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I know that dunn.test is generally used as a post hoc after Kruskall Wallis to see which groups are different, but to generalize the function I am writing, I was wondering if when only using two groups, under what conditions is the p value from dunn.test equivalent to that of wilcox.test?

For example, if I do:

library(dunn.test)
a = rnorm(n=500, m=1.1, sd=1)
b = rnorm(n=500, m=1, sd=1)

And do dunn.test(list(a, b))$P, I get exactly half the result of wilcox.test(a, b), as dunn.test seems to be doing a one sided test by default. That is easy to fix.

However, when I do:

c = c(0.026448555266779, 0.024129847627784, 0.027900932579116, 0.025760587066198)

d = c(0.029862915965958, 0.028563420475972, 0.026703358304031)

Then the p-value of dunn.test is 0.03 (one sided) and wilcox.test is 0.11 (two sided). Is this to be expected? Under what conditions?

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  • $\begingroup$ This seems to be about a couple of specific functions in R (& is borderline on-topic, IMO); you should at least list the packages you are using. $\endgroup$ Jul 13, 2018 at 14:06
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    $\begingroup$ @gung Sounds good, will do. I just used the R examples as a way to reproduce my results, but any insight from a statistical point of view as to why the answers are theoretically different is what I am looking for. $\endgroup$ Jul 13, 2018 at 14:16
  • $\begingroup$ I am the author of dunn.test, which only does two-sided tests. The problem is that some folks (like Olive Dunn in the article where she introduced the test) conventionally define two-sided p values as $p = P(Z \ge |z|)$ in contrast with others who conventionally define them as $p = P(|Z| \ge |z|)$. The former gives exactly 1/2 the latter, and so rejections are made when $p \le \frac{\alpha}{2}$ for the former, whereas they are made when $p \le \alpha$ for the latter. Both conventions give identical rejection decisions. $\endgroup$
    – Alexis
    Dec 18, 2021 at 19:15

1 Answer 1

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They will be the same if you make some adjustments to the options in the functions.

For wilcox.test, you can disable the exact calculation of the p-value, and the continuity correction.

For dunn.test, you can choose altp = TRUE to change the output to be what we think of as the full two-sided p-value.

C = c(0.026448555266779, 0.024129847627784, 0.027900932579116, 0.025760587066198)

D = c(0.029862915965958, 0.028563420475972, 0.026703358304031)

wilcox.test(C,D, correct=FALSE, exact=FALSE)

   ### Wilcoxon rank sum test
   ### 
   ### W = 1, p-value = 0.0771

library(dunn.test)

dunn.test(list(C,D), altp=TRUE)

   ### Comparison of x by group                            
   ### (No adjustment)                                
   ###
   ### Col Mean-|
   ### Row Mean |          1
   ### ---------+-----------
   ###        2 |  -1.767766
   ###          |     0.0771
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    $\begingroup$ Apparently, the dunn.test function reports by default what looks like a one-sided p-value because that's how the original test was formulated, with the decision rule: Reject Ho if p <= alpha/2 $\endgroup$ Jul 14, 2018 at 13:56
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    $\begingroup$ In general I prefer the dunnTest function in the FSA package. But it appeared to fail with only two groups. $\endgroup$ Jul 14, 2018 at 13:58
  • $\begingroup$ +1 Sal, see my comment to the original question. Aside: The FSA version is just a "repackaging" of my test. $\endgroup$
    – Alexis
    Dec 18, 2021 at 19:14
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    $\begingroup$ Hi, @Alexis , in fairness to FSA, the documentation does say, This is largely a wrapper for the dunn.test function in dunn.test. Please see and cite that package.. I do like the table output from that package, and the p-value that's reported. $\endgroup$ Dec 19, 2021 at 13:55

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