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An improved Bonferroni procedure for multiple tests of significance

SIMES, R. J.·1986·Biometrika

DOI 10.1093/biomet/73.3.751

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Abstract

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, α, for a variety of multivariate normal and multivariate gamma test statistics. For independent tests the procedure has type I error probability equal to α. The method appears particularly advantageous over the classical Bonferroni procedure when several highly-correlated test statistics are involved.

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Authors: SIMES, R. J.
Affiliations: The University of Sydney (AU)
Corresponding author: SIMES, R. J.
ORCID: SIMES, R. J.
Venue: Biometrika
Publisher: Oxford University Press (OUP)
Published: 1986
Volume: 73
Issue: 3
Pages: 751-754
ISSN: 0006-3444 (ISSN-L)
1464-3510
DOI: 10.1093/biomet/73.3.751
OpenAlex: W2099107563
Cited by: 2,396
References: 5
Citations by year: 2026: 61 · 2025: 77 · 2024: 92 · 2023: 89 · 2022: 97 · 2021: 93 · 2020: 129 · 2019: 143 · 2018: 98 · 2017: 100 · 2016: 110 · 2015: 98 · 2014: 119 · 2013: 97 · 2012: 89
FWCI: 10.84
Type: journal article
Language: en
Open access: closed
Locations: Biometrika (publishedVersion)
Funders: Medical Research Council
National Cancer Institute
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: Bonferroni procedure, multiple comparisons, type I error probability

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An improved Bonferroni procedure for multiple tests of significance

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