Mann-Whitney U Test Calculator

About the Mann-Whitney U test

The Mann-Whitney U test compares two independent groups by ranking their pooled observations. It is also called the Wilcoxon rank-sum test. Unlike an independent-samples t test, it does not require normally distributed measurements. It is useful for ordinal outcomes, skewed continuous data, small samples, or situations where strong outliers make a mean-based comparison questionable. The null hypothesis states that observations from the two populations have the same distribution. The calculation combines both samples, sorts every value, and assigns ranks from smallest to largest. Tied observations receive the average of the ranks they occupy. The rank total for the first sample is converted to U, and the complementary U value is computed for the second sample. This calculator reports the smaller U statistic because it is the conventional test statistic for a two-sided comparison. A small U indicates that values from one group tend to occupy consistently lower or higher ranks than values from the other. For inference, the calculator standardizes U using its null mean and variance. The variance includes a tie correction, because repeated values reduce the variability of the rank sum. It then obtains a two-sided p value from the standard normal approximation. A p value below a chosen significance threshold, commonly 0.05, is evidence against the null hypothesis. It is not the probability that the null hypothesis is true, and it does not by itself describe the size or practical importance of a difference. Interpretation needs care. If the group distributions have similarly shaped spreads, the test is often described as a comparison of locations or medians. When their shapes differ substantially, the result is more generally evidence that one distribution tends to generate larger observations. Samples must be independent: a participant should not contribute to both groups. Paired before-and-after measurements require a paired method such as the Wilcoxon signed-rank test instead. For very small samples, an exact U distribution can be preferable to the normal approximation. This page uses the transparent large-sample approximation with tie correction so its results are reproducible and easy to audit. Report sample sizes, U, the p value, an effect-size estimate, and descriptive summaries whenever possible.

Mann-Whitney examples

How to run the U test

1. Paste numeric observations for Sample A, separated by commas or spaces.
2. Paste independent observations for Sample B in the second field.
3. Select Calculate Mann-Whitney U to rank the combined data.
4. Interpret the two-sided p value alongside the U statistic and sample context.