Mann-Whitney U Test Calculator
Compare two independent groups without assuming normality. Enter numeric values separated by commas, spaces, or line breaks.
This calculator reports an approximate p-value using the normal distribution with tie correction.
What this U Mann-Whitney test calculator does
The Mann-Whitney U test (also called the Wilcoxon rank-sum test) is a nonparametric method for comparing two independent groups. It is especially useful when your data is skewed, has outliers, or does not clearly follow a normal distribution.
This calculator takes two samples, ranks all values together, computes the U statistic, and returns an approximate p-value and effect size. That means you can quickly test whether one group tends to have higher or lower values than the other.
How to use the calculator
- Paste Group 1 values into Sample A.
- Paste Group 2 values into Sample B.
- Select two-sided or one-sided hypothesis.
- Set alpha (commonly 0.05).
- Click Calculate to get U, z, p-value, and interpretation.
Data can be entered as comma-separated values, one value per line, or space-separated values.
When should you use Mann-Whitney instead of a t-test?
Use Mann-Whitney U when:
- Your outcome is ordinal or continuous but not normally distributed.
- You have small sample sizes and want a robust rank-based method.
- Your data includes outliers that may distort means.
- You care about relative ordering (who tends to score higher), not only mean differences.
Use a t-test when:
- Group distributions are reasonably normal.
- You specifically want to test differences in means.
- Parametric assumptions are met and appropriate.
How the U statistic is calculated
The core logic is straightforward:
- Combine both groups into one list.
- Rank all values from smallest to largest (average ranks for ties).
- Sum ranks for each group.
- Convert rank sums into U statistics: U1 and U2.
- Compute p-value from the standardized z-score (with tie-corrected variance).
If there are many tied values, tie correction matters because ties reduce rank variability.
How to interpret the results
- U1 / U2: Test statistics for each group orientation.
- Smaller U: Often used in classical two-sided reporting.
- p-value: Probability of seeing this level of rank separation if there is no true difference.
- Rank-biserial correlation: Effect size from -1 to +1 showing direction and magnitude.
- Common language effect (A): Approximate probability that a random value from Sample A exceeds one from Sample B.
If p-value is below alpha, you typically reject the null hypothesis of equal distributions.
Assumptions and limitations
- Groups must be independent.
- Observations within each group should be independent.
- The test detects location/tendency differences, not just median differences in all cases.
- This tool provides a normal-approximation p-value; exact p-values are preferred for very small samples.
Practical example
Suppose you compare response times for two interfaces. If Sample A values are consistently lower than Sample B, the U statistic will reflect that ordering and the one-sided p-value (A lower than B) may be significant. This gives a strong, distribution-robust decision framework for A/B analysis, UX testing, clinical research, and behavioral science.
Quick FAQ
Is Mann-Whitney only for medians?
Not exactly. It compares rank distributions between groups. Under certain shape conditions, it is interpreted as a median shift test, but more generally it measures stochastic dominance.
Can sample sizes be different?
Yes. Unequal sample sizes are fully supported.
Can I use decimals and negative values?
Absolutely. Any numeric values are accepted.