Which test is employed for related or paired samples in ordinal data?

The Wilcoxon signed rank test is the appropriate choice for analyzing related or paired samples when dealing with ordinal data. This non-parametric test is specifically designed to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ.

What sets the Wilcoxon signed rank test apart is its ability to handle situations where the distribution of the differences between pairs is not necessarily normal, making it well-suited for ordinal data where only rank order is meaningful but not the actual numeric value of the differences. The test involves calculating the differences between each pair of observations, ranking these differences, and then testing whether the sum of positive ranks differs significantly from the sum of negative ranks.

In contrast, the paired t-test is not suitable here because it assumes interval or ratio data and that the differences are normally distributed. The sign test, while also applicable for paired samples, does not utilize the magnitude of differences, only their signs, which often results in less statistical power. The Mann Whitney U test is intended for independent samples rather than paired ones, further confirming that the Wilcoxon signed rank test is indeed the proper approach in this scenario.