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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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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