Kolmogorov-Smirnov Z is used to compare two samples and tends to have better power than Mann-Whitney for small samples.

• A. Mann-Whitney U
• B. Kolmogorov-Smirnov Z
• C. Wilcoxon rank-sum
• D. ANOVA

Answer: (B)

The main idea is comparing two samples using a distribution-based nonparametric test that looks at the entire distribution rather than just a central tendency. The Kolmogorov-Smirnov test does this by examining the largest difference between the empirical distribution functions of the two samples, testing whether they come from the same distribution. This approach captures differences in location and shape, not only shifts in the center, and the KS Z statistic on small samples can have greater power than a rank-based test like the Mann-Whitney U, which mainly detects differences in medians when the shapes are similar. The Wilcoxon rank-sum is essentially the same rank-based idea as Mann-Whitney, so it shares similar limitations, while ANOVA compares means across groups and relies on parametric assumptions, making it inappropriate for this two-sample distribution comparison.