Mann-Whitney U Test Calculator
Perform the Mann-Whitney U Test (also known as the Wilcoxon rank-sum test) — a non-parametric test to compare two independent samples. This test determines whether the two populations have the same distribution without assuming normality. The calculator provides rankings, U statistics, z-score, and p-value with step-by-step calculations.
What Is the Mann-Whitney U Test?
The Mann-Whitney U Test (also known as the Wilcoxon rank-sum test) is a non-parametric statistical test used to compare two independent samples. It tests whether the two populations have the same distribution without assuming normality.
When to Use This Test
- Your data is not normally distributed (non-parametric alternative to the t-test).
- You have two independent samples (different groups of subjects).
- Your data is ordinal or continuous.
- You want to test whether one group tends to have higher values than the other.
How the Test Works
- Combine: Combine all data from both groups into a single dataset.
- Rank: Rank all values from smallest to largest. Ties are assigned the average rank.
- Sum Ranks: Sum the ranks for each group (R₁ and R₂).
- Calculate U: Compute U₁ and U₂ using the formulas below.
- Test Statistic: U = min(U₁, U₂).
- Normal Approximation: Calculate z-score and p-value.
The U Formulas
U₁ = n₁·n₂ + n₁·(n₁+1)/2 − R₁
U₂ = n₁·n₂ + n₂·(n₂+1)/2 − R₂
U = min(U₁, U₂)
Interpretation
- Small U: Indicates a significant difference between groups (one group tends to have larger values).
- Large U: Suggests the groups are similar.
- p-value: The probability of observing the test statistic (or more extreme) under the null hypothesis.
- α = 0.05: If p < 0.05, reject the null hypothesis — there is a significant difference between groups.
Why Use This Mann-Whitney U Test Calculator?
- Complete Analysis: Get U statistic, z-score, p-value, and rank sums.
- Step-by-Step: See the ranking and calculation process.
- Visual: Distribution chart comparing both groups.
- Alternative Hypotheses: Supports two-sided, greater-than, and less-than tests.
- Free & Private: No registration, no data storage.
❓ Mann-Whitney U Test FAQ
What is the Mann-Whitney U Test?
The Mann-Whitney U Test is a non-parametric test that compares two independent samples to determine if they come from the same distribution.
When should I use the Mann-Whitney U Test instead of a t-test?
Use the Mann-Whitney U Test when your data is not normally distributed, when you have ordinal data, or when you have small sample sizes with non-normal distributions.
What is the difference between Mann-Whitney U and Wilcoxon rank-sum?
They are the same test. The Mann-Whitney U Test and the Wilcoxon rank-sum test are two names for the same statistical procedure.
How do I interpret the U statistic?
The U statistic measures the degree of separation between the two groups. A smaller U indicates a greater difference between the groups.
What is the null hypothesis of the Mann-Whitney U Test?
The null hypothesis is that the two populations have the same distribution (i.e., there is no difference between the groups).
What is the alternative hypothesis?
You can choose from three alternatives: two-sided (the distributions differ), greater (Group 1 tends to have larger values), or less (Group 1 tends to have smaller values).
How are ties handled in the Mann-Whitney U Test?
Ties are handled by assigning the average rank to all tied values. The calculator uses a tie-adjusted standard deviation for the z-score calculation.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required. All calculations are performed in your browser.