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An improved Bonferroni procedure for multiple tests of significance. (English) Zbl 0613.62067
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, $$\alpha$$, for a variety of multivariate normal and multivariate gamma test statistics. For independent tests the procedure has type I error probability equal to $$\alpha$$. The method appears particularly advantageous over the classical Bonferroni procedure when several highly-correlated test statistics are involved.

##### MSC:
 62H15 Hypothesis testing in multivariate analysis 65C99 Probabilistic methods, stochastic differential equations 62J15 Paired and multiple comparisons; multiple testing
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