# How do I interpret the p-value in a Dunn-test?

I conducted a Kruskal Wallis test for my sample sizes, and this is what I got:

Kruskal-Wallis chi-squared = 12.138, df = 4, p-value = 0.01635

The p-value is below 0.05, so I know there is a significant difference among my compared groups. So I did a dunn-test to find the differences:

dunnTest(personal.value ~ income, data=ordinal, method="bh")

And this is what I got:

Yet, none of the adjusted p-values are below 0.05. Does that mean I can accept the null hypothesis? How do I interpret this?

• Ha! That's based on my dunn.test package, that version of dunnTest is... if you are concerned about statistical power, use the Conover-Iman test: a post hoc pairwise test like Dunn's test, but is strictly more powerful. It is implemented in the conover.test package, and uses the same syntax. Commented Dec 18, 2021 at 16:16
• Aside: When you are using step-up (e.g., Holm) or step down (e.g., Benjamini-Hochberg) procedures, you cannot quite interpret rejection decisions based on comparing adjusted p values to $\alpha$, since the rejection decisions also factor in the ordering of the unadjusted p values. Commented Dec 18, 2021 at 16:20
• @Alexis I just used your conover.test package, and it worked wonderfully. Thank you so much. Commented Dec 18, 2021 at 20:16
• I suppose if we are mentioning R packages, the PMCMRplus package has Dunn test, Conover test, and Nemenyi test for post-hoc analysis after Kruskal-Wallis. It also has post-hoc tests for Friedman and Quade and other rank-based tests. Commented Dec 19, 2021 at 17:06

By looking at all $${5 \choose 2} = 10$$ ad hoc comparisons among levels of this factor you may be paying a penalty with adjusted P-values larger than than necessary to avoid false discovery.