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Chebyshev's inequality for nonparametric testing with small N and α in microarray research

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

Abstract

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.

Suggested Citation

  • T. Mark Beasley & Grier P. Page & Jaap P. L. Brand & Gary L. Gadbury & John D. Mountz & David B. Allison, 2004. "Chebyshev's inequality for nonparametric testing with small N and α in microarray research," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 95-108, January.
    • Handle: RePEc:bla:jorssc:v:53:y:2004:i:1:p:95-108
    DOI: 10.1111/j.1467-9876.2004.00428.x
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    Cited by:

    1. Algo Carè & Simone Garatti & Marco C. Campi, 2017. "A coverage theory for least squares," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1367-1389, November.

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