Mann-Whitney U Test Calculator
Compare two independent samples using the Mann-Whitney U test (also called the Wilcoxon rank-sum test). This nonparametric test does not require the data to be normally distributed.
The Mann-Whitney U test is the nonparametric alternative to the independent samples t-test. It compares two groups by ranking all observations together and comparing the sum of ranks between groups.
How it works: All values from both samples are combined and ranked. The U statistic is calculated from the rank sum: U = n1n2 + n1(n1+1)/2 - R1, where R1 is the sum of ranks for sample 1. For larger samples, the distribution of U is approximately normal, allowing a z-test.
When to use it: Use the Mann-Whitney test when your data is ordinal, when normality assumptions are violated, when you have outliers, or when sample sizes are small and you cannot verify normality. It tests whether one group tends to have larger values than the other.