What is the primary purpose of the Kruskal-Wallis test?

• A. Test correlation between two variables
• B. Test difference between two paired samples
• C. Compare three or more independent samples
• D. Estimate population mean

Answer: (C)

Kruskal-Wallis is a nonparametric method used to compare three or more independent samples by ranking all observations together and then evaluating how the ranks distribute across the groups. It mirrors one-way ANOVA but for data that aren’t normally distributed or are ordinal, so it doesn’t rely on means or variance assumptions. The key idea is to ask whether the different groups come from the same distribution; a significant result suggests that at least one group differs from the others, though it doesn’t specify which ones. If a difference is found, follow-up post hoc tests can identify the specific pairings that differ. This approach is not about measuring correlation between two variables, nor about comparing paired samples, nor about estimating a population mean, which is why the other options don’t fit.