# Calculating 'k' in the bonferroni procedure when there are both post-hoc and planned constrasts

I have run an experiment with a 2 x 2 factorial design. From what I understand there is no need to adjust the alpha-level for multiple comparisons because all main-effects and interactions are planned.

However I have had a reviewer come back and suggest analyses of some simple effects and as a result I am starting to wonder about error-correction for multiple post-hoc comparisons.

My question is when calculating something like a Bonferroni error correction, how many comparisons should be in the formula? Should I only correct for the post-hoc tests or does doing post-hoc tests mean I should include all planned contrasts as well? So, if performing the bonferroni procedure, what should the k in $\alpha$/$k$ be for a 2 x 2 ANOVA with 2 tests of simple effects?

• Thank you @juod. The reviewer's suggestions are not blind in the sense that there are differences that appear on the graph, but they are blind in the sense that they were not originally planned and are not justified given that there is no two-way interaction between the two categorical predictors. In other words these tests would be well and truly post-hoc. So would you suggest $\alpha$/2 then if there are two of these thoroughly post-hoc comparisons? – llewmills Feb 28 '17 at 13:33