# Compute the power of Tukey's Honest Significance Difference (or cognates)?

I've got a simple computational model I can run experiments with. Experiments are "free" but I don't want to run it more times than necessary because it still takes time.

All the simulation use the same parameters except for one condition which I vary and can take 4 different values (categorical condition).

I know how many times to run the model if I want the power to be $x$ for the ANOVA test that tells me that not all categorical variables have the same mean.
What I don't know how to do is compute the power of the post-hoc analysis that follows where I use Tukey's HSD to tell me pairwise which categorical variable is on average better/worse than the other.

Is there a table (or function) anywhere that compute the HSD power? so far I am using the t-tests tabls but even they are not taking into consideration the bonferroni correction that the R package automatically applies when running it pairwise (sensibly, so).

• You can approximate it (conservatively) by an ordinary power calculation, but dividing alpha by the number of pairwise comparisons. That would actually give you the power of the Bonferroni corrected comparisons. – rvl Oct 26 '17 at 12:45