Reversing Bonferroni

What Is the Bonferroni Correction?

The Bonferroni correction is an adjustment made to P values when several dependent or independent statistical tests are being performed simultaneously on a single data set. To perform a Bonferroni correction, divide the critical P value (α) by the number of comparisons being made. For example, if 10 hypotheses are being tested, the new critical P value would be α/10. The statistical power of th...

Holm ’ s Sequential Bonferroni Procedure

The more statistical tests we perform, the more likely we are to reject the null hypothesis when it is true (i.e., a “false alarm,” also called a “Type 1” error). This is a consequence of the logic of hypothesis testing: We reject the null hypothesis for rare events, and the larger the number of tests, the easier it is to find rare events which are false alarms. This problem is called the infla...

What's wrong with Bonferroni adjustments.

A Bayesian perspective on the Bonferroni adjustment

Bayes/frequentist correspondences between the p-value and the posterior probability of the null hypothesis have been studied in univariate hypothesis testing situations. This paper extends these comparisons to multiple testing and in particular to the Bonferroni multiple testing method, in which p-values are adjusted by multiplying by k, the number of tests considered. In the Bayesian setting, ...

Bonferroni-Galambos Inequalities for Partition Lattices

In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type ∑ π∈P(U)(−1)(|π| − 1)!f(π) where U is a finite set, P(U) is the partition lattice of U and f : P(U) → R is some suitable non-negative function. Applications of this new analogue are given to counting connected k-uniform hypergraphs, network reliability, and cum...