Which nonparametric test is used for more than two related samples (repeated measures)?

Which nonparametric test is used for more than two related samples (repeated measures)?

• A. Sign test
• B. Wilcoxon signed-ranks test
• C. Friedman two-way ANOVA by ranks
• D. Kruskal-Wallis ANOVA by ranks

Answer: (C)

When you have more than two related samples from the same subjects (a repeated-measures design) and you can’t assume normality, you need a nonparametric approach that respects the within-subject structure. The Friedman test is exactly that: a nonparametric alternative to repeated-measures ANOVA. It works by ranking each subject’s scores across the different conditions, then examining whether the average ranks differ across those conditions. Because it uses within-subject ranks, it accounts for the dependency among repeated measurements. If the Friedman test turns out significant, you can follow up with post hoc pairwise comparisons using Wilcoxon signed-rank tests (with appropriate p-value adjustments) to identify which conditions differ. The other tests don’t fit this scenario: the sign test handles only two related samples and ignores the magnitude of differences; the Wilcoxon signed-ranks test handles two related samples as well, not more than two; and the Kruskal-Wallis test applies to more than two groups that are independent, not related samples.

When you have more than two related samples from the same subjects (a repeated-measures design) and you can’t assume normality, you need a nonparametric approach that respects the within-subject structure. The Friedman test is exactly that: a nonparametric alternative to repeated-measures ANOVA. It works by ranking each subject’s scores across the different conditions, then examining whether the average ranks differ across those conditions. Because it uses within-subject ranks, it accounts for the dependency among repeated measurements. If the Friedman test turns out significant, you can follow up with post hoc pairwise comparisons using Wilcoxon signed-rank tests (with appropriate p-value adjustments) to identify which conditions differ. The other tests don’t fit this scenario: the sign test handles only two related samples and ignores the magnitude of differences; the Wilcoxon signed-ranks test handles two related samples as well, not more than two; and the Kruskal-Wallis test applies to more than two groups that are independent, not related samples.