Which non-parametric statistic is used for related samples on ordinal data?

Which non-parametric statistic is used for related samples on ordinal data?

• A. Mann-Whitney U
• B. Chi-square
• C. Wilcoxon Signed Rank test
• D. Pearson correlation

Answer: (C)

When you have related (paired) samples and the data are ordinal or not normally distributed, you need a test that compares the median difference between the pairs without relying on parametric assumptions. The Wilcoxon Signed Rank test does exactly this. It looks at the differences between each pair, ignores any zero differences, ranks the absolute differences, and then applies the signs of the differences to those ranks. By summing the positive and negative ranks, it tests whether there is a consistent directional difference between the two related conditions. This makes it appropriate for ordinal data because it uses ranks rather than raw values and doesn’t require normality. This test is the non-parametric counterpart to the paired t-test, meant for matched or before/after designs. Other choices aren’t suitable here: a Mann-Whitney U test compares two independent groups, Chi-square handles categorical data, and Pearson correlation assesses linear relationships in interval data with normality assumptions.

When you have related (paired) samples and the data are ordinal or not normally distributed, you need a test that compares the median difference between the pairs without relying on parametric assumptions. The Wilcoxon Signed Rank test does exactly this. It looks at the differences between each pair, ignores any zero differences, ranks the absolute differences, and then applies the signs of the differences to those ranks. By summing the positive and negative ranks, it tests whether there is a consistent directional difference between the two related conditions. This makes it appropriate for ordinal data because it uses ranks rather than raw values and doesn’t require normality.

This test is the non-parametric counterpart to the paired t-test, meant for matched or before/after designs. Other choices aren’t suitable here: a Mann-Whitney U test compares two independent groups, Chi-square handles categorical data, and Pearson correlation assesses linear relationships in interval data with normality assumptions.