© 1986 by Biometrika Trust
An improved Bonferroni procedure for multiple tests of significance
Ludwig Institute for Cancer Research, University of Sydney Sydney, N.S.W. 2006, Australia
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, 
, for a variety of multivariate normal and multivariate gamma test statistics. For independent tests the procedure has type I error probability equal to . The method appears particularly advantageous over the classical Bonferroni procedure when several highly-correlated test statistics are involved.
Key Words: Bonferroni inequality • Multiple comparisons • Simultaneous test procedures
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