A Sequentially Rejective Test Procedure Based on a Modified Bonferroni Inequality

Abstract

A sharper Bonferroni procedure for multiple tests of significance is derived. This procedure is an improvement of Hochberg's (1988) procedure which contrasts the individual P-values with corresponding critical points. It is shown that Hochberg's original procedure is conservative, and can be made more powerful by enlarging the rejection region so that the type-one error is exactly at the nominal level. It is also shown that the modified procedure retains all the desired properties of the original procedure.