Mann-Whitney U Test Calculator
Perform the Mann-Whitney U Test (Wilcoxon Rank-Sum) on large datasets. Features automatic data ranking, U and Z-score calculation, and p-value estimation for non-normal distributions.
About
When your data does not meet the strict assumptions of the Student's t-test—specifically, when it is not normally distributed or consists of ordinal variables (like survey rankings)—the Mann-Whitney U test is the gold standard alternative. It compares the distribution of two independent samples to determine if one is stochastically greater than the other.
This calculator handles the tedious work of Ranking. Normally, you would have to combine all data points, sort them, assign ranks (handling ties by averaging), and then sum them back up. This tool does it instantly, even for large datasets. It outputs the U statistic and the Z-score (using the normal approximation for samples n > 20), making it suitable for professional research.
Formulas
The U statistic is calculated for both groups:
For large samples, we use the Z-approximation:
Reference Data
| n1 | n2 | Critical U (α=0.05) | Critical U (α=0.01) |
|---|---|---|---|
| 5 | 5 | 2 | 0 |
| 5 | 10 | 8 | 4 |
| 10 | 10 | 23 | 16 |
| 10 | 15 | 39 | 29 |
| 15 | 15 | 64 | 51 |
| 20 | 20 | 127 | 105 |
| >20 | >20 | Use Z-Approx | Use Z-Approx |