As in ANOVA, we often want to carry out a multiple-comparisons procedure following a Kruskal-Wallis test to tell us which groups differ signi?cantly.29 Here is a simple method: If we carry out k tests at ?xed signi?cance level 0.05/k, the probability of any false rejection among the k tests is always no greater than 0.05. That is, to get overall signi?cance level 0.05 for all of k comparisons, do each individual comparison at the 0.05/k level. In Exercise 15.43 you found a signi?cant difference among the lengths of three varieties of the ?ower Heliconia. Now we will explore multiple comparisons.
(a) Write down all of the pairwise comparisons we can make, for example, bihai versus caribaea red. There are three possible pairwise comparisons.
(b) Carry out three Wilcoxon rank sum tests, one for each of the three pairs of ?ower varieties. What are the three two-sided P-values?
(c) For purposes of multiple comparisons, any of these three tests is signi?cant if its P-value is no greater than 0.05/3 = 0.0167. Which pairs differ signi?cantly at the overall 0.05 level?