Which test would be used to compare three or more independent samples?

Which test would be used to compare three or more independent samples?

• A. Student's t-test
• B. Chi-square test
• C. ANOVA
• D. Kruskal-Wallis Test

Answer: (D)

When you have three or more independent samples and you can’t assume the data are normally distributed, a test that compares the overall distributions across groups is needed. Kruskal-Wallis is the nonparametric alternative to one-way ANOVA and is designed for exactly this situation: it ranks all the data together and asks whether the groups differ in their central tendency (medians) rather than assuming equal means. It’s robust to nonnormal data and does not require equal variances, which makes it a good choice when the data are ordinal or violate parametric assumptions. If the result is significant, you’d follow up with post hoc pairwise comparisons to determine which groups differ. The other options don’t fit as well here. A t-test compares means between two groups, not three or more. Chi-square tests handle categorical data, testing associations or goodness-of-fit rather than comparing a continuous outcome across multiple groups. ANOVA would be appropriate if the data were normally distributed with similar variances, but Kruskal-Wallis is preferred when those parametric assumptions aren’t met.

When you have three or more independent samples and you can’t assume the data are normally distributed, a test that compares the overall distributions across groups is needed. Kruskal-Wallis is the nonparametric alternative to one-way ANOVA and is designed for exactly this situation: it ranks all the data together and asks whether the groups differ in their central tendency (medians) rather than assuming equal means. It’s robust to nonnormal data and does not require equal variances, which makes it a good choice when the data are ordinal or violate parametric assumptions. If the result is significant, you’d follow up with post hoc pairwise comparisons to determine which groups differ.

The other options don’t fit as well here. A t-test compares means between two groups, not three or more. Chi-square tests handle categorical data, testing associations or goodness-of-fit rather than comparing a continuous outcome across multiple groups. ANOVA would be appropriate if the data were normally distributed with similar variances, but Kruskal-Wallis is preferred when those parametric assumptions aren’t met.