Mann-Whitney U Test Calculator

The Mann-Whitney U test (also called the Wilcoxon rank-sum test) is a non-parametric statistical test used to compare two independent groups. It tests whether one group tends to have larger values than the other, without assuming the data follows a normal distribution. It is the non-parametric alternative to the independent samples t-test.

Use the Mann-Whitney U test when your data is ordinal or continuous but not normally distributed, when you have small sample sizes, or when outliers are present that would distort a parametric test. If your data meets the normality assumption and you have interval/ratio scale data, an independent t-test may be more appropriate.

The U statistic counts the number of times a value from one group precedes a value from the other group when all values are ranked together. Two U values are computed — one for each group — and the smaller of the two (U_min) is used as the test statistic. A very small U suggests the groups differ substantially.

For larger samples (n > 8), the U statistic is converted to a z-score using the mean and standard deviation of the U distribution under the null hypothesis. The p-value is then derived from the standard normal distribution. For smaller samples, exact distribution tables are more appropriate, but the z-approximation is commonly used and provided here.

The null hypothesis states that the distributions of both groups are equal — or equivalently, that the probability a randomly chosen value from Group 1 is greater than a randomly chosen value from Group 2 equals 0.5. Rejecting the null suggests the two groups differ in their central tendencies or distributions.

A two-tailed test checks whether the groups differ in either direction (Group 1 could be larger or smaller than Group 2). A one-tailed test checks a specific directional hypothesis — either that Group 1 tends to be greater (right-tailed) or smaller (left-tailed) than Group 2. Choose one-tailed only when you have a strong prior directional hypothesis.

When two or more values across the groups are identical (ties), they are assigned the average of the ranks they would have received. This calculator handles ties using average rank assignment and applies a tie correction factor to the z-score calculation, improving accuracy when ties are present in your data.

If your two groups are independent (subjects appear in only one group), use the Mann-Whitney U test for non-normal data or the independent t-test for normal data. If your groups are paired or matched (same subjects measured twice), use the Wilcoxon signed-rank test for non-normal data or a paired t-test for normal data.