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Zbl 0613.62067
Simes, R.J.
An improved Bonferroni procedure for multiple tests of significance.
(English)
[J] Biometrika 73, 751-754 (1986). ISSN 0006-3444; ISSN 1464-3510/e

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 2000:
*62H15 Multivariate hypothesis testing
65C99 Numerical simulation
62J15 Multiple comparisons

Keywords: Bonferroni inequality; modified Bonferroni procedure; power comparisons; testing multiple hypotheses; ordered p-values; simulation study; multivariate normal; multivariate gamma; highly-correlated test statistics

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