarus checks

- **independence** (severity: error; on violation: reroute)
- **similar distribution shapes** (severity: warning; on violation: warn_only)

## Effect size reported

- **epsilon squared** (Tomczak & Tomczak (2014); Kelley (1935))

## Honest limitations

- Kruskal-Wallis tests whether one group tends to have larger values than another; it is a difference in medians ONLY when the group distributions have similar shapes and spreads.
- A significant result does not, by itself, say WHICH groups differ -- use the Holm-adjusted Dunn post-hoc comparisons for that.
- With small groups (n < 5) the chi-square p-value is an approximation and may be inaccurate; an exact or permutation test is preferable.
- A difference between groups is not causal unless the groups were formed by random assignment.
- Results generalize only to the sampled population.

## Primary sources

- Kruskal, W. H., & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583-621. https://doi.org/10.2307/2280779
- Dunn, O. J. (1964). Multiple comparisons using rank sums. Technometrics, 6(3), 241-252. https://doi.org/10.2307/1266041
- Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.). Wiley.
- Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited: An overview of some recommended measures of effect size. Trends in Sport Sciences, 1(21), 19-25.
- Field, A. (2013). Discovering Statistics Using IBM SPSS (4th ed.). Sage. Ch.15.

## 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, "Kruskal-Wallis H test", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/kruskal_wallis.md

**APA**

Clarus. (2026). Kruskal-Wallis H test (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/kruskal_wallis.md

**BibTeX**

```bibtex
@misc{clarus-kruskal-wallis,
  author       = {Clarus},
  title        = {Kruskal-Wallis H test},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/kruskal_wallis.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.KIND.KW · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library