A sharper Bonferroni procedure for multiple tests of significance. (English) Zbl 0661.62067

Hochberg, Yosef

Biometrika 75, No. 4, 800-802 (1988).

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

MSC:

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

Keywords:

familywise error rate; hypotheses-free association; strong and weak control; multiple comparison problems; Bonferroni inequality; improved Bonferroni procedure; multiple tests of significance; p-values; sequentially rejective procedure