Mann–Whitney U Test Calculator
Compare two independent samples without assuming normality — U statistic, tie-corrected z, two-sided p-value and the rank-biserial effect size.
How it works
U₁ = R₁ − n₁(n₁+1)/2; U = min(U₁, U₂); z = (U − n₁n₂/2 + 0.5) ÷ σᵤ, σᵤ² = n₁n₂/12 · [(n+1) − Σ(t³−t)/(n(n−1))]
The Mann–Whitney U test (Wilcoxon rank-sum) pools both samples, ranks every value and asks whether one sample tends to have higher ranks than the other. It needs no normality assumption and is robust to outliers, which makes it the usual choice for skewed data or small samples. The normal approximation with tie correction is accurate from about 8 observations per group; the rank-biserial correlation turns U into an effect size between −1 and 1.
Worked example
Samples of 7 and 8 values: U = 4, z = −2.72, p = 0.006, rank-biserial 0.86 — sample 1 is reliably higher.
Frequently asked questions
Is this the same as the Wilcoxon rank-sum test?
Yes — U and W are linear transforms of each other and give identical p-values.
What does it actually test?
Stochastic dominance: whether a random value from one group tends to exceed one from the other. Only under equal shapes does that reduce to a difference in medians.
Related calculators
For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.