I have 243 participants and 4 different conditions. As a first step I tried to do one-way ANOVA, but the assumption of normality was not met. After that I transformed my data but the normality was not met again. I then decided to do The Kruskal-Wallis H test and it is non significant. I now want to do a post hoc test in order to compare certain conditions between them. My question is; can I do a post hoc test even if The Kruskal-Wallis H test is non-significant? If yes, which one is the most appropriate?
A question might be asked: why would you conduct a Kruskal-Wallis test if you don't care about the result? ... It might make sense to skip the omnibus KW test, and simply run a post-hoc test, if that's what you were really interested in in the first place. The validity of this may depend on the test chosen. For the KW test, an appropriate post-hoc is the Dunn test (1964)... Also, anova and KW test different kinds of hypotheses. You might consider which hypothesis you really want to test. If you are really interested in the anova-type hypothesis, there may be methods like permutation tests that are appropriate for your situation.