---
title: "Mann-Whitney U test"
method_id: SM.DIF.NPA.2IND.MWU
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/mann_whitney_u.md
source: Clarus method library
---

# Mann-Whitney U 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:** Mann-Whitney-Wilcoxon test; Wilcoxon rank-sum test; MWU; two-sample rank test.

## Hypotheses

- **Null (H0):** f = g — the two distributions are identical (Mann & Whitney 1947, the strong null); equivalently P(X_{group1} > X_{group2}) = P(X_{group2} > X_{group1}).
- **Alternative (H1):** P(X_{group1} > X_{group2}) != P(X_{group2} > X_{group1}) — one group is stochastically dominant.

## When to use it

Use this method when your goal is to:
- compare two independent groups

## Data it expects

- **dependent:** 1 ordinal or continuous (rank-able)
- **independent:** 1 nominal with exactly 2 levels (grouping)
- **pairing:** independent (between-subjects)
- **distribution:** non-normal, skewed, ordinal, or small-n where parametric assumptions are doubtful

## Assumptions Clarus checks

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

## Effect size reported

- **rank biserial** (Wendt (1972); Kerby (2014). RBC = 1 - (2*U1)/(n1*n2), where U1 is the U statistic of the first group.)

## Honest limitations

- Mann-Whitney U compares whole distributions; it equals a median comparison only when the two group distributions have similar shapes and spreads — otherwise read it as one group tending to score higher.
- Many tied values reduce the test's accuracy and force a normal approximation rather than an exact null; report that ties were present.
- A significant rank difference is not causal unless groups were formed by random assignment.
- Results generalize only to the population the sample was drawn from.

## Primary sources

- Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18(1), 50-60. https://doi.org/10.1214/aoms/1177730491
- Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83. https://doi.org/10.2307/3001968
- Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11.IT.3.1. https://doi.org/10.2466/11.IT.3.1
- McGraw, K. O., & Wong, S. P. (1992). A common language effect size statistic. Psychological Bulletin, 111(2), 361-365. https://doi.org/10.1037/0033-2909.111.2.361
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.), 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, "Mann-Whitney U test", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/mann_whitney_u.md

**APA**

Clarus. (2026). Mann-Whitney U test (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/mann_whitney_u.md

**BibTeX**

```bibtex
@misc{clarus-mann-whitney-u,
  author       = {Clarus},
  title        = {Mann-Whitney U test},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/mann_whitney_u.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.2IND.MWU · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library