When to use the Mann–Whitney test, and how to report it

The non-parametric alternative to the t-test for two independent groups. When it fits, what it actually tests, and how to write the result in APA style.

Part of the series: Statistical Analysis for a Seminar Paper or Thesis: The Complete Guide

The Mann–Whitney test (also called the Wilcoxon rank-sum test) compares two independent groups, like a t-test, but uses the ranks of the values instead of the values themselves.

When it fits

• The dependent variable is ordinal, for example a single Likert item or a ranking.
• The variable is continuous, but the sample is small and the distribution is far from normal, or there are extreme outliers.
• You have two groups of different people. If the same people were measured twice, the right test is the Wilcoxon signed-rank test.

When the sample is large and the distribution is reasonable, a t-test is usually better, because it has more power.

What the test actually checks

The test checks whether values in one group tend to be higher than values in the other. It's often said to "compare medians", but that's only true when the distributions have a similar shape in both groups. So in the write-up, describe the finding as a difference in distributions or ranks, and report the medians for description.

How to run it in SPSS

Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples. Put the dependent variable in the Test Variable List and the group variable in Grouping Variable, define the two group values, and tick Mann–Whitney U.

In the output, look for U, Z and Asymp. Sig. (2-tailed).

Effect size

SPSS doesn't compute an effect size for this test, but it's easy to calculate yourself:

r = Z / √N

where N is the total number of participants. An r of .10 is usually read as small, .30 as medium and .50 as large.

How to report it in APA style

Satisfaction scores in the experimental group (Mdn = 4.00) were higher than in the control group (Mdn = 3.00), U = 312.50, z = −2.41, p = .016, r = .27.

A few rules to remember:

• Statistic symbols (U, z, p, r, Mdn) in italics.
• No zero before the decimal point for values that can't exceed 1, such as p and r.
• An exact p value; only when it's very small do you write p < .001.

Next steps

Mann–Whitney is one of several non-parametric tests - for the whole family (Wilcoxon, Kruskal–Wallis, Friedman, Spearman): non-parametric tests. Before giving up on the t-test, check whether you really need to: normality testing. And how the finding goes into the paper: effect sizes and how to write a results chapter.

Last updated: 2026-09-27