What does the p-value tell me?

A p-value below your significance level (e.g., 0.05) suggests the two groups differ significantly in their distributions. A high p-value means you lack evidence to conclude a difference.

How is this different from a t-test?

The Mann-Whitney U test does not assume the data are normally distributed. It works on ranks rather than raw values, making it suitable for ordinal data, skewed distributions, or small samples.

What is the U statistic?

U counts the number of times a value from Group A exceeds a value from Group B across all pairs. The test uses min(U1, U2) to compute significance. U ranges from 0 to n1 × n2.

When is the normal approximation valid?

The normal approximation is generally reliable when both groups have at least 8–10 observations. For very small samples (n < 8 per group), use exact critical-value tables instead.

Does the test handle ties?

Yes. The tool applies a standard tie-correction to the variance used in the z-score calculation, which improves accuracy when tied ranks are present.

Is this a one-tailed or two-tailed test?

The p-value reported is two-tailed, testing whether either group tends to be larger. Halve it for a one-tailed hypothesis.

Mann-Whitney U Test

Name: Mann-Whitney U Test
Availability: InStock
Author: Nham Vu

Enter two independent samples to compute the Mann-Whitney U statistic and approximate p-value without assuming normality.

Enter Sample Data

Group A (one value per line or comma-separated)

Group B (one value per line or comma-separated)

Load Example

Enter data and click Run Test to see results.

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U₁ (Group A)

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U₂ (Group B)

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z-score

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p-value (2-tail)

Statistic	Group A	Group B
Sample size (n)	—	—
Median	—	—
Mean rank	—	—
Rank sum (W)	—	—
U statistic	—	—

Summary

Enter two independent samples to compute the Mann-Whitney U statistic and approximate p-value without assuming normality.

How it works

Enter the values for Group A, one per line or comma-separated.
Enter the values for Group B in the same format.
Click "Run Test" to combine and rank all values jointly.
The tool sums the ranks for each group and computes U1 and U2.
A z-score is derived using the normal approximation and converted to a two-tailed p-value.
Interpret the p-value against your chosen significance level (commonly 0.05).

Use cases

Compare test scores between two teaching methods without assuming normality.
Assess whether two product variants differ in user ratings.
Analyze clinical trial outcomes when data is ordinal or skewed.
Evaluate whether two groups differ in response time or task duration.
Non-parametric alternative to the independent samples t-test.
Compare ranks in any survey or Likert-scale study.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu