Mann-Whitney U Test Calculator
Paste two independent samples below (numbers separated by commas, spaces, or new lines), choose your hypothesis, then click Calculate.
What is the Mann-Whitney U test?
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) is a nonparametric method used to compare two independent groups. It is especially useful when your data are not normally distributed, include outliers, or are measured on an ordinal scale.
Instead of comparing means directly, the test ranks all values from both groups together and then checks whether one group tends to receive higher ranks than the other.
When should you use this online calculator?
- You have two independent samples (e.g., treatment vs. control).
- Your data are skewed, ordinal, or violate normality assumptions.
- You want a robust alternative to the independent samples t-test.
- You need a quick way to estimate statistical significance and effect direction.
How to use the calculator
1) Enter your two datasets
Place Group A and Group B numbers in their respective boxes. You can separate values with commas, spaces, semicolons, or line breaks.
2) Choose hypothesis type
- Two-sided (A ≠ B): tests for any difference between groups.
- One-sided (A > B): tests whether A tends to be larger.
- One-sided (A < B): tests whether A tends to be smaller.
3) Set significance level α
Most users choose α = 0.05. Lower values (like 0.01) are stricter.
4) Click “Calculate Test”
You will see sample sizes, rank sums, U statistics, z-score (normal approximation with tie correction), p-value, and a decision statement.
What the output means
- U1 / U2: two equivalent U-statistics based on each group’s rank sum.
- z-score: standardized test statistic using a continuity correction.
- p-value: probability of observing your result under the null hypothesis.
- Rank-biserial correlation: effect size indicating direction and magnitude.
- Common language effect size: probability a random A value exceeds a random B value.
Assumptions and caveats
- Observations should be independent.
- The response should be at least ordinal.
- The test compares distributions; interpretation as “median difference” is safest when shapes are similar.
- This calculator uses the normal approximation, which is common for practical use and supports ties.
Example interpretation
If your p-value is below α (e.g., p = 0.012, α = 0.05), you reject the null hypothesis and conclude the groups differ statistically. If rank-biserial correlation is positive, Group A tends to have larger values; if negative, Group B tends to have larger values.
FAQ
Is this the same as a t-test?
No. A t-test compares means under stronger assumptions (especially normality). Mann-Whitney compares rank tendencies and is more robust for non-normal data.
Can I use this with paired samples?
No. For paired/repeated measurements, use the Wilcoxon signed-rank test instead.
Can I include decimals and negative values?
Yes. The calculator accepts any real numbers.