# $P$-value correction for ANOVA on repeated simulation

First of all, I would like to ask you if you know good literature that explains the theoretical underpinnings of multiple testing. Although I think I understand pretty well the basic principles, I would like to really understand it in order to apply it correctly in all the different situations I encounter.

I analyze activity of neurons in a simulated neural network containing 1000 neurons. I am interested in knowing how many neurons are influenced by different variables (A, B, C) and their interactions (A*B, A*C, B*C, A*B*C) with ANOVA. So I do multiple testing on each neuron, and so far, with correction independently for each neuron. But I suppose I should adjust also between neurons (with FDR) because the chances that I find neurons significant is higher with more neurons in the simulations.

What is the procedure here? Should I correct the ANOVA posthoc tests p-values first and then do a second correction on all the neurons? If so, in the second correction, should I correct each test independently (p-value correction for influence of factor A for all neurons, then same for factor B, and so on...) or correct all previously corrected tests with all neurons? Or should I correct the p-values of all tests and all neurons at once?

Thanks

• this might help stats.stackexchange.com/questions/143325/… Unless there is a way to justify why each test is unique (unlikely, for so many neurons), I'd argue for at least providing the correction factor for all comparisons as a reference (note, not 'correcting' the raw p-values but giving correction factor alongside). – katya Aug 16 '15 at 19:12