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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 the distributions of two independent groups. Unlike the independent samples t-test, the Mann-Whitney U test does not assume that the data are normally distributed, making it ideal for ordinal data, skewed distributions, or small sample sizes where normality cannot be verified. It was developed by Henry B. Mann and Donald R. Whitney in 1947 and is one of the most widely used non-parametric tests in behavioral science, medicine, and social research.

When to Use the Mann-Whitney U Test

The Mann-Whitney U test is the non-parametric alternative to the independent samples t-test. Use it when one or more of the following conditions apply: your data are measured on an ordinal scale (e.g., Likert-type items), the assumption of normality is violated, your sample sizes are very small (e.g., n < 15 per group), or your data contain outliers that would distort parametric results. It is especially common in clinical trials, quality-of-life research, and educational studies where rating scales are used.

Mann-Whitney U Test vs. Independent Samples T-Test

Assumptions of the Mann-Whitney U Test

While the Mann-Whitney U test is less restrictive than the t-test, it still has assumptions that should be verified:

Understanding the Rank-Biserial Correlation

The rank-biserial correlation (r) is the recommended effect size measure for the Mann-Whitney U test. It ranges from -1 to +1 and represents the proportion of favorable comparisons minus unfavorable comparisons between the two groups.

How to Report Mann-Whitney U Results in APA Format

According to APA 7th edition guidelines, report the U statistic, z value, p-value, effect size, and descriptive statistics (medians and sample sizes) for each group:

Note: Report U to one decimal place, z to two decimal places, and p to three decimal places. Use p < .001 when the value is below .001. Always include the rank-biserial r as the effect size measure.

Common Mistakes to Avoid

• Using a t-test on non-normal data: If your data are ordinal or clearly non-normal with small samples, the t-test may give misleading results. Use Mann-Whitney U instead.
• Interpreting U as a difference in means: The Mann-Whitney U test compares rank distributions, not means. Report medians, not means, as the descriptive statistic.
• Ignoring tied ranks: When many observations share the same value, ties can affect the test. StatMate handles tied ranks automatically using the average rank method.
• Using Mann-Whitney for paired data: If your data are paired or matched, use the Wilcoxon signed-rank test instead.
• Forgetting effect size: A significant p-value alone does not tell you the magnitude of the difference. Always report the rank-biserial correlation alongside the test result.