How to Report Mann-Whitney U Test Results

Most authors get the first decision right. The outcome is skewed, or ordinal, or the sample is small, so they run a Mann-Whitney U test instead of an independent t-test. The manuscript then reports "mean 4.3 vs 1.8 mm, P < .05" and nothing else, and the reviewer's comment writes itself: the descriptive contradicts the test, the P value is a threshold rather than a number, and there is no effect size. This guide covers the sentence, not the choice. A separate guide walks through when the Mann-Whitney is the right test in the first place.

The five elements a complete result needs

The SAMPL guidelines for statistical reporting in biomedical journals ask, for any comparison, that the descriptive summary match the analysis, that the test statistic be given with its P value rather than a threshold, and that an estimate of the size of the effect accompany the test.³ Applied to a Mann-Whitney U test, that produces this checklist.

SPSS prints the first three and stops. The effect size is the element most often missing from submitted manuscripts, and it is the one this post spends the most time on.

A real result: tumour thickness and ulceration

The melanoma cohort from Andersen and colleagues records 205 patients who had radical surgery for malignant melanoma at Odense University Hospital between 1962 and 1977, with the Breslow thickness of each tumour in millimetres and whether it was ulcerated.¹ Thickness is strongly right-skewed in both groups: Shapiro-Wilk gives P < .001 for each, and a handful of very thick tumours sit far from the rest. The engine therefore routes the comparison to the Mann-Whitney U test rather than the t-test, and reports it as follows.

Example data: melanoma cohort, Odense, Denmark (Andersen, Borgan, Gill, and Keiding, 1993); see references. Computed with scipy, not generated.

Why medians and IQR, not mean (SD)

The means in this dataset are 4.34 mm in the ulcerated group and 1.81 mm in the non-ulcerated group. The medians are 3.54 and 1.29 mm. The gap between mean and median in the ulcerated group is 0.8 mm, and it is entirely the work of a few very thick tumours pulling the average upwards. A reader who sees "mean 4.34 mm" pictures a typical tumour that is thicker than the typical tumour actually is.

There is a second reason, and it is the one reviewers act on. You chose a rank test because the data are not well described by a mean. Reporting a mean anyway tells the reviewer that the descriptive statistic and the test were picked by different logic, and it invites the question of whether the test was chosen after the P value was seen. The AMA Manual's own guidance on descriptive statistics is to report the median and interquartile range when the distribution is not normal, and the mean (SD) only when it is.² Match the summary to the test: median (IQR) for each group, with its n.

The effect size: rank-biserial r or the Hodges-Lehmann shift

Two effect sizes are standard for a Mann-Whitney comparison, and the engine reports both. The rank-biserial correlation, r, is the difference between the proportion of pairs (one patient from each group) in which the first group's value is higher and the proportion in which it is lower.⁵ It runs from −1 to 1; here it is 0.65, meaning that in a randomly chosen ulcerated-versus-non-ulcerated pair, the ulcerated tumour is the thicker one about 82% of the time. By the usual correlation benchmarks that is a large effect.

Note the sign. The engine prints r = −0.646 because it ranks 'Ulceration' relative to 'No ulceration' in the order the groups were read, and the sign only records which group was listed first. Report the magnitude, 0.65, and let the words carry the direction: ulcerated tumours were thicker. A signed r with no statement of which group is which is unreadable.

The Hodges-Lehmann estimate is the median of every pairwise difference between the two groups, expressed in the outcome's own units, with a confidence interval.⁶ Here it is 2.09 mm (95% CI, 1.61–2.58). Of the two, this is the more clinically legible: a surgeon knows what a 2 mm difference in Breslow thickness means, and the interval shows the difference is unlikely to be smaller than 1.6 mm. It is the rank-based counterpart of the mean difference and its CI in a t-test report.

If you are working from SPSS output, which gives U and z but no effect size, the rank-biserial r can be recovered by hand as r = z / √N. Say the formula in your Methods section so the reviewer can check it.

What the test actually tests, and what you are licensed to say

Mann and Whitney's 1947 paper frames the test as asking whether one of two random variables is stochastically larger than the other, that is, whether values from one group tend to exceed values from the other.⁴ It is not, strictly, a test of the difference between two medians. The two coincide when the distributions have the same shape and differ only by a shift; when the shapes differ, the test can be significant while the medians are equal, and Fagerland and Sandvik show this is not a theoretical curiosity in clinical data.⁷

The practical rule: write "tumours with ulceration were thicker," which is what the test supports, and quote the medians as descriptives. Write "the median thickness differed" only if you have looked at the two distributions and they have a similar shape. In the melanoma data both groups are right-skewed in the same direction, but the first phrasing is always safe and needs no such inspection.

