If you have paired data and the differences are not normally distributed, which test is appropriate?

• A. Paired t-test
• B. McNemar test
• C. Mann-Whitney U test
• D. Wilcoxon signed-rank test

Answer: (D)

When you have paired data, you’re looking at how each subject’s measurement changes from one condition to the next. The paired t-test works well only if the differences between the paired measurements are roughly normally distributed. If those differences aren’t normal, you should use a nonparametric alternative that doesn’t assume normality: the Wilcoxon signed-rank test.

This test takes each pair’s difference, ignores any that are zero, and then looks at the magnitude of those differences by ranking the absolute values from smallest to largest. It assigns the sign of the actual difference to each rank and sums these signed ranks to form a test statistic. Under the null hypothesis of no systematic change (the median difference is zero), this statistic has a known distribution from which a p-value can be derived. Because it uses the ranks of the differences and their direction, it’s robust to non-normal shapes and still takes into account both how much and in which direction the measurements shift.

In contrast, the paired t-test relies on normal differences; McNemar is for paired binary data, and Mann-Whitney U compares two independent groups. So for paired data with non-normal differences, the Wilcoxon signed-rank test is the appropriate choice.