# Extending Dunn's Test

*From*: Norman B. Grover <norman@xxxxxxxxxxxxx>*Date*: Wed, 7 Mar 2007 10:39:58 +0200

It is common practise to use Dunn's post test when a Kruskal-Wallis

test turns out significant, in order to compare any pairs of samples of

interest. In particular, Dunn's statistic is a z with the absolute

difference of the mean ranks in the numerator and a standard error in the

denominator derived from the variance of the total sample (modified by the

number and length of the ties, if any) and the sizes of the two samples

being compared. The individual p-values are two-tailed and compared with

alpha/[k(k-1)/2], where alpha is the significance level of the Kruskal-

Wallis test and k is the total number of groups (so that k(k-1)/2 is the

total number of pairs).

What if one is interested only in a small number m of a priori

comparisons? Can one compute z as above but compare the individual p-values

(one-tailed, if so specified in advance) to alpha/m? For example, if I have

k=4 samples and I am interested in m=3 comparisons: sample1-sample2,

sample1-sample3 and sample3-sample4 (in those directions) if the overall

Kruskal-Wallis is significant at the 0.05 level, then the standard Dunn's

test would compare the individual two-sided p-values to 0.05/6 whereas my

question is whether one can compare the individual one-sided p-values to

0.05/3?

Any help or guidance or references would be greatly appreciated.

--

Norman B. Grover

Jerusalem, Israel

.

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