Mann–Whitney U test
Compare two independent groups without assuming normality.
When to use it
Use Mann–Whitney U instead of an independent-samples t-test when the outcome is ordinal or the scores are skewed. It asks whether one group tends to rank higher than the other.
Assumptions
The two groups are independent. The outcome is at least ordinal. Tensr does not run a normality check for this test.
Running it in Tensr
Options
Prop
Type
Reading the output
Lecture versus workshop ranks on the exam. The workshop scores tend to sit higher, and the two lists still overlap, so U is not zero.
| Group | n | Median | Mean rank | Rank sum | Status |
|---|---|---|---|---|---|
| Lecture | 32 | 69.1 | 26.312 | 842 | included |
| Workshop | 32 | 72.95 | 38.688 | 1,238 | included |
Significant difference in score between Workshop and Lecture (U = 314, p = .008, r = 0.332). Effect size (medium; r < 0.1 negligible, 0.1 ≤ r < 0.3 small, 0.3 ≤ r < 0.5 medium, r ≥ 0.5 large). Cutoffs: Cohen, 1988. The primary result is significant (p = .008). This is large enough, in this sample, to treat the comparison this page is about as a real association rather than noise. Metrics: U statistic = 314; p-value = .008; Effect size r = 0.332; Effect size = medium.
Reporting (APA 7)
Significant difference in score between Workshop and Lecture (U = 314, p = .008, r = 0.332). Effect size (medium; r < 0.1 negligible, 0.1 ≤ r < 0.3 small, 0.3 ≤ r < 0.5 medium, r ≥ 0.5 large). Cutoffs: Cohen, 1988. This result is significant (p = .008). The effect is moderate, so report its size with the p-value.
Coming from SPSS
Analyze → Nonparametric Tests → 2 Independent Samples. SPSS often prints Wilcoxon W and a z alongside U.