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Sedgwick gives a brief account of the use of the 'Bonferroni Correction' for multiple testing. He omits some points which should be considered.
Firstly the theory assumes that all 41 (or however many) tests are independent. This may be true if one is looking at different sub-populations but is perhaps implausible when looking at different outcomes in the same populations (at least the assumption can be tested). Using Bonferroni in this situation may be very conservative and lead to considerable loss of power. Multivariate methods do not make this assumption. If they are not considered suitable perhaps one should not be doing so many measurements.
Journals (including the BMJ) now encourage the use of confidence intervals. If a significance level of 0.05 becomes 0.001 under Bonferroni, should the 99.9% interval be reported?