mann whitney u test calculator

What this Mann-Whitney U test calculator does

This calculator compares two independent samples and tests whether one group tends to have larger values than the other. It is a nonparametric alternative to the independent samples t-test and is useful when your data are skewed, ordinal, or include outliers.

You provide two groups, and the tool computes:

• Rank sums for each group
• U1, U2, and the smaller U
• Normal-approximation z score
• Two-tailed p-value
• Effect size metrics (r, AUC, and Cliff’s delta)

When should you use the Mann-Whitney U test?

Use it when:

• You have exactly two independent groups.
• Your outcome is ordinal, continuous but non-normal, or has strong outliers.
• You want a robust comparison of distributions/central tendency between groups.

Avoid it when:

• Data are paired or repeated measures (use Wilcoxon signed-rank instead).
• You need more than two groups (consider Kruskal-Wallis).
• Observations are not independent.

How to use this calculator

1. Paste Group A values in the first box.
2. Paste Group B values in the second box.
3. Set alpha (commonly 0.05).
4. Click Calculate Mann-Whitney U.

The p-value interpretation is straightforward: if p < α, reject the null hypothesis of equal distributions.

Interpretation tips

A significant result tells you the groups differ in rank tendency. It does not automatically tell you the exact size of practical impact, which is why effect sizes are reported:

• Effect size r: rough guideline 0.1 small, 0.3 medium, 0.5 large.
• AUC: probability that a random value from Group A is greater than a random value from Group B.
• Cliff’s delta: range from -1 to +1; sign gives direction, magnitude gives strength.

Assumptions and notes

• Independent observations within and between groups.
• Outcome measured at least on an ordinal scale.
• Ties are allowed; this calculator applies tie-corrected variance for the z approximation.
• For very small samples, exact methods can be preferred over normal approximation.

Example

Suppose Group A is a treatment group and Group B is control. If the calculator gives U = 18, z = -2.31, p = 0.021, and α = 0.05, you would conclude there is evidence of a difference between groups.