Mann-Whitney U Test Calculator

Reviewed by CalcMulti Editorial Team·Last updated: February 2026·← Statistics Hub

The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups without assuming normality. It is the non-parametric alternative to the independent two-sample t-test and is appropriate for ordinal data, skewed continuous data, or any situation where the normality assumption cannot be justified.

Enter your two groups (values comma-separated) to compute the U-statistic, z-approximation, and two-tailed p-value.

How the Mann-Whitney U test works: all observations from both groups are combined and ranked from lowest (1) to highest. Tied values receive average ranks. The test then counts, for each observation in Group 1, how many observations in Group 2 have lower values — summing these counts gives U₁. Similarly for U₂. The formulas are: U₁ = n₁n₂ + n₁(n₁+1)/2 − R₁, where R₁ is the sum of ranks assigned to Group 1. Note that U₁ + U₂ = n₁ × n₂ always.

When to use Mann-Whitney vs. t-test: use the t-test when data are continuous and approximately normally distributed — it has more statistical power (detects differences more reliably) when assumptions hold. Use Mann-Whitney when data are ordinal (rating scales, pain scores, Likert items), when distributions are clearly skewed (e.g., income data, reaction times), when sample sizes are small and normality cannot be confirmed, or when outliers are present that you cannot remove.

Interpreting the results: if the p-value is below your significance level (typically 0.05), reject the null hypothesis that the two population distributions are identical. The effect size r = z / √(n₁ + n₂) indicates practical significance: r ≈ 0.1 is small, 0.3 is medium, 0.5 is large (Cohen's benchmarks). The median of each group is the appropriate measure of central tendency to report alongside this test — not the mean, since normality is not assumed.