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Mann–Whitney U test calculator

Nonparametric comparison of two independent groups — the rank-based alternative to the independent t-test. Returns U, z, p and effect size r.

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Your data

Paste one column of numbers per group. Groups may differ in size; ties are handled with average ranks.

n = 0
n = 0
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When to use this

The Mann–Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups when the assumptions of the t-test are doubtful: skewed distributions, ordinal outcomes (pain ratings, Likert responses), small samples, or outliers you cannot justify removing. It ranks all observations together and asks whether one group’s ranks are systematically higher than the other’s. It tests for a difference in the distributions’ location — commonly summarized with medians — rather than a difference in means.

Key assumptions

  • The two groups are independent (different cases in each).
  • The outcome is at least ordinal — values can be ranked.
  • Observations are independent within and across groups.
  • To interpret the result as a median difference, the two distributions should have a similar shape.

Common mistakes

  • Using it for paired data — the paired analogue is the Wilcoxon signed-rank test.
  • Reporting means with a Mann–Whitney result; report medians (and the effect size r).
  • Assuming it tests medians under all circumstances — with very different distribution shapes it is a test of stochastic dominance, not of medians.
  • Thinking it is assumption-free; independence and ordinal-or-better measurement still matter.

Frequently asked questions

When should I prefer Mann–Whitney over the t-test?
When the outcome is ordinal, the samples are small and clearly non-normal, or outliers dominate the means. With roughly normal data the t-test has slightly more power; with heavy tails or skew, Mann–Whitney often has more.
What does the effect size r mean here?
r = |z|/√N, ranging from 0 to about 1. Benchmarks: .10 small, .30 medium, .50 large. It is the standard effect size to report alongside U and p.
Why does the output show a z statistic?
For all but tiny samples, the p-value is computed from a normal approximation of U’s distribution (with tie and continuity corrections) — the z value is that standardized statistic, and it is conventional to report it.

Related free tools

Sample size calculatorSample size for two groupsEffect size (Cohen's d)Descriptive statisticsOne-sample t-testIndependent t-testPaired t-testz-table (standard normal)t-table (critical values)Chi-square table

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