# Extending Dunn's Test

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
.