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A modification of the Bonferroni procedure for testing multiple hypotheses is presented. The method, based on the ordered p-values of the individual tests, is less conservative than the classical Bonferroni procedure but is still simple to apply. A simulation study shows that the probability of a type I error of the procedure does not exceed the nominal significance level, α, for a variety of multivariate normal and multivariate gamma test statistics. For independent tests the procedure has type I error probability equal to α. The method appears particularly advantageous over the classical Bonferroni procedure when several highly-correlated test statistics are involved.
R. J. Simes (Mon,) studied this question.