Mann-Whitney U Test Calculator
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) compares two independent groups without assuming normality — the go-to alternative to the independent t-test for skewed data, ordinal scales or small samples. Paste both groups and get U, the z approximation with tie and continuity correction, the two-tailed p-value and the rank-based effect size r = |z|/√N. Results match R's wilcox.test(x, y) (normal approximation) to at least four significant digits, tie handling included. The group medians and their difference are shown as well, since Mann-Whitney conclusions are usually phrased in terms of medians or rank distributions.
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Frequently asked questions
How do I report a Mann-Whitney U test in APA 7 format?
Report U, the z approximation, the exact p and an effect size, e.g.: "Group A scores were higher than Group B, U = 58, z = 1.50, p = .133, r = .35", ideally with the group medians. The AI Report button generates the complete APA 7 results paragraph from your data.
When should I use Mann-Whitney instead of the independent t-test?
When the t-test's assumptions are shaky: clearly skewed distributions, ordinal (Likert-type) outcomes, small samples with outliers. If the data are roughly normal, the t-test has slightly more power — running Shapiro-Wilk on each group (see our t-test tool) is a good way to decide.
Does the calculator handle ties, and why is my p slightly different from a table?
Yes — the variance is tie-corrected and a 0.5 continuity correction is applied, exactly like R's wilcox.test with exact=FALSE. Small-sample tables use the exact permutation distribution instead, so tiny differences from table values are expected; the normal approximation is standard practice for n ≳ 10 per group.