Chebyshev's Inequality for Nonparametric Testing with Small N and α in Microarray Research
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.
G. L. Gadbury et al., "Chebyshev's Inequality for Nonparametric Testing with Small N and α in Microarray Research," Royal Statistical Society, Jan 2004.
The definitive version is available at https://doi.org/10.1111/j.1467-9876.2004.00428.x
Mathematics and Statistics
Keywords and Phrases
Tchebysheff's inequality; alpha; probability distribution
Article - Journal
© 2004 Royal Statistical Society, All rights reserved.