Bonferroni correction; that is, p_corrected = 1 – (1-p_uncorrected)^n where n denotes the number of tests done. An estimate of the effective number of independent “within” tests is hence n_effective = log(1-p_corrected)/log(1-p_uncorrected), approximately 110 (compared with 242 non-independent tests in total). Making the simplifying assumptions that 1) the “total” tests exhibit similar correlation between tests as the “within” test and 2) that the “within” and “total” tests are independent, the total number of effectively independent tests is ∼220. Since the “within” and “total” tests are in fact correlated, the most appropriate correction for multiple testing based on the “effective number of independent tests” would be correction for between 110 and 220 tests. That is, a p-value smaller than 0.00045 (and perhaps as small as 0.000225) is required for study wide significance.
