Which test is used for related samples and ordinal data in testing differences?

Which test is used for related samples and ordinal data in testing differences?

• A. The Wilcoxon (T) matched pairs signed ranks test
• B. The Mann-Whitney U test
• C. The Sign test
• D. ANOVA

Answer: (A)

This question tests a nonparametric method for comparing related samples when the data are ordinal. The Wilcoxon matched-pairs signed-ranks test is the nonparametric alternative to the paired t-test. It looks at the differences between each pair of related observations, uses the magnitude of those differences (ignoring zeros), ranks those magnitudes, and then assigns the sign of each difference to the corresponding rank. If there’s no real difference between the two related conditions, positive and negative ranks should balance out; if there is a systematic difference, one sign will dominate, making the sum of ranks for that sign unlikely under the null hypothesis. This approach accommodates ordinal data and does not assume normality, which is why it’s preferred for related samples with non-normal or ordinal data. It also works well with smaller sample sizes. In contrast, the Mann-Whitney U test handles independent samples rather than paired data; the Sign test uses only the direction of differences and ignores their magnitudes, making it less powerful; ANOVA is a parametric test for normally distributed continuous data and is not appropriate for ordinal data or related samples.

This question tests a nonparametric method for comparing related samples when the data are ordinal. The Wilcoxon matched-pairs signed-ranks test is the nonparametric alternative to the paired t-test. It looks at the differences between each pair of related observations, uses the magnitude of those differences (ignoring zeros), ranks those magnitudes, and then assigns the sign of each difference to the corresponding rank. If there’s no real difference between the two related conditions, positive and negative ranks should balance out; if there is a systematic difference, one sign will dominate, making the sum of ranks for that sign unlikely under the null hypothesis. This approach accommodates ordinal data and does not assume normality, which is why it’s preferred for related samples with non-normal or ordinal data. It also works well with smaller sample sizes.

In contrast, the Mann-Whitney U test handles independent samples rather than paired data; the Sign test uses only the direction of differences and ignores their magnitudes, making it less powerful; ANOVA is a parametric test for normally distributed continuous data and is not appropriate for ordinal data or related samples.