How does Kruskal-Wallis extend Mann-Whitney to more than two groups?

• A. It compares means across k independent groups using an ANOVA on ranks
• B. It ignores group structure and tests a single sample
• C. It compares medians across k independent groups; uses rank-based statistic
• D. It tests correlation between two variables

Answer: (C)

Kruskal-Wallis extends Mann-Whitney by using ranks across all groups to compare more than two independent samples. It tests whether the groups come from the same distribution, which is interpreted as differences in central tendency (medians) when the distributions have similar shapes. All observations are ranked together, and the sums of ranks for each group are used to compute a rank-based statistic. If the groups share the same distribution, their average ranks should be similar; a large difference among these sums signals that at least one group differs. Being nonparametric, it avoids normality assumptions and serves as a generalization of the two-sample Mann-Whitney to multiple groups. If the result is significant, follow-up pairwise comparisons with appropriate adjustments can identify which groups differ.