Wilcoxon Signed-Rank Test Calculator

The Wilcoxon Signed-Rank Test is a non-parametric statistical test used to compare two related samples or repeated measurements on the same subjects. It tests whether the median difference between paired observations is zero, making it a robust alternative to the paired t-test when data does not meet normality assumptions.

Use the Wilcoxon Signed-Rank Test when your paired differences are not normally distributed, when your data is ordinal, or when the sample contains significant outliers. If your data is continuous, roughly normally distributed, and free of extreme outliers, the paired t-test is generally more powerful.

The W statistic is derived by ranking the absolute differences between paired values and then summing the ranks associated with positive differences (W+) and negative differences (W−) separately. In a two-tailed test, the smaller of W+ and W− is typically used as the test statistic. A large imbalance between W+ and W− suggests a significant difference between the two groups.

For small samples (n ≤ 25), this calculator uses a normal approximation with continuity correction to estimate the p-value. The Z-score is computed from the W statistic, its expected value, and its standard deviation under the null hypothesis. The p-value is then derived from the standard normal distribution, adjusted for the selected tail type.

If the p-value is less than your chosen significance level (α), you reject the null hypothesis. This means there is statistically significant evidence that the median difference between the two paired groups is not zero — in other words, the treatment or condition had a measurable effect.

Pairs where the difference between Group 1 and Group 2 equals zero (after subtracting μ₀) are excluded from the analysis. They do not contribute to the rank sums and are not counted in the effective sample size n. This is standard practice for the Wilcoxon Signed-Rank Test.

Yes. You can enter your single sample in Group 1, enter a column of your hypothesized median values (or zeros) in Group 2, and set μ₀ accordingly. Alternatively, treat the Group 2 column as the constant null hypothesis value. The calculation logic remains the same — it tests whether the median difference departs from μ₀.

When two or more pairs share the same absolute difference value, they receive the average of the ranks they would have been assigned. For example, if two pairs tie for ranks 3 and 4, both receive rank 3.5. This calculator automatically applies average rank assignment for all ties.