Chebyshev’s Inequality for Nonparametric Testing with Small N and α in Microarray Research

Beasley, T. Mark; Page, Grier P.; Brand, Jaap P. L.; Gadbury, Gary L.; Mountz, John D.; Allison, David B.

doi:10.1111/j.1467-9876.2004.00428.x

Cited by 15Gene expression and cancer classificationProbability and Statistical ResearchStatistical Methods in Clinical Trials

Chebyshev’s Inequality for Nonparametric Testing with Small N and α in Microarray Research

Beasley, T. Mark, Page, Grier P., Brand, Jaap P. L., Gadbury, Gary L., Mountz, John D., Allison, David B.·2004·Journal of the Royal Statistical Society Series C: Applied Statistics

DOI 10.1111/j.1467-9876.2004.00428.x

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Summary: Microarrays are a powerful new technology that allow for the measurement of the expression of thousands of genes simultaneously. Owing to relatively high costs, sample sizes tend to be quite small. If investigators apply a correction for multiple testing, a very small p-value will be required to declare significance. We use modifications to Chebyshev’s inequality to develop a testing procedure that is nonparametric and yields p-values on the interval [0, 1]. We evaluate its properties via simulation and show that it both holds the type I error rate below nominal levels in almost all conditions and can yield p-values denoting significance even with very small sample sizes and stringent corrections for multiple testing.

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When the number of clusters, K, per treatment group is small, the maximum number of different bootstrap samples is also small, resulting in a problem of a limited number of 'distinct' p-values.
“When the number of clusters, K, per treatment group is small, the maximum number of different bootstrap samples is also small, resulting in a problem of a limited number of “distinct” p-values [31].”
From Evaluation of the type I error rate when using parametric bootstrap analysis of a cluster randomized controlled trial with binary outcomes and a small number of clusters (2022) · cites this paper as [31]

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Evaluation of the type I error rate when using parametric bootstrap analysis of a cluster randomized controlled trial with binary outcomes and a small number of clusters
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Authors: Beasley, T. M., Page, G. P., Brand, J. P. L., Gadbury, G. L., Mountz, J. D., & Allison, D. B.
Affiliations: University of Alabama at Birmingham (US)
Missouri University of Science and Technology (US)
Corresponding author: Beasley, T. Mark
ORCID: Beasley, T. Mark
Page, Grier P.
Mountz, John D.
Allison, David B.
Venue: Journal of the Royal Statistical Society Series C: Applied Statistics
Publisher: Oxford University Press (OUP)
Published: 2004-01-01
Volume: 53
Issue: 1
Pages: 95-108
ISSN: 0035-9254 (ISSN-L)
1467-9876
DOI: 10.1111/j.1467-9876.2004.00428.x
OpenAlex: W2158417484
Cited by: 15
References: 61
Citations by year: 2024: 1 · 2022: 1 · 2021: 1 · 2019: 1 · 2018: 1 · 2016: 2 · 2014: 1 · 2012: 1
FWCI: 0.47
Type: journal article
Language: en
Open access: closed
Licence: academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
Locations: Journal of the Royal Statistical Society Series C (Applied Statistics) (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Funders: National Institutes of Health
Topics: Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
Keywords: Chebyshev inequality, nonparametric tests, microarray data, gene expression, small sample size, multiple testing correction, p-values, type I error rate, significance testing

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Chebyshev’s Inequality for Nonparametric Testing with Small N and α in Microarray Research

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