Wilcoxon signed-rank test
Compare two paired measurements without assuming normal differences.
When to use it
Use the Wilcoxon signed-rank test instead of a paired t-test when the differences are skewed or the scores are ordinal. It ranks the size of each person’s change and looks at the direction.
Assumptions
Each row is one pair. Differences of zero are ties and drop out of the rank sum.
Running it in Tensr
Options
Prop
Type
Reading the output
The before and after course scores. Most people gain, some lose a little, so the signed-rank statistic is not zero.
| N | Mean rank | Sum of ranks | |
|---|---|---|---|
| Positive ranks | 15 | 19.9 | 298.5 |
| Negative ranks | 33 | 26.591 | 877.5 |
| Ties | 0 | — | — |
Wilcoxon signed-rank test comparing before and after on 48 paired rows (W = 298.5, p = .003, r = 0.429). 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 = .003). This is large enough, in this sample, to treat the comparison this page is about as a real association rather than noise. Metrics: W statistic = 298.5; p-value = .003; Median difference = -4.4; Effect size r = 0.429; Effect size = medium; 95% CI median diff (HL) = [-8.3, -0.4].
Reporting (APA 7)
Wilcoxon signed-rank test comparing before and after on 48 paired rows (W = 298.5, p = .003, r = 0.429). 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 = .003). The effect is moderate, so report its size with the p-value.
Coming from SPSS
Analyze → Nonparametric Tests → 2 Related Samples. SPSS may label the statistic T rather than W.