Which test is used to analyze the differences in two related groups?

The Wilcoxon signed-rank test is specifically designed for analyzing the differences between two related groups, also known as paired data. This non-parametric test assesses whether the median of the differences between paired observations is significantly different from zero. It is particularly useful when the data does not meet the assumptions necessary for parametric tests, such as normality.

In situations where you have two conditions and you wish to see if there is a statistically significant change or difference in scores (for example, pre-test and post-test scores from the same subjects), the Wilcoxon signed-rank test provides an appropriate method. It takes into account the ranks of the differences considering both the direction and magnitude of the changes.

Other tests listed serve different purposes. The Mann-Whitney U test compares differences between two independent groups rather than related ones. The Chi-square test analyzes categorical data to assess how likely it is that any observed difference between groups arose by chance. The Kruskal-Wallis test extends the Mann-Whitney U test to more than two groups, assessing whether there are statistically significant differences across multiple independent groups. These distinctions highlight why the Wilcoxon signed-rank test is the correct choice for scenarios involving related groups.