What is the non-parametric test for more than two independent samples?

What is the non-parametric test for more than two independent samples?

• A. Kruskal-Wallis
• B. Friedman
• C. Mann-Whitney U
• D. Wilcoxon

Answer: (A)

When you need to compare more than two independent groups and you don’t want to assume normal distribution, the Kruskal-Wallis test is the go-to non-parametric method. It works by ranking all observations across all groups and then comparing the sum of those ranks for each group. If the groups come from the same population, the rank sums should be similar; a large discrepancy yields an H statistic that, under the null hypothesis, follows a chi-square distribution with the number of groups minus one degrees of freedom. A significant result suggests that at least one group differs in central tendency from the others. Since it doesn’t tell you which groups differ, you’d perform post-hoc pairwise comparisons (like Dunn’s test) with appropriate p-value adjustments to identify where the differences lie. The test requires independent samples and at least ordinal data, and it’s robust to non-normality, making it the non-parametric counterpart to one-way ANOVA. Other non-parametric options are for different designs: two independent groups use a Mann-Whitney U test, while related or paired samples use the Wilcoxon signed-rank test or, when there are more than two related samples, Friedman's test.

When you need to compare more than two independent groups and you don’t want to assume normal distribution, the Kruskal-Wallis test is the go-to non-parametric method. It works by ranking all observations across all groups and then comparing the sum of those ranks for each group. If the groups come from the same population, the rank sums should be similar; a large discrepancy yields an H statistic that, under the null hypothesis, follows a chi-square distribution with the number of groups minus one degrees of freedom.

A significant result suggests that at least one group differs in central tendency from the others. Since it doesn’t tell you which groups differ, you’d perform post-hoc pairwise comparisons (like Dunn’s test) with appropriate p-value adjustments to identify where the differences lie. The test requires independent samples and at least ordinal data, and it’s robust to non-normality, making it the non-parametric counterpart to one-way ANOVA.

Other non-parametric options are for different designs: two independent groups use a Mann-Whitney U test, while related or paired samples use the Wilcoxon signed-rank test or, when there are more than two related samples, Friedman's test.