Multiple comparisons for plants and hummingbirds. As in ANOVA, we often want to carry out a multiple-comparisons procedure following a Kruskal-Wallis test to tell us which groups differ significantly.20 Here is a simple method: If we carry out k tests at fixed significance 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 significance level 0.05 for all of k comparisons, do each individual comparison at the 0.05/k level. In Exercise 15.35 you found a significant difference among the lengths of three varieties of the flower Heliconia. Now we will explore multiple comparisons.
(a) Write down all 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 flower varieties. What are the three two-sided P-values?
(c) For purposes of multiple comparisons, any of these three tests is significant if its P-value is no greater than 0.05/3 = 0.0167. Which pairs differ significantly at the overall 0.05 level?