Mann-Whitney U Test

The Mann-Whitney U test compares two independent groups without assuming normally distributed data. It ranks all observations from both groups together and tests whether those ranks are distributed evenly, making it the non-parametric counterpart to the independent-samples t-test.

Use it when the outcome is ordinal, such as Likert items treated as ranks or satisfaction ratings, when the sample is small, or when normality checks show a clear departure that transformation does not resolve. It compares distributions in general, and medians specifically when the two distributions have similar shapes.

Report U, the z approximation, and the exact p-value for small samples, along with group medians and an effect size (r calculated as z divided by the square root of N). The Wilcoxon signed-rank test is its paired equivalent, and the Kruskal-Wallis test extends the same logic to three or more groups.