Which nonparametric test is a nonparametric version of the t-test for independent samples?

Which nonparametric test is a nonparametric version of the t-test for independent samples?

• A. The Wilcoxon signed ranks test
• B. The Mann-Whitney U test
• C. The Sign test
• D. The Kruskal-Wallis test

Answer: (B)

When you need to compare two independent groups without assuming the data are normally distributed, the nonparametric counterpart to the independent-samples t-test is the Mann-Whitney U test. This test works by ranking all observations from both groups together and then comparing the sum of ranks between the groups. If the two groups come from the same distribution, the ranks tend to be mixed and the rank sums are similar; if one group tends to have higher values, its ranks will be higher and the rank sum will stand out. It only requires independent observations and at least ordinal data, and it does not rely on normality, making it more robust to skewed data or outliers. The other options serve different purposes: the Wilcoxon signed-rank test is for paired or matched samples, testing differences within pairs; the Sign test is a simpler test focusing on the direction of differences with minimal assumptions and generally less statistical power; the Kruskal-Wallis test extends to more than two groups rather than the two-sample case. Therefore, the Mann-Whitney U test is the appropriate nonparametric choice for comparing two independent groups.

When you need to compare two independent groups without assuming the data are normally distributed, the nonparametric counterpart to the independent-samples t-test is the Mann-Whitney U test. This test works by ranking all observations from both groups together and then comparing the sum of ranks between the groups. If the two groups come from the same distribution, the ranks tend to be mixed and the rank sums are similar; if one group tends to have higher values, its ranks will be higher and the rank sum will stand out. It only requires independent observations and at least ordinal data, and it does not rely on normality, making it more robust to skewed data or outliers.

The other options serve different purposes: the Wilcoxon signed-rank test is for paired or matched samples, testing differences within pairs; the Sign test is a simpler test focusing on the direction of differences with minimal assumptions and generally less statistical power; the Kruskal-Wallis test extends to more than two groups rather than the two-sample case. Therefore, the Mann-Whitney U test is the appropriate nonparametric choice for comparing two independent groups.