Ranks Instead of Means

This Mann-Whitney U test calculator pools two independent samples, ranks every observation (averaging ties), and sums the ranks per group. U derives directly from those rank sums — no normality assumption needed, and outliers can't dominate.

The Normal Approximation

U is centered at n₁n₂/2 with a tie-corrected standard deviation, so z = (U − μ)/σ follows the standard normal for moderate samples. The two-tailed p-value comes from the normal CDF — computed here exactly via the incomplete gamma function.

Reading the Result

A small p-value means the groups' value distributions differ — one tends to rank higher. The test says nothing about the size of the difference, only that it is unlikely to be chance. Report the U statistic and p-value together.