Mann-Whitney U Test Calculator
Compare two independent groups without assuming normality — the rank-based alternative to the t-test, also called the Wilcoxon rank-sum test.
Pool both samples, rank them from smallest to largest, and sum the ranks in each group.
How the mann-whitney u test calculator works
Pool both samples, rank them from smallest to largest, and sum the ranks in each group. U measures how often a value from one group beats a value from the other; if the groups are alike, U lands near n₁n₂/2.
Because it uses only the ordering, it is unaffected by outliers and works on ordinal data. The normal approximation used here is reliable once both groups have about eight or more observations.
Formula: U₁ = R₁ − n₁(n₁+1)/2; z = (U − n₁n₂/2) / σ_U
Worked examples
| Inputs | U statistic (smaller) | Note |
|---|---|---|
| Two groups of seven | 12 | group 1 sits higher, but p = 0.125 — not significant on seven each |
| Identical groups | 12.5 | p = 1 |
| Complete separation | 0 | U = 0 — every group-1 value wins |
FAQFrequently asked questions
When should I use Mann-Whitney instead of a t-test?
When the data is ordinal, badly skewed, or has outliers you cannot justify removing. It compares distributions rather than means.
Is it the same as the Wilcoxon rank-sum test?
Yes — two names for the same test, derived independently in 1945 and 1947.
What exactly does it test?
Whether one group tends to produce larger values than the other. Only under an added assumption of identical shapes does it become a test of medians.
How do I read the effect size?
The rank-biserial correlation runs from −1 to +1. The AUC is more intuitive: the probability that a random value from group 1 exceeds one from group 2.
Does it handle ties?
Yes — tied values share an average rank, and the variance is corrected for them, which this calculator does.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.