Which non-parametric test is used for more than two independent groups and is the non-parametric analogue of one-way ANOVA?

Which non-parametric test is used for more than two independent groups and is the non-parametric analogue of one-way ANOVA?

• A. Friedman's ANOVA
• B. Mann-Whitney U
• C. Kruskall-Wallis test
• D. Wilcoxon rank-sum

Answer: (C)

This question tests identifying the non-parametric method used when you have more than two independent groups and you want a counterpart to one-way ANOVA. The Kruskal-Wallis test does exactly that: it ranks all observations across all groups, sums the ranks within each group, and uses those sums to test whether the groups come from populations with the same distribution. It doesn't assume normality, only that the data are at least ordinal and that observations are independent. The test statistic, H, follows a chi-square distribution with the number of groups minus one degrees of freedom under the null hypothesis of identical distributions, so a significant result suggests at least one group differs. If you do find a difference, you typically follow up with post hoc pairwise comparisons like Dunn's test with a correction for multiple comparisons. Friedman’s ANOVA is for related (repeated) measures, not independent groups. Mann-Whitney U compares two independent groups, not more than two. Wilcoxon rank-sum is another name for the two-group version of Mann-Whitney. Wilcoxon signed-rank is for paired data. Therefore, the Kruskal-Wallis test is the correct choice.

This question tests identifying the non-parametric method used when you have more than two independent groups and you want a counterpart to one-way ANOVA. The Kruskal-Wallis test does exactly that: it ranks all observations across all groups, sums the ranks within each group, and uses those sums to test whether the groups come from populations with the same distribution. It doesn't assume normality, only that the data are at least ordinal and that observations are independent. The test statistic, H, follows a chi-square distribution with the number of groups minus one degrees of freedom under the null hypothesis of identical distributions, so a significant result suggests at least one group differs. If you do find a difference, you typically follow up with post hoc pairwise comparisons like Dunn's test with a correction for multiple comparisons.

Friedman’s ANOVA is for related (repeated) measures, not independent groups. Mann-Whitney U compares two independent groups, not more than two. Wilcoxon rank-sum is another name for the two-group version of Mann-Whitney. Wilcoxon signed-rank is for paired data. Therefore, the Kruskal-Wallis test is the correct choice.