Mann-Whitney U Test Calculator
Calculate the Mann-Whitney U statistic and its z-approximation to compare two independent samples without assuming a normal distribution.
About the Mann-Whitney U Test Calculator
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups without assuming their data is normally distributed. Instead of comparing means directly, it combines both groups, ranks every value together, and checks whether one group's ranks tend to be systematically higher or lower than the other's.
Formula: Rank all combined values (averaging tied ranks), sum Group 1's ranks as R₁, then U₁ = R₁ − n₁(n₁+1)/2 and U₂ = n₁n₂ − U₁ · For larger samples, z = (U − n₁n₂/2) ÷ √(n₁n₂(n₁+n₂+1)/12)
The reported U statistic is the smaller of U₁ and U₂; a small U (far from its expected value of n₁n₂/2) suggests the two groups' distributions differ. This test is the standard alternative to the two-sample t-test for ordinal data, small samples, or data with outliers or skew that would violate the t-test's normality assumption, since it only relies on the relative ordering of values rather than their exact magnitudes.