Which option lists two nonparametric tests for comparing two independent samples?

Which option lists two nonparametric tests for comparing two independent samples?

• A. Paired t-test and Wilcoxon signed-rank test
• B. Mann-Whitney U test and Wilcoxon rank-sum test
• C. ANOVA and Kruskal-Wallis test
• D. Chi-square test and Fisher's exact test

Answer: (B)

Nonparametric methods for two independent samples rely on ranks rather than assuming a specific shape for the data, so they don’t require normality. When you want to compare two separate groups on an outcome that’s ordinal or not normally distributed, two standard options are the Mann-Whitney U test and the Wilcoxon rank-sum test. Both work by combining all observations from both groups, ranking them from smallest to largest, and then comparing the distribution of those ranks between the groups. If one group tends to have higher values, its ranks will tend to be higher, and the test detects that difference. This pair fits two independent samples because there’s no pairing between individuals in one group and individuals in the other; the focus is on how the two groups differ in their distributions overall, not on matched pairs. They’re the nonparametric stand-ins for the two-sample t-test when the data aren’t normally distributed. Other options mix different ideas: pairing the t-test with its nonparametric counterpart for paired data won’t address independent groups, and a parametric test plus a nonparametric one for more than two groups isn’t the same scenario. Tests like chi-square or Fisher’s exact handle categorical data in contingency tables, which is a different data type and question than comparing a numeric or ordinal outcome across two independent samples.

Nonparametric methods for two independent samples rely on ranks rather than assuming a specific shape for the data, so they don’t require normality. When you want to compare two separate groups on an outcome that’s ordinal or not normally distributed, two standard options are the Mann-Whitney U test and the Wilcoxon rank-sum test. Both work by combining all observations from both groups, ranking them from smallest to largest, and then comparing the distribution of those ranks between the groups. If one group tends to have higher values, its ranks will tend to be higher, and the test detects that difference.

This pair fits two independent samples because there’s no pairing between individuals in one group and individuals in the other; the focus is on how the two groups differ in their distributions overall, not on matched pairs. They’re the nonparametric stand-ins for the two-sample t-test when the data aren’t normally distributed.

Other options mix different ideas: pairing the t-test with its nonparametric counterpart for paired data won’t address independent groups, and a parametric test plus a nonparametric one for more than two groups isn’t the same scenario. Tests like chi-square or Fisher’s exact handle categorical data in contingency tables, which is a different data type and question than comparing a numeric or ordinal outcome across two independent samples.