Contaminated Chi-Square Modeling and Large-Scale ANOVA Testing
Richard Charnigo1*, Feng Zhou1 and Hongying Dai2
1Department of Statistics, 725 Rose Street, University of Kentucky, Lexington KY, USA
2Research Development and Clinical Investigation, 2420 Pershing Road, Children’s Mercy Hospital, USA
- *Corresponding Author:
- Richard Charnigo
Department of Statistics
725 Rose Street
University of Kentucky
Lexington KY, USA
E-mail: [email protected]
Received Date: November 26, 2012; Accepted Date: December 15, 2012; Published Date: December 22, 2012
Citation: Charnigo R, Zhou F, Dai H (2013) Contaminated Chi-Square Modeling and Large-Scale ANOVA Testing. J Biomet Biostat 4:157. doi: 10.4172/2155-6180.1000157
Copyright: © 2013 Charnigo R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
We propose a convenient moment-based procedure for testing the omnibus null hypothesis of no contamination of a central chi-square distribution by a non-central chi-square distribution. In sharp contrast with likelihood ratio tests for mixture models, there is no need for re-sampling or random field theory to obtain critical values. Rather, critical values are available from an asymptotic normal distribution, and there is excellent agreement between nominal and actual significance levels. This procedure may be used to model numerous chi-square statistics, obtained via monotonic transformations of F statistics, from large-scale ANOVA testing, such as that encountered in microarray data analysis. In that context, modeling chi-square statistics instead of p-values may improve detection of differential gene expression, as we demonstrate through simulation studies, while also reducing false declarations of the same, as we illustrate in a case study on aging and cognition. Our procedure may also be incorporated into a gene filtration process, which may reduce type II errors on genewise null hypotheses by justifying lighter controls for Type I errors.