I have data for a test on three groups. The measured variable is ratio scaled. The R code is
g1a<-c(7, 3, 40) g2a<-c(1,1,2) g3a<-c(0,0,0)
Since the sample is small and normality cannot be guaranteed, I run a Kruskal Wallis test to check for significance:
The p-value is 0.02336, which is nice.
Now I run a post-hoc test, using the Mann-Whitney U:
wilcox.test(g1a,g2a,paired=FALSE,exact=TRUE) wilcox.test(g2a,g3a,paired=FALSE,exact=TRUE) wilcox.test(g1a,g3a,paired=FALSE,exact=TRUE)
All the resulting p-values are above 0.05 (0.07652, 0.0636, 0.05935). This is very strange. Shouldn't one of these tests give a much lower p-value? Especially since I'd have to use some sort of correction to account for the multiple comparisons in the post-hoc test. In other words: how can I interpret this result?