Wilcoxon Signed-Rank Test Calculator
The Wilcoxon signed-rank test is the non-parametric counterpart of the paired t-test: it compares two measurements on the same subjects (before/after, condition A/B) using the ranks of the differences, so it does not require normally distributed differences. Paste the two paired columns and get V (the positive-rank sum, as reported by R), the tie-corrected z approximation, the two-tailed p and the effect size r = |z|/√n. Zero differences are removed before ranking — the standard Wilcoxon procedure and R's default. Results match R's wilcox.test(x, y, paired=TRUE) with exact=FALSE to at least four significant digits.
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Frequently asked questions
How do I report a Wilcoxon signed-rank test in APA 7 format?
Report the statistic, z, exact p and effect size, e.g.: "Scores did not change significantly from pre-test to post-test, V = 27, z = −0.47, p = .635, r = .15", usually with the median difference. The AI Report button writes the full APA 7 paragraph for you.
When should I use Wilcoxon instead of the paired t-test?
When the paired differences are clearly non-normal, the outcome is ordinal, or the sample is small with outliers. If the differences look roughly symmetric and normal, the paired t-test is slightly more powerful. The test assumes at least a symmetric distribution of differences under the null.
What happens to pairs with zero difference?
They are dropped before ranking, and n is reduced accordingly — the classic Wilcoxon procedure and R's default behaviour. If many pairs are tied at zero, the effective sample shrinks noticeably and the result should be interpreted with care.