I have the same group and want to test differences for two (unrelated) variables - Do I use Wilcoxon signed-rank test or Wilcoxon rank sum test?

Question

I wonder if this is a case that it not clearly specified:

Typically, Wilcoxon rank sum test / Mann–Whitney U test is used for independent groups and testing the values of different variables against each other. Typically, Wilcoxon Signed Rank Test is used for dependent groups (same group) and testing the values for the changes in one variable (like in time series study).

But which test is used when I want to test differences for the same group (the same people are asked) for two different variables (non-parametric)? This is not clearly specifiable with the usual definition for these two tests.

For my question the following example: The same teachers are asked about how deeply (or not) they have integrated a specific topic in their courses (Virtual Reality and Data Mining). Here I used a Wilcoxon rank sum test / Mann–Whitney U test with which I want to test if there is a significant difference between the two:

wilcox.test(Bothque$VR_integr, Bothque$DM_integr, exact = FALSE, correct = TRUE, conf.int = TRUE)

Answer 1

Assuming I have correctly understood the situation, if you have the data so that it can be paired, you should do so, and use the paired analysis.