Mann Whitney U or Wilcoxon Sign Rank test?

Question

I have been collecting data where participants have been allocated to one of three different conditions and had to answer some questions. The data looked like this:

  Condition  Response
1  a            5
2  b            2
3  a            7
4  c            6
5  b            3

I was planning to do an ANOVA but the assumptions of normality was broken so I did a Kruskal-Wallis test. For the post-hoc would I do Mann-Whitney or the Wilcoxon Sign-rank test? I am unsure of the difference between the two other than with r coding I believe one to use wilcox.test and the other to use wilcox_test (please correct me if I'm wrong).

If this is necessary to know, I hypothesised the results from the questions the participants answered should be affected by the condition they were allocated. Specifically, condition 'a' would be the most effective.

So I guess what I'm asking is: Should I use Mann-Whitney or Wilcoxon Signed Ranked or something else entirely as the post hoc?

Answer 1

Wilcoxon Signed Ranked test is performed when the samples are paired. An example would be if for every individual you had different measurements (for instance at different phases of an experiment) and you wanted to see if there is a difference between each phase.

It seems that in your case your samples are independent because every participant has a single condition and participates one time. In this case, you can use the Mann-Whitney test.

That being said, it is recommended that you use the Dunn's posthoc test rather than the Mann-Whitney test as per here or here.