Which test would you use for two correlated samples with scores that are not normally distributed?

Which test would you use for two correlated samples with scores that are not normally distributed?

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

Answer: (C)

The Wilcoxon signed-rank test is the appropriate choice for analyzing two correlated samples when the scores do not follow a normal distribution. This non-parametric test is specifically designed to assess whether the median of the differences between paired observations is zero. It is particularly useful in situations where the assumptions required for parametric tests, like the paired t-test, are violated due to non-normality. In cases involving correlated samples, such as pre-test and post-test scores from the same subjects, the Wilcoxon signed-rank test considers the ranks of the differences between pairs instead of the actual score values. This method allows for robust analysis even when the underlying distribution deviates from normality. By using ranks, the test reduces the influence of outliers, further ensuring valid results. Other options do not suit this context. The Kruskal-Wallis test is used for comparing more than two independent groups rather than paired samples. The Mann-Whitney U test is designed for comparing two independent groups, not correlated samples. The Chi-square test is employed for categorical data, assessing relationships between different groups, making it inappropriate for directly measuring differences in scores from correlated samples. Thus, the Wilcoxon signed-rank test is the optimal choice in this scenario.

The Wilcoxon signed-rank test is the appropriate choice for analyzing two correlated samples when the scores do not follow a normal distribution. This non-parametric test is specifically designed to assess whether the median of the differences between paired observations is zero. It is particularly useful in situations where the assumptions required for parametric tests, like the paired t-test, are violated due to non-normality.

In cases involving correlated samples, such as pre-test and post-test scores from the same subjects, the Wilcoxon signed-rank test considers the ranks of the differences between pairs instead of the actual score values. This method allows for robust analysis even when the underlying distribution deviates from normality. By using ranks, the test reduces the influence of outliers, further ensuring valid results.

Other options do not suit this context. The Kruskal-Wallis test is used for comparing more than two independent groups rather than paired samples. The Mann-Whitney U test is designed for comparing two independent groups, not correlated samples. The Chi-square test is employed for categorical data, assessing relationships between different groups, making it inappropriate for directly measuring differences in scores from correlated samples. Thus, the Wilcoxon signed-rank test is the optimal choice in this scenario.