Which nonparametric test is used for paired data?

Which nonparametric test is used for paired data?

• A. Mann-Whitney U test
• B. Sign test
• C. Wilcoxon signed-rank test
• D. Chi-square test

Answer: (C)

Nonparametric test for paired data is used when you have two related samples and you want to know if there’s a systematic difference between them without assuming the differences are normally distributed. The Wilcoxon signed-rank test is the best choice because it uses both the direction and the size of the differences between paired observations. You take the difference for each pair, drop any pairs with zero difference, rank the absolute values of the differences, and then reattach the signs to those ranks and sum the positive and negative ranks. The resulting statistic reveals whether one measurement tends to be consistently higher or lower than the other. This approach is more powerful than the sign test, which only considers whether differences are positive or negative and ignores how large they are. By contrast, the Mann-Whitney U test compares two independent groups, not paired data, and the chi-square test operates on categorical data, not paired numeric measurements.

Nonparametric test for paired data is used when you have two related samples and you want to know if there’s a systematic difference between them without assuming the differences are normally distributed. The Wilcoxon signed-rank test is the best choice because it uses both the direction and the size of the differences between paired observations. You take the difference for each pair, drop any pairs with zero difference, rank the absolute values of the differences, and then reattach the signs to those ranks and sum the positive and negative ranks. The resulting statistic reveals whether one measurement tends to be consistently higher or lower than the other. This approach is more powerful than the sign test, which only considers whether differences are positive or negative and ignores how large they are. By contrast, the Mann-Whitney U test compares two independent groups, not paired data, and the chi-square test operates on categorical data, not paired numeric measurements.