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An improved Bonferroni procedure for multiple tests of significance
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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“evidence suggesting that MBIs, compared to active controls, were more effective in enhancing state and trait attentional skills [91], executive functioning [92], and emotional clarity [93].”
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Metadata
- 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
- 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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