Which test would you use to compare three or more related samples when the data are not normally distributed?

Which test would you use to compare three or more related samples when the data are not normally distributed?

• A. One-Way ANOVA
• B. Friedman’s ANOVA
• C. Paired t-test
• D. Mann-Whitney U

Answer: (B)

When you have three or more related samples (repeated measures on the same subjects) and the data aren’t normally distributed, you use a nonparametric test that compares the central tendencies across multiple related groups. The Friedman test is designed for this situation: it’s the nonparametric counterpart to the repeated-measures ANOVA. It works by ranking the scores within each subject across the different conditions and then testing whether these ranks differ across the conditions. Because it relies on ranks rather than assumptions about normality, it doesn’t require the data to be normally distributed. If the Friedman test shows a difference, you’d typically follow up with post hoc pairwise comparisons using a nonparametric method to identify which conditions differ. This is different from a one-way ANOVA, which assumes independence of observations and normality and is meant for independent groups. It’s also different from a paired t-test, which compares only two related samples, and from the Mann-Whitney U test, which compares two independent samples.

When you have three or more related samples (repeated measures on the same subjects) and the data aren’t normally distributed, you use a nonparametric test that compares the central tendencies across multiple related groups. The Friedman test is designed for this situation: it’s the nonparametric counterpart to the repeated-measures ANOVA. It works by ranking the scores within each subject across the different conditions and then testing whether these ranks differ across the conditions. Because it relies on ranks rather than assumptions about normality, it doesn’t require the data to be normally distributed. If the Friedman test shows a difference, you’d typically follow up with post hoc pairwise comparisons using a nonparametric method to identify which conditions differ.

This is different from a one-way ANOVA, which assumes independence of observations and normality and is meant for independent groups. It’s also different from a paired t-test, which compares only two related samples, and from the Mann-Whitney U test, which compares two independent samples.