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We present a procedure for controlling FWER when sequentially consideringsuccessive subfamilies of null hypotheses and rejecting at most one from eachsubfamily. Our procedure differs from previous procedures for controlling FWERby adjusting the critical values that are applied in subsequent rejectiondecisions by subtracting from the global significance level $\alpha$ quantitiesbased on the p-values of rejected null hypotheses and the numbers of nullhypotheses considered.

Controlling Familywise Error When Rejecting at Most One Null Hypothesis Each From a Sequence of Sub-Families of Null Hypotheses