Free Mann–Whitney U Test Calculator
Paste two independent samples below (numbers separated by commas, spaces, or new lines). This calculator returns the Mann–Whitney U statistic, z-score, p-value (normal approximation with tie correction), and a quick decision at your chosen alpha level.
What is the Mann–Whitney U test?
The Mann–Whitney U test (also called the Wilcoxon rank-sum test) is a nonparametric method for comparing two independent groups. Instead of comparing means directly, it compares the rank ordering of observations across groups.
It is useful when your data are skewed, ordinal, contain outliers, or when you do not want to assume normality as strongly as a two-sample t-test does.
When should you use this calculator?
- You have two independent samples (e.g., control vs treatment).
- Your outcome is at least ordinal (rankable).
- You want to test whether one group tends to have larger values than the other.
- You prefer a robust rank-based test instead of a parametric mean-based test.
Quick assumptions checklist
- Observations are independent within and between groups.
- The response scale supports ranking.
- The two groups are randomly sampled or reasonably comparable.
How this Mann–Whitney calculator computes results
After combining both samples, each value receives a rank from smallest to largest. Tied values receive average ranks. From rank sums, the calculator computes:
- U1 for Sample A
- U2 for Sample B
- Expected mean of U under H0:
n1 * n2 / 2 - Variance of U with tie correction
- z-score and p-value using a normal approximation
For large samples this approximation is standard. For very small samples, exact p-values can differ slightly from approximate values.
How to interpret the output
1) U statistic
U summarizes how much the ranks in one group tend to be above or below the other. Smaller/larger values (depending on direction) indicate stronger separation.
2) p-value
The p-value estimates how surprising your observed rank difference would be if there were truly no group difference. If p is below alpha (for example 0.05), you reject the null hypothesis.
3) Effect size
The calculator also returns rank-biserial correlation and common-language effect estimate. These help interpret practical importance, not just statistical significance.
Mann–Whitney vs. independent t-test
- t-test: compares means, assumes roughly normal residual behavior (or large-sample robustness).
- Mann–Whitney: compares rank tendencies/distributional shift and is less sensitive to outliers.
If your data are clearly non-normal, ordinal, or heavily skewed, Mann–Whitney is often preferred.
Common mistakes to avoid
- Using this test for paired/repeated measurements (use Wilcoxon signed-rank instead).
- Ignoring dependence between observations.
- Interpreting significance as a guarantee of large practical effect.
- Assuming the test always compares medians regardless of distribution shape.
Example use case
Suppose you compare completion times for two onboarding flows in an app. Times are skewed and include outliers. A Mann–Whitney test can evaluate whether one flow tends to produce shorter completion times without relying heavily on normality assumptions.
FAQ
Can I enter decimals and negative values?
Yes. The parser accepts integers and decimals, including negatives.
What separators are accepted?
Commas, spaces, semicolons, tabs, and line breaks.
Does this tool handle ties?
Yes. Average ranks are used for tied values, and tie correction is applied in the variance term.
Is this calculator suitable for publication-grade analysis?
It is great for fast analysis and learning. For manuscripts, verify results in statistical software and report full methodological details.