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Bonferroni Inequalities and Intervals

  1. T. Costigan

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a15014

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Costigan, T. 2005. Bonferroni Inequalities and Intervals. Encyclopedia of Biostatistics. 1.

Author Information

  1. Ross Laboratories, Cleveland, OH, USA

Publication History

  1. Published Online: 15 JUL 2005


The first-order Bonferroni inequality relates the probability that at least one of a series of events occurs to the sum of the probabilities of the individual events. In statistical applications, it provides an upper bound to the probability of falsely rejecting at least one of a series of true null hypotheses, and therefore, a possible correction to a significance level to account for multiplicity of hypotheses tested. Further developments include sequential rejection procedures and the use of higher-order Bonferroni inequalities.


  • multiple comparisons;
  • simultaneous inference;
  • experiment-wise error rate;
  • multiple endpoints