Which nonparametric test is used for two related samples (paired data)?

Which nonparametric test is used for two related samples (paired data)?

• A. Sign test
• B. McNemar test
• C. Paired t-test
• D. Wilcoxon signed-ranks test

Answer: (D)

When comparing two related samples, a nonparametric method that handles paired data by using both the direction and the size of the differences is appropriate. The Wilcoxon signed-ranks test does this by taking the differences between each paired observation, ranking the absolute values of those differences, and then summing the ranks for the positive and negative differences. If there is no real change, the positive and negative rank sums should be similar; if there is a genuine median difference, one sign will dominate, leading to a noticeable imbalance in the rank sums. This test does not assume normality and works with ordinal or non-normally distributed continuous data, making it more informative than the sign test because it incorporates the magnitude of differences, not just their direction. In contrast, the paired t-test is a parametric test that assumes the differences are normally distributed, which isn’t required for the Wilcoxon approach. The sign test uses only the direction of change and ignores how large the differences are, resulting in less statistical power. The McNemar test is designed for paired binary outcomes in a 2x2 framework and isn’t suitable for using magnitude information from non-normal data.

When comparing two related samples, a nonparametric method that handles paired data by using both the direction and the size of the differences is appropriate. The Wilcoxon signed-ranks test does this by taking the differences between each paired observation, ranking the absolute values of those differences, and then summing the ranks for the positive and negative differences. If there is no real change, the positive and negative rank sums should be similar; if there is a genuine median difference, one sign will dominate, leading to a noticeable imbalance in the rank sums. This test does not assume normality and works with ordinal or non-normally distributed continuous data, making it more informative than the sign test because it incorporates the magnitude of differences, not just their direction.

In contrast, the paired t-test is a parametric test that assumes the differences are normally distributed, which isn’t required for the Wilcoxon approach. The sign test uses only the direction of change and ignores how large the differences are, resulting in less statistical power. The McNemar test is designed for paired binary outcomes in a 2x2 framework and isn’t suitable for using magnitude information from non-normal data.