Mann-Whitney U Test Calculator

The Mann-Whitney U test, also called the Wilcoxon rank-sum test, checks whether two independent samples come from the same distribution. It is nonparametric, so it does not assume the data are normally distributed and works on ranks instead of raw values. A significant result means one group tends to produce larger values than the other.

Use the Mann-Whitney U test when your data are ordinal, skewed, or have outliers, or when the samples are too small to trust a normal-distribution assumption. The t-test compares means and assumes roughly normal data, while this test compares ranks and is more robust. If your data are clearly normal with similar variances, a t-test usually has slightly more statistical power.

First, pool both samples and rank every value from smallest to largest, giving tied values the average of the ranks they share. Add the ranks within each group to get R1 and R2, then compute U1 as R1 minus n1(n1+1)/2 and U2 as R2 minus n2(n2+1)/2. The reported U is the smaller of U1 and U2, and the two always add up to n1 times n2.

It uses the large-sample normal approximation. The calculator standardizes U into a z-score using the mean (n1 times n2 divided by 2) and the standard deviation of U, applying a 0.5 continuity correction and a tie correction to the variance. That z-score becomes a one-tailed or two-tailed p-value. For groups smaller than 8, the approximation is rough, so compare U against an exact critical-value table instead.

On its own, U measures how much the two samples overlap in rank. A U close to n1 times n2 divided by 2 means the groups overlap heavily and differ little, while a U near 0 means almost no overlap and a strong separation. The rank-biserial correlation shown alongside scales this to a range of -1 to 1 as an effect size, where 0 is no difference.

Yes. Tied values receive average (mid) ranks, and the variance of U is reduced by a tie correction so the p-value stays accurate. The two samples do not need to be the same size, because every value is ranked within one combined pool. If every value is identical there is no variation to test, so the calculator returns no result.