What is the non-parametric equivalent of the paired t-test?

The non-parametric equivalent of the paired t-test is the Wilcoxon test, specifically the Wilcoxon signed-rank test. This test is used for assessing whether there is a statistically significant difference between the medians of two related groups. When data does not meet the assumptions required for a paired t-test, such as normality, the Wilcoxon signed-rank test provides a robust alternative. It relies on the ranks of the differences between paired observations rather than the raw data, which makes it particularly useful for non-normally distributed data or ordinal scales.

In contrast, the other options, such as the Kruskal-Wallis test and ANOVA, serve different purposes and target different types of data. The Kruskal-Wallis test is a non-parametric alternative to one-way ANOVA, used for comparing more than two independent groups, while ANOVA itself is a parametric test designed to compare means across multiple groups under the assumption of normality and homogeneity of variance. The Friedman test is the non-parametric equivalent of the one-way repeated measures ANOVA, which serves a similar function for related groups measured under different conditions, but it is not applicable for pairs of observations as the paired t-test or Wilcoxon test