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A sharper Bonferroni procedure for multiple tests of significance. (English) Zbl 0661.62067
For multiple comparison problems the Bonferroni inequality ensures that the probability of rejecting at least one of m hypotheses when all are true is not greater than \(\alpha\) if each specific hypothesis is rejected with a risk of the first kind not greater than \(\alpha\) /m.
In the present paper a simple improved Bonferroni procedure for multiple tests of significance based on individual p-values is derived and it is shown that this procedure is sharper than S. Holm’s sequentially rejective procedure [Scand. J. Statistics, Theory Appl. 6, 65-70 (1979; Zbl 0402.62058)].
Reviewer: D.Rasch

62J15 Paired and multiple comparisons; multiple testing
62F03 Parametric hypothesis testing
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