---
title: "Mood's median test (k groups)"
method_id: SM.DIF.NPA.KIND.MOODMED
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/mood_median_test.md
source: Clarus method library
---

# Mood's median test (k groups)

> 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:** Mood median test; median test; Brown-Mood median test; k-sample median test.

## Hypotheses

- **Null (H0):** median_{g1} = median_{g2} = ... = median_{gk}
- **Alternative (H1):** at least one group median differs from the others

## When to use it

Use this method when your goal is to:
- compare central tendency across k independent groups
- compare medians robust to outliers
- compare groups with heavy skew or extreme values

## Data it expects

- **dependent:** 1 ordinal or continuous
- **independent:** 1 nominal/2+ levels
- **pairing:** independent

## Assumptions Clarus checks

- **independence** (severity: error; on violation: reroute)
- **ordinal or continuous dv** (severity: error; on violation: warn_only)
- **adequate expected cell counts** (gate: expected_frequency; severity: warning; on violation: correct)

## Honest limitations

- Mood's median test only uses whether each value is above or at-or-below the grand median, discarding most of the data's information; it is therefore less powerful than Kruskal-Wallis for detecting shifts and should be preferred mainly when medians are the specific quantity of interest or when extreme outliers make rank or mean comparisons untrustworthy.
- A non-significant result is absence of evidence for a median difference, not proof that medians are equal.
- A significant difference is not causal unless groups were formed by random assignment.
- Many ties exactly at the grand median can substantially reduce power and bias the above/below split.
- Results generalize only to the sampled population.

## Primary sources

- Mood, A. M. (1950). Introduction to the Theory of Statistics. McGraw-Hill, New York.
- Brown, G. W., & Mood, A. M. (1951). On median tests for linear hypotheses. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 159-166.
- Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.). Wiley.
- Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences (2nd ed.). McGraw-Hill.

## 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, "Mood's median test (k groups)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/mood_median_test.md

**APA**

Clarus. (2026). Mood's median test (k groups) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/mood_median_test.md

**BibTeX**

```bibtex
@misc{clarus-mood-median-test,
  author       = {Clarus},
  title        = {Mood's median test (k groups)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/mood_median_test.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.MOODMED · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library