Wilcoxon Rank-Sum Test Calculator
Calculate the Wilcoxon rank-sum (Mann-Whitney U) test statistic and its normal approximation z-score from your two group sizes and rank sum.
What the Wilcoxon rank-sum test does
The Wilcoxon rank-sum test (equivalent to the Mann–Whitney U test) is a nonparametric test used to determine whether two independent samples come from populations with the same distribution, without assuming normality.
The formula
After ranking all combined observations, U1 = W1 − n1(n1+1)/2, where W1 is the sum of ranks for group 1. U2 is found from U1 + U2 = n1n2, and the test statistic U is the smaller of the two. For larger samples, U is approximately normal with mean n1n2/2 and standard deviation √(n1n2(n1+n2+1)/12), giving a z-score for significance testing.
This calculator is for general statistics education; exact p-values for small samples should be looked up in a Mann–Whitney U table or computed with dedicated statistical software.