Mann–Whitney U: what it means and how to read it
In the report: Mann-Whitney U — How often a value of one group comes before a value of the other when all values are sorted (ties count half) — the smaller of the two counts, as SPSS.
How to read it
Small U — one group tends to lie below the other; n₁·n₂/2 — the groups are mixed evenly. In a report: U = 1175.5, Z = 0.52, p = .600.
In plain words
A teacher had two groups of 10 students with ratings from 1 to 5, and could not say whether one group rated higher. She asked for U. It looks at every pair made of one student from each group, 100 pairs in all, and counts how often the student of one group has the higher rating; a tie counts as half. If the groups were mixed evenly, U would be about 50. Hers came out 12. Now she can say that in only 12 of 100 pairs this group came out on top, so this group tends to rate lower.
How it is computed
U₁ = R₁ − n₁(n₁ + 1)/2, U = min(U₁, n₁n₂ − U₁), R₁ — the sum of ranks of the first groupExample
The cell with Mann-Whitney U is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — two-sided
=STATS_MANN_WHITNEY(Data!A1:T51, "before,after")
Where you see it
STATS_MANN_WHITNEY— Mann–Whitney U test for two independent samples — the rank replacement for STATS_INDEPENDENT when the data are not normal (see STATS_NORMALITY), are ranks or rating scales (1–5), or have outliers.
Related values
- Wilcoxon W — The rank sum of the group whose U is the smaller one — Wilcoxon's rank-sum form of the same test, as SPSS.
- Kruskal–Wallis H — How far the mean ranks of the groups are apart, with the tie correction.
- Statistic — The test statistic.
- Pearson chi-square — Pearson's chi-square: how far the observed counts are from those expected if the two variables were unrelated. No continuity correction.
- Pearson Chi-Square — The same test as the chi2 at the top of the report, in the SPSS table: value, df and the asymptotic p from the chi-square distribution. No continuity correction.
Get it in your sheet
One formula in a cell gives the whole report, Mann–Whitney U included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)