I am comparing 8 means and want to set up a planned comparisons, rather than having my Bonferroni adjustment become overly-conservative in a post-hoc. For my groups I need to make a total of 16 comparisons, and some of these comparisons are orthogonal to each other, while others are not. I am curious if there is a way to adjust my alpha without being penalized for all of my comparisons. Here's a summary of my comparisons:
Groups: A B C D E F G H
1: 1 -1 0 0 0 0 0 0
2: 0 0 1 -1 0 0 0 0
3: 0 0 0 0 1 -1 0 0
4: 0 0 0 0 0 0 1 -1
5: 1 0 -1 0 0 0 0 0
6: 1 0 0 0 -1 0 0 0
7: 1 0 0 0 0 0 -1 0
8: 0 0 1 0 -1 0 0 0
9: 0 0 1 0 0 0 -1 0
10: 0 0 0 0 1 0 -1 0
11: 0 1 0 -1 0 0 0 0
12: 0 1 0 0 0 -1 0 0
13: 0 1 0 0 0 0 0 -1
14: 0 0 0 1 0 -1 0 0
15: 0 0 0 1 0 0 0 -1
16: 0 0 0 0 0 1 0 -1
So, some comparisons (e.g. 1-4) are orthogonal to each other, while other comparisons are not. Each mean gets used for a total of 4 comparisons, so is it a stretch to assume an alpha of 0.05 needs to only be adjusted to 0.0125 to account for increased chance of type I error? Or is the rule more strict?