I have 3 groups: one of healthy subjects (control) and two groups of two different clinical forms of a disease. I always thought the correct way to statistically compare them was to use Kruskal-Wallis test or ANOVA. However, more than one time I saw papers in which each patient group is compared to the control group individually by Mann-Whitney or Student's t test. The same thing occurs when comparing more than 3 culture conditions to the unstimulated cells, as pairs. For this analysis of different stimuli, I've also seen some papers using Friedman test or Repeated Measures ANOVA. Is it correct?
Probably a preferred way would be to use Kruskal-Wallis, and then use a post-hoc test that compares one treatment to all other treatments. There are a few different tests like this. For a list, see the following, the functions that begin
"kwManyOne"... https://rdrr.io/cran/PMCMRplus/man/ .
That being said, other approaches are probably fine. a) Use KW with a Dunn (1964) post-hoc, and ignore the comparisons you are not interested in. Or b) (my least favorite) Use multiple Mann-Whitney tests.
Whether one would use e.g. Kruskal-Wallis or e.g. Friedman test has to do with the experimental design. The latter assumes an unreplicated complete block design. That is, that a subject or experimental unit undergoes all treatments. From your description, I can't tell if your data are paired or dependent in some way.
Kruskal Wallis, ANOVA test can all do the job depending on the data meeting assumptions. There is nothing if you want to use repeated approaches, but I think it will consume space and time. Why not stick with ANOVA or Kruskal Walis? as Salvatore S. Mangiafico suggested.
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