If I get no significant difference when using Kruskal- Wallis test, is any post hoc test mandatory?
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$\begingroup$ Mandatory? no. Who would make you do it? The circumstances of your question are unclear. $\endgroup$– Glen_bApr 7, 2017 at 11:00
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No, only conduct post-hoc tests when you find something significant and need to do further analysis to see where this significance/difference lies.
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$\begingroup$ You can do post-hoc tests (but note that the Wilcoxon test is not the one to use) even if the overall "chunk" test is insignificant, if you are very careful about controlling for multiplicities. But it is definitely not as safe as if the initial test were 'significant'. The Kruskal-Wallis test, like parametric ANOVA, contains a perfect multiplicity adjustment. $\endgroup$ Apr 7, 2017 at 13:41