Writing the AMA sentence

The AMA Manual of Style, which sets the format for JAMA Network journals and most surgical and clinical journals, writes P as a capital italic with no leading zero, keeps the leading zero on effect sizes, italicises Latin statistic symbols (U, z, r, N), and gives a confidence interval as "95% CI, 1.61–2.58".² A complete results sentence for the example reads:

"Tumours with ulceration were thicker than those without (median [IQR], 3.54 [2.25–5.16] vs 1.29 [0.65–1.94] mm; Mann-Whitney U = 8519.5; P < .001; rank-biserial r = 0.65; Hodges-Lehmann difference in medians, 2.09 mm; 95% CI, 1.61–2.58)."

One point on digits. StatsPlease prints every P value to three decimals (P = .075, for instance). The Manual's convention is two digits when P is .01 or larger, three digits between .001 and .01, and P < .001 below that, keeping a third digit only where rounding would move a value across .05.² The example above is below the floor, so P < .001 is correct in both; for a value such as .075, the card shows .075 and the manuscript sentence takes .08. Never write P = .000, which is a rounding artefact, and never "NS".

The Methods section should say why the rank test was used and which effect size accompanies it: "Tumour thickness was not normally distributed (Shapiro-Wilk P < .001 in both groups) and was compared between groups with the Mann-Whitney U test, reported as median (IQR) with the rank-biserial correlation and the Hodges-Lehmann estimate of the difference in medians with its 95% CI. Tests were two-sided with α = .05." Journals following APA style instead want a lowercase italic p, square brackets around the confidence interval, and Mdn for the median; StatsPlease renders AMA by default and offers an APA rendering through the Reporting Style picker in the Analyze flow.

This is also the sentence ChatGPT will write for you fluently and wrongly. Ask an LLM to report a Mann-Whitney result and it produces a grammatically perfect AMA sentence around a U and a P it never computed from your data, with an effect size that may not correspond to either. The numbers above are computed with scipy, not generated; run the same two columns through R or SPSS and U = 8519.5 comes back to the decimal.

Frequently asked questions

Should I report the mean or the median with a Mann-Whitney U test?

The median with its interquartile range, for each group, with the group sizes. The test was chosen because the outcome is skewed or ordinal, and a mean (SD) describes a skewed variable badly: in the melanoma example the mean thickness in the ulcerated group is 4.34 mm while the median is 3.54 mm, because a few very thick tumours pull the mean up. Reporting mean (SD) next to a rank test also tells the reviewer that the descriptive and the test were chosen by different logic.

Do I report U or z for a Mann-Whitney test?

Either is acceptable, and many journals accept both together. U is the test statistic itself; z is the standardised version SPSS prints beside it, and it is the one you need if you want to compute the rank-biserial effect size by hand as z divided by the square root of N. Whichever you report, give both group sizes, because a U value cannot be interpreted without them.

What effect size goes with a Mann-Whitney U test?

Two are in common use. The rank-biserial correlation r is the difference between the proportion of favourable and unfavourable pairs across the two groups; it runs from minus 1 to 1 and 0.65 is a large effect. The Hodges-Lehmann estimate is the median of all pairwise differences between the groups, in the outcome's own units, and comes with a confidence interval, so it reads like a mean difference. Report at least one; the Hodges-Lehmann shift is the more clinically legible of the two.

References

1. Andersen PK, Borgan Ø, Gill RD, Keiding N. Statistical Models Based on Counting Processes. New York, NY: Springer-Verlag; 1993.
2. Christiansen SL, Iverson C, Flanagin A, et al. AMA Manual of Style: A Guide for Authors and Editors. 11th ed. New York, NY: Oxford University Press; 2020. https://doi.org/10.1093/jama/9780190246556.001.0001
3. Lang TA, Altman DG. Basic statistical reporting for articles published in biomedical journals: the "Statistical Analyses and Methods in the Published Literature" or the SAMPL Guidelines. Int J Nurs Stud. 2015;52(1):5-9. https://doi.org/10.1016/j.ijnurstu.2014.09.006
4. Mann HB, Whitney DR. On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat. 1947;18(1):50-60. https://doi.org/10.1214/aoms/1177730491
5. Kerby DS. The simple difference formula: an approach to teaching nonparametric correlation. Compr Psychol. 2014;3:11.IT.3.1. https://doi.org/10.2466/11.IT.3.1
6. Hodges JL, Lehmann EL. Estimates of location based on rank tests. Ann Math Stat. 1963;34(2):598-611. https://doi.org/10.1214/aoms/1177704172
7. Fagerland MW, Sandvik L. The Wilcoxon-Mann-Whitney test under scrutiny. Stat Med. 2009;28(10):1487-1497. https://doi.org/10.1002/sim.3561