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How do I read the results from Dunn's test? Specifically, what do the values in the table below tell me?

I have non-parametric data in 4 groups, and I first did a Kruskal-Wallis test to confirm that the groups' distributions were dissimilar from one another and the aggregate dataset. I then used Dunn's test to see which groups were dissimilar from one another, and which were not. 

library(dunn.test)
dunn.test(data, g=area, kw=TRUE)
Kruskal-Wallis rank sum test

data: x and area
Kruskal-Wallis chi-squared = 1730.4401, df = 3, p-value = 0


                        Comparison of x by area                            
                            (No adjustment)                                
Row Mean-|
Col Mean |          A          B          C
---------+---------------------------------
       B |   20.62310
         |     0.0000
         |
       C |   26.66519  -0.087499
         |     0.0000     0.4651
         |
       D |   39.09084   7.401256   9.469204
         |     0.0000     0.0000     0.0000
Community
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bubbalouie
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1 Answers1

19

The output following the Kruskal-Wallis test provides all possible pairwise comparisons (six in the case of four groups). So the one on the first row compares group B with group A, the first on the second row compares group C with group A, etc.).

The upper number for each comparison is Dunn's pairwise z test statistic. The lower number is in this example the raw p-value associated with the test (i.e. you would compare to $\alpha/2$, although this p-value changes depending on the family-wise error rate or false discovery rate multiple comparisons adjustment option. For stepwise multiple comparison adjustments (e.g. Holm, Benjamini-Hochberg, etc.), the adjusted p-values will have an asterisk next to them if your would reject the null hypotheses at the specified significance level (which is not necessarily directly indicated by the adjusted p-values since rejection depends on ordering... see the documentation and citations therein for more details.).

I am the author of this package (emailing me, as explicitly indicated in the documentation, would likely be the best way to get in touch with me directly).

Alexis
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  • Sorry if this is taking the question in a different direction, but when would you adjust the test? What criteria are necessary in your data for you to want to choose an adjustment? – pocketlizard Jan 26 '15 at 17:42
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    @pocketlizard See [family-wise error rate](https://en.wikipedia.org/wiki/Familywise_error_rate) and [false discovery rate](https://en.wikipedia.org/wiki/False_discovery_rate). – Alexis Jan 26 '15 at 18:39
  • I have seen that the Kruskal-Wallis values obtained with `kruskal.test` slightly differ from the ones obtained with the option `kw=TRUE` in the above package. Is this due to some approximations or are they two different things? – gented Sep 21 '15 at 08:35
  • @GennaroTedesco `kruskal.test` does not adjust for ties, while `dunn.test` does adjust for ties. As it says in the documentation... just above where it give the email to contact for support questions. – Alexis Sep 22 '15 at 19:03