How to Report a Mann-Whitney U Test in APA 7

The Mann-Whitney U test is the non-parametric counterpart to the independent-samples t, and its write-up has a trap almost everyone falls into: describing groups with means after having given up the mean for good reasons. Here is which numbers go in and in what order. The full picture is in how to report non-parametric tests.

Which numbers go in

Four things: the U statistic, the normal-approximation z, the p value and an effect size. With small samples (below roughly 20 per group) many packages give an exact p, and then z is optional — say so if that is your case.

The usual effect size is r = |z| / √N, where N is the combined sample size. It reads like a correlation: around .10 small, .30 medium, .50 large. An increasingly recommended alternative is the common language effect size, or probability of superiority, which interprets cleanly: the probability that a randomly chosen person from group A scores higher than one from group B.

U and z are italicized. U can exceed 1, so it keeps its leading zero and decimals; p and r take no leading zero.

Medians, not means

This is the most repeated mistake. If you chose Mann-Whitney it is because the mean does not describe your data well — skew, outliers, an ordinal scale. Describing the groups afterwards with M and SD is incoherent, and reviewers flag it.

The right choice is the median with the interquartile range: "Mdn = 14.0, IQR = 9.0–19.0". Add the full range if the journal asks. And since Mann-Whitney compares ranks, many authors also include each group’s mean rank, which is what the test actually contrasts.

One precision that avoids arguments: Mann-Whitney does not test medians unless both distributions have the same shape. In the general case it tests whether one sample tends to produce larger values than the other. Writing "medians differed significantly" is, strictly speaking, claiming more than the test supports.

Example in the text

"Anxiety scores were higher in the clinical group (Mdn = 18.0, IQR = 14.0–23.0) than in the control group (Mdn = 12.0, IQR = 8.0–16.0). A Mann-Whitney U test indicated that the difference was significant, U = 512.50, z = −2.34, p = .019, r = .23. A non-parametric test was used because scores were markedly skewed in both groups."

Note the order: group description first, then the test, then the effect size, and finally the justification for choosing this test over the t. That last sentence is the one missing from nine manuscripts out of ten.

If you have the SPSS output in front of you with its two tables — Ranks and Test Statistics — and cannot tell which row is which, paste it into the output interpreter.

Already drafted it? Paste your Results section into Review one section before it goes to your supervisor or the journal. You get the first thing a reviewer would object to, with your own sentence quoted.

When not to use it

With repeated measures. If the two groups are the same group measured twice, the test is Wilcoxon signed-rank, not Mann-Whitney.

With three or more groups. That calls for Kruskal-Wallis, followed by corrected pairwise comparisons. Running three separate Mann-Whitney tests inflates the Type I error rate.

By default, without looking at the data. The t test is fairly robust to moderate departures from normality, especially with balanced groups and decent samples. Always reaching for the non-parametric option "just in case" costs power. The decision belongs before the analysis, based on the distribution, and it is explained in the text.

As a patch for outliers you have not examined. Mann-Whitney is robust to outliers, but that does not excuse you from inspecting them: an outlier can be a coding error, and that is information to correct, not to absorb with a rank test.

Frequently asked questions

What do I report for a Mann-Whitney U test in APA 7?

The U statistic, the normal-approximation z, the p value and an effect size (usually r = |z| / √N). Alongside that, each group described with median and interquartile range, and a sentence explaining why a non-parametric test was used instead of the t test.

Do I report means or medians with Mann-Whitney?

Medians with the interquartile range. If you chose this test it is because the mean does not describe your data well, so describing the groups afterwards with mean and standard deviation is contradictory and gets flagged in review. Many authors also add the mean rank, which is what the test actually compares.

How is the Mann-Whitney effect size computed?

The most common form is r = |z| / √N, where N is the combined size of both samples, interpreted like a correlation. Another increasingly recommended option is the common language effect size, or probability of superiority: the probability that a randomly chosen case from one group exceeds one from the other.

Does Mann-Whitney compare medians?

Only if both distributions have the same shape. In the general case it tests whether one sample tends to produce larger values than the other, which is a broader hypothesis. Writing "medians differed significantly" claims slightly more than the test supports, however widespread that shorthand is.

When do I use Wilcoxon instead of Mann-Whitney?

When the measurements are paired: the same group before and after, or two conditions within the same participant. Mann-Whitney is for two independent groups. It is the same distinction as between the independent-samples t test and the paired-samples t test.

With U, z, an effect size and medians rather than means, your Mann-Whitney test is properly reported. If you are unsure whether the t test or the non-parametric option fits your data, we can look at it in my statistical consulting.