I am trying to do multiple ANOVA tests testing a single response against about 7 different explanatory variables in turn. Obviously, I need a Bonferroni correction here, but I'm unsure how to use it. The naive way would be to just use n=7 in calculating the corrected alpha, but these 7 variables are strongly collinear so that would result in loss of power.
Three principle components account for more than 99% of the variability in the explanatory variable data, which leads me to think that I am only really doing the equivalent of 3 independent tests rather than 7. Can I use n=3 in calculating the Bonferroni-corrected alpha?
