Wilcoxon signed-rank test
The Wilcoxon signed-rank test compares two related measurements (before/after on the same cases) using the ranks of the differences — the nonparametric alternative to the paired t test.
Menu: Analyze → Nonparametric Tests → Legacy Dialogs → 2 Related Samples…
When should I use Wilcoxon signed-rank test?
- Paired ordinal data, or paired scale data whose differences are clearly non-normal.
What are the assumptions?
- Differences roughly symmetric around their median. Zero differences are dropped.
How do I run it in StatLab?
- Choose Variable 1 and Variable 2. Differences are Variable 2 − Variable 1.
How do I read the output?
| Output | Meaning |
|---|---|
| Negative / Positive Ranks | Cases where Variable 2 is lower / higher, with mean and sum of ranks. |
| Ties | Zero differences (excluded from the test). |
| Z, Asymp. Sig. | Tie-corrected normal approximation. |
| r = |Z|/√N | Effect size. |
Worked example
Compare pre and post 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): 109 positive and 41 negative differences, Z = −5.96, p < .001.
How would I report it in APA style?
A Wilcoxon signed-rank test indicated that post-test scores were significantly higher than pre-test scores, z = −5.96, p < .001, r = .49.
Numbers above were computed by StatLab’s validated engine from the sample dataset when this page was built.
What are common mistakes?
- Using it for two independent groups — that is Mann-Whitney.