The Mann-Whitney U test evaluates the null hypothesis that the two independent samples come from distributions that are the same. Which of the following reflects that idea?

The Mann-Whitney U test evaluates the null hypothesis that the two independent samples come from distributions that are the same. Which of the following reflects that idea?

• A. Means are equal
• B. Medians are equal
• C. The distributions are the same for two independent samples
• D. Variances are equal

Answer: (C)

The key idea is that Mann-Whitney U looks at whether two independent samples come from the same distribution, not just their means or variances. It works by ranking all observations across both groups and comparing the sums of ranks between the groups. If the two populations truly share the same distribution, the ranks should be mixed about equally between the groups, and no systematic shift will appear. A significant result indicates the distributions differ in general—one group tends to have larger values than the other—rather than just implying equal means or equal variances. This test is appropriate when data are ordinal or not normally distributed, and it doesn’t require equal means or variances. Medians can differ even when the distributions are similar in shape, and the test’s conclusion is about the entire distribution, not a single moment. So the statement that best reflects the null hypothesis is that the distributions are the same for the two independent samples.

The key idea is that Mann-Whitney U looks at whether two independent samples come from the same distribution, not just their means or variances. It works by ranking all observations across both groups and comparing the sums of ranks between the groups. If the two populations truly share the same distribution, the ranks should be mixed about equally between the groups, and no systematic shift will appear. A significant result indicates the distributions differ in general—one group tends to have larger values than the other—rather than just implying equal means or equal variances.

This test is appropriate when data are ordinal or not normally distributed, and it doesn’t require equal means or variances. Medians can differ even when the distributions are similar in shape, and the test’s conclusion is about the entire distribution, not a single moment. So the statement that best reflects the null hypothesis is that the distributions are the same for the two independent samples.