Which test tends to have better power than the Mann-Whitney test for small sample sizes (n < 25 per group) when comparing two groups?

Which test tends to have better power than the Mann-Whitney test for small sample sizes (n < 25 per group) when comparing two groups?

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

Answer: (A)

The key idea is that a test which compares the entire distribution can sometimes be more powerful than a test that focuses on a single aspect like central tendency, especially with small samples. The Kolmogorov-Smirnov two-sample test looks at the maximum difference between the empirical distribution functions of the two groups, so it is sensitive to differences in location, spread, and overall shape, not just a shift in the median. With small samples (fewer than about 25 per group), that broader sensitivity can translate into higher power in detecting distribution differences than the Mann-Whitney test, which relies on ranks to detect a difference in central tendency when the group distributions are similar in shape. The Mann-Whitney test is very good for a shift in medians, but if the true difference involves more than a simple location change, KS can pick it up more effectively. The Wilcoxon rank-sum is essentially the same idea as Mann-Whitney, so it doesn’t offer a distinct power advantage here. The t-test would usually outperform nonparametric tests only when the data are approximately normal and variances are similar; with unknown distribution and small samples, KS’s broader sensitivity can be advantageous.

The key idea is that a test which compares the entire distribution can sometimes be more powerful than a test that focuses on a single aspect like central tendency, especially with small samples. The Kolmogorov-Smirnov two-sample test looks at the maximum difference between the empirical distribution functions of the two groups, so it is sensitive to differences in location, spread, and overall shape, not just a shift in the median.

With small samples (fewer than about 25 per group), that broader sensitivity can translate into higher power in detecting distribution differences than the Mann-Whitney test, which relies on ranks to detect a difference in central tendency when the group distributions are similar in shape. The Mann-Whitney test is very good for a shift in medians, but if the true difference involves more than a simple location change, KS can pick it up more effectively.

The Wilcoxon rank-sum is essentially the same idea as Mann-Whitney, so it doesn’t offer a distinct power advantage here. The t-test would usually outperform nonparametric tests only when the data are approximately normal and variances are similar; with unknown distribution and small samples, KS’s broader sensitivity can be advantageous.