Multiple testing

A reviewer can understandably become uneasy if a manuscript reports a large number of hypothesis tests without any Type I error correction. I was wondering if the manuscript presents some results as statistical hypothesis tests when doing so isn't necessary or even accurate. Assuming you are only going to report the results of a single "best" model for each brain region, I would suggest the following. First, for each region, compare the AICs of all four candidate models to one another once all have been fitted (and not in a pairwise manner), and select the one with the smallest AIC. Do not frame this model selection in terms of statistical "significance." Model-selection by AIC is not a statistical hypothesis test in any sense; instead, it approximates cross-validation, for a particular loss metric and given certain assumptions. Second, from each best model, report confidence intervals only for parameters of substantive interest to the study. You could acknowledge in the text that the confidence intervals will only have marginal coverage probability of 95%, whereas their joint coverage probability would be lower than that.