Wilcoxon Mann-Whitney U Calculator
Enter two independent samples to run a nonparametric rank-sum test.
What this calculator does
This tool computes the Wilcoxon Mann-Whitney test (also called the Mann-Whitney U test or Wilcoxon rank-sum test) for two independent groups. It is a popular nonparametric alternative to the independent samples t-test.
Instead of comparing means directly, the test ranks all observations from smallest to largest and checks whether one group tends to have higher ranks than the other. This makes it useful when data are skewed, ordinal, or contain outliers.
When to use the Mann-Whitney U test
- You have two independent groups (e.g., treatment vs. control).
- Your outcome is at least ordinal (rankable).
- You do not want to assume normality required by a t-test.
- You want a robust comparison based on rank information.
Common examples
- Comparing pain scores between two medications.
- Comparing time-to-complete tasks between two interfaces.
- Comparing customer satisfaction ratings across two service methods.
How to use this calculator
- Paste Group A values into the first field.
- Paste Group B values into the second field.
- Select a two-sided or one-sided alternative hypothesis.
- Set your significance level (commonly α = 0.05).
- Click Calculate Test.
The output includes sample sizes, rank sums, U statistics, z-score, p-value, and effect size estimates.
How to interpret the output
Key statistics
- U1 and U2: Two equivalent forms of the U statistic.
- z: Standardized test statistic from normal approximation.
- p-value: Probability of observing data this extreme under the null hypothesis.
- AUC (common language effect): Probability a random A value exceeds a random B value (ties count as 0.5).
- Rank-biserial correlation: Effect size from -1 to +1.
Decision rule
If p-value < α, reject the null hypothesis and conclude there is statistically significant evidence for your selected alternative. If p-value ≥ α, results are not statistically significant.
Assumptions and practical notes
- Groups must be independent.
- Observations should be randomly sampled or assigned.
- The test compares distributions; when shapes are similar, it is often interpreted as a location/median shift.
- Ties are allowed. This calculator applies tie correction in the variance formula.
- p-values here use the normal approximation with continuity correction.
Reporting template
You can report your result like this:
“A Mann-Whitney U test showed that Group A had [higher/lower/no significant difference] than Group B, U = [value], z = [value], p = [value], rank-biserial r = [value].”
FAQ
Is this the same as the Wilcoxon signed-rank test?
No. The signed-rank test is for paired or matched data. Mann-Whitney is for independent groups.
Can I use this with Likert-scale data?
Yes, Likert responses are ordinal and commonly analyzed with rank-based methods like this.
What if my sample sizes are small?
This calculator still works, but the p-value is based on normal approximation. For very small samples, exact methods in dedicated stats software may be preferable.
Bottom line
The Wilcoxon Mann-Whitney test is a strong, practical method when data are non-normal or ordinal. Use this calculator for quick analysis, then report both statistical significance and effect size for a more complete interpretation.