Mann-Whitney U test
The Mann-Whitney U test compares two independent groups using ranks instead of raw values, so it is the usual alternative to the independent-samples t test for ordinal or clearly non-normal data.
Menu: Analyze → Nonparametric Tests → Legacy Dialogs → 2 Independent Samples…
When should I use Mann-Whitney U test?
- Two independent groups; ordinal outcome (e.g. a Likert item) or skewed scale data.
What are the assumptions?
- Independent observations. To read it as a comparison of medians, the two distributions should have similar shapes.
How do I run it in StatLab?
- Choose test variable(s), the grouping variable and (optionally) the two group codes.
How do I read the output?
| Output | Meaning |
|---|---|
| Mean Rank / Sum of Ranks | Higher mean rank = higher values in that group. |
| Mann-Whitney U | The smaller of the two U statistics. |
| Wilcoxon W | Rank sum of the group with the smaller mean rank. |
| Z, Asymp. Sig. | Normal approximation with tie correction (no continuity correction). Exact p for small samples is planned. |
| r = |Z|/√N | Effect size: .1 small, .3 medium, .5 large. |
Worked example
Compare score by gender in the bundled sample dataset (File → Sample dataset: 150 survey respondents with gender, programme group, age, pre/post test scores, five satisfaction items, income, smoking and education): U = 2593.0, Z = −0.76, p = .447.
How would I report it in APA style?
A Mann-Whitney U test showed no significant difference in wellbeing between men (Mdn = 69.99) and women (Mdn = 68.68), U = 2593.0, z = −0.76, p = .447, r = .06.
Numbers above were computed by StatLab’s validated engine from the sample dataset when this page was built.
What are common mistakes?
- Saying “medians differ” when the group distributions have very different shapes.