Wilcoxon Signed-Rank Test Calculator
Test paired or single-sample data without assuming normality.
What the Wilcoxon signed-rank test does
The Wilcoxon signed-rank test is the non-parametric alternative to the paired t-test. It uses the size and direction of each difference between two measurements on the same subjects. It also works as a one-sample test of whether a median differs from a value. It does not assume normality, only that the differences are roughly symmetric.
Worked example
Nine people were measured before and after a treatment. The differences are ranked by size, and the ranks of the positive and negative differences are added up. The smaller sum is W = 5. The exact two-tailed p-value is 0.0391, and the one-tailed test (the first measurement is greater) gives p = 0.0195. So there is a significant change at the 5% level.
How it is calculated
- Find the difference for each pair, and drop any pair with a difference of zero.
- Rank the absolute differences from smallest to largest, using the average rank for ties.
- Add up the ranks of the positive differences (W⁺) and of the negative differences (W⁻).
- For a two-tailed test, W is the smaller of the two sums. The p-value is exact when there are no ties and no zero differences and n ≤ 30. Otherwise the calculator uses the normal approximation with tie and continuity corrections.
Which test should I use?
| Data | Test |
|---|---|
| Paired, differences roughly normal | Paired t-test |
| Paired, skewed or ordinal differences | Wilcoxon signed-rank |
| One sample against a hypothesised median | Wilcoxon signed-rank (one-sample tab) |
| Paired, only the direction of change matters | Sign test |
The effect size r = |z| ÷ √n is about 0.1 for a small effect, 0.3 for medium and 0.5 for large. For two independent groups, use the Mann-Whitney U test instead.
How to cite this page
CalcPulse. (2026). Wilcoxon Signed-Rank Test Calculator. https://calcpulse.com/wilcoxon-signed-rank-test-calculator/
Frequently asked questions
What is the Wilcoxon signed-rank test?
A non-parametric test for paired data or a single sample, based on the ranks of the differences.
What is the difference between Wilcoxon signed-rank and the paired t-test?
The paired t-test compares mean differences and assumes normality. The Wilcoxon test uses ranks, so it suits skewed or ordinal data.
What happens to pairs with zero difference?
They are dropped, because they carry no information about the direction of change.
Is the p-value exact?
Yes when there are no ties or zeros and n is 30 or less. Otherwise a normal approximation with corrections is used, and the page says which.
Can I use it for one sample?
Yes. The one-sample tab tests whether the median differs from a value you choose.
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