# Mann-Whitney U Test Calculator

Free Mann-Whitney U test calculator. Compare two independent samples without normality assumption. Get U statistic, z-score, and p-value instantly.

## What this calculates

Compare two independent samples using the Mann-Whitney U test (also called the Wilcoxon rank-sum test). This nonparametric test does not require the data to be normally distributed.

## Inputs

- **Sample 1 Count** — min 2, max 10 — Number of values in sample 1 (2-10).
- **S1 Value 1** — Sample 1, value 1.
- **S1 Value 2** — Sample 1, value 2.
- **S1 Value 3** — Sample 1, value 3.
- **S1 Value 4** — Sample 1, value 4.
- **S1 Value 5** — Sample 1, value 5.
- **S1 Value 6** — Sample 1, value 6.
- **S1 Value 7** — Sample 1, value 7.
- **S1 Value 8** — Sample 1, value 8.
- **S1 Value 9** — Sample 1, value 9.
- **S1 Value 10** — Sample 1, value 10.
- **Sample 2 Count** — min 2, max 10 — Number of values in sample 2 (2-10).
- **S2 Value 1** — Sample 2, value 1.
- **S2 Value 2** — Sample 2, value 2.
- **S2 Value 3** — Sample 2, value 3.
- **S2 Value 4** — Sample 2, value 4.
- **S2 Value 5** — Sample 2, value 5.
- **S2 Value 6** — Sample 2, value 6.
- **S2 Value 7** — Sample 2, value 7.
- **S2 Value 8** — Sample 2, value 8.
- **S2 Value 9** — Sample 2, value 9.
- **S2 Value 10** — Sample 2, value 10.

## Outputs

- **U Statistic** — The Mann-Whitney U test statistic (minimum of U1 and U2).
- **Z-Score (approx.)** — Normal approximation z-score for the U statistic.
- **P-Value (approx.)** — Approximate two-sided p-value using normal approximation.
- **Significant (α = 0.05)?** — formatted as text — Whether the difference is statistically significant.

## Details

The Mann-Whitney U test is the nonparametric alternative to the independent samples t-test. It compares two groups by ranking all observations together and comparing the sum of ranks between groups.

How it works: All values from both samples are combined and ranked. The U statistic is calculated from the rank sum: U = n1n2 + n1(n1+1)/2 - R1, where R1 is the sum of ranks for sample 1. For larger samples, the distribution of U is approximately normal, allowing a z-test.

When to use it: Use the Mann-Whitney test when your data is ordinal, when normality assumptions are violated, when you have outliers, or when sample sizes are small and you cannot verify normality. It tests whether one group tends to have larger values than the other.

## Frequently Asked Questions

**Q: What is the difference between Mann-Whitney and t-test?**

A: The t-test assumes data is normally distributed and compares means. Mann-Whitney is nonparametric (no normality assumption) and compares the entire distribution via ranks. Mann-Whitney is more robust to outliers and skewness but has slightly less power when normality holds.

**Q: How are tied values handled?**

A: Tied values receive the average of the ranks they would have occupied. For example, if two values tie for ranks 3 and 4, both receive rank 3.5. A correction factor can be applied to the variance formula for many ties, but for small samples this has minimal impact.

**Q: Is the normal approximation reliable for small samples?**

A: For very small samples (n1 or n2 < 8), exact tables should be consulted as the normal approximation may not be accurate. This calculator uses the normal approximation with continuity correction, which is adequate for most practical purposes when both samples have at least 5 observations.

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Source: https://vastcalc.com/calculators/statistics/mann-whitney
Category: Statistics
Last updated: 2026-04-21