Mann–Whitney U Test: How to Run It Online and Report It in APA7
The Mann–Whitney U test compares two independent groups using ranks instead of means, so it does not need normally distributed data.
What is Mann–Whitney U Test?
The Mann–Whitney U test compares two independent groups using ranks instead of means, so it does not need normally distributed data.
When to use it
Use it as the non-parametric alternative to the independent-samples t-test: for ordinal outcomes (such as pain ratings), strongly skewed data, small samples or data with outliers.
Example question: Do the treatment and control groups differ in pain ratings?
Preparing your data
Long format: one row per participant, a group column with two categories and an outcome column (numeric or ordinal).
Example dataset (simulated; first rows of 40): id, group (Treatment or Control), pain (0 to 10 rating).
| id | group | pain |
|---|---|---|
| 1 | Treatment | 2 |
| 2 | Treatment | 2 |
| 3 | Treatment | 2 |
| 4 | Treatment | 4 |
| 5 | Treatment | 3 |
| 6 | Treatment | 2 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Mann–Whitney U Test tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Select the outcome and the grouping variable with two categories.
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- The outcome is at least ordinal.
- Observations are independent; each person is in one group.
- To interpret the test as a comparison of medians, the two distributions should have a similar shape; otherwise it compares the overall distributions (whether one group tends to score higher).
- Many tied values are acceptable, but the test applies a tie correction.
Key numbers to look at
- U statistic and the standardised z.
- Asymptotic or exact p-value.
- Mean ranks and sample sizes per group.
- Medians and interquartile ranges to describe the groups.
Effect size
Report r = z / √N (about .10 small, .30 medium, .50 large) or the rank-biserial correlation, and say which you used.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Mann–Whitney U Test in APA7 style
Template
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Describing it as a test of medians when the group distributions differ in shape.
- Using it for paired data.
- Reporting the p-value without a measure of effect size.
Related analyses and alternatives
- Independent t-Test: If the data are continuous and roughly normal.
- Kruskal-Wallis Test: Three or more independent groups.
- Wilcoxon Test: Paired data.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
Is Mann–Whitney the same as the Wilcoxon rank-sum test?
Yes. They are equivalent tests with different names and statistics.
When should I use it instead of a t-test?
When the outcome is ordinal, strongly skewed, or the sample is small and clearly non-normal.
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.