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If I carry out a Kruskal Wallis test and the result comes out as significant, how do I then go about describing those differences and also which groups the difference is present between? For example if I have group A, B and C and I get signiciant difference Do I carry out a certain test for A + B, A + C? Or do I just report percentages/medians? Keep in mind my data was likert scale which I have converted into 1-5 numbers for the purpose of this analysis

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You could do Wilcoxon 2-sample tests ad hoc to determine what differences among groups significant result with K-W implies. You should use some method to avoid 'false discovery' with repeated testing on the same data.

The Bonferroni method can be too conservative (unlikely to declare differences) if you have many ad hoc comparisons. But to compare A with B and B with C would be be only two. Then you would want to declare significant differences only for Wilcoxon P-values < 2.5%.

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  • $\begingroup$ Could I do a "dunn test"? Like the one offered on this website: astatsa.com/KruskalWallisTest , what is "Benjamini-Hochberg FDR method" correction and other corrections btw? And would significance alpha change for the Dunn test if my significance level is.05 for KW test do I have to divide it by a certain number to get a new alpha for the posthoc test? $\endgroup$
    – Chaudry Shahid Iqbal
    Jun 14, 2020 at 10:58
  • $\begingroup$ And what do I use to state the order of differences? Do I use the median (+/- SD)? and if significant mention these or what? $\endgroup$
    – Chaudry Shahid Iqbal
    Jun 14, 2020 at 10:59
  • $\begingroup$ You can say one population is 'shifted to the right' or 'shifted to the left' relative to the other. $\endgroup$
    – BruceET
    Jun 14, 2020 at 15:22

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