I have multiple sets of comparisons I am running together. Normally I would do an FDR correction on the p-values to control the family-wise error rate. However, the p-values from a Tukey HSD are already adjusted for multiple comparisons (within a single test).
Does this pose problems for adjusting the p-values again?
As an example, let's say I am testing the difference among 3 treatments, first in group A (one test), and separately in group B (the second test). This gives me a total of 6 pairwise comparisons, 3 in each group. Normally I would adjust the resulting 6 p-values. But with Tukey HSD, the p-values have already been adjusted within each group (accounting for 3 comparisons), so to correct all 6 p-values as if they have not already been adjusted seems not quite right.
*EDIT: I neglected to say, this is after an omnibus ANOVA as well as simple effects test (because of significant interactions), both with corrected p-values. Having partitioned within levels of one factor, I proceed to Tukey's to examine combinations of the remaining factor.