Wilcoxon signed-rank test is ...

• A. A non-parametric test that looks for differences between two related samples and is the non-parametric counterpart of the paired t-test.
• B. A non-parametric test for two independent samples.
• C. A parametric test for two related samples.
• D. A non-parametric test for one sample.

Answer: (A)

When comparing two related samples, you want to know if there is a consistent difference between the conditions without assuming the differences are normally distributed. The Wilcoxon signed-rank test does exactly that in a non-parametric way. It uses each subject’s paired observations (for example, measurements before and after on the same person), computes the difference for each pair, and then looks at both the size and the direction of those differences.

Instead of comparing means, this test ranks the absolute differences and then incorporates the sign of each difference. If there is no real effect, the positive and negative differences should balance out, and the sum of the ranks in each direction should be about equal. A significant result suggests a systematic difference between the two related conditions.

This approach is the non-parametric counterpart to the paired t-test: it serves the same purpose—testing whether there’s a median difference between the two related conditions—but it doesn’t assume that the differences are normally distributed. It’s particularly useful with small samples or skewed data.

It’s not used for two independent samples (that’s a different non-parametric test) and it’s not a one-sample test.