American Board of Surgery Qualifying Exam (ABS QE) Practice Test

What is a valid application of the Mann-Whitney U test?

1. Comparing means of paired data

2. Testing differences in ranks between two independent samples

3. Evaluating variance among groups

4. Comparing proportions in a single group

The correct answer is: Testing differences in ranks between two independent samples

The Mann-Whitney U test is a non-parametric statistical test designed to assess whether there is a difference in the distribution of ranks between two independent samples. It is particularly useful when the assumptions of the t-test (such as normality of the data) cannot be met. In practice, this test ranks all data points from both groups together and then compares the sum of these ranks between the two groups. A significant difference in the ranks suggests that one sample tends to have higher or lower values than the other, making it a suitable method for analyzing differences when the data does not fit a normal distribution, or when dealing with ordinal data. The other applications listed, such as comparing means of paired data, evaluating variance among groups, or comparing proportions in a single group, are associated with different statistical tests that are designed for those specific analyses. For instance, paired data would more commonly be analyzed using tests like the paired t-test, ANOVA is used for variance, and chi-squared tests are often applied for proportions. Therefore, the application of the Mann-Whitney U test to compare ranks between two independent samples is both valid and widely accepted in statistical practice.