Distributions for p-Values

• Activity Number: 609
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Daniel Zelterman and Chang Yu*+
• Companies: Vanderbilt University Medical Center and Yale University
• Keywords: multiple hypothesis testing ; microarray experiments ; quantile function ; extreme order statistics

Abstract

What is the distribution of the p-value under the alternative hypothesis? We derive two such distributions that include the uniform as a special case. The first distribution is useful when there is a single, well-defined alternative hypothesis that is known up to parameter values to be estimated. This distribution allows us to provide separate estimates of these parameters and a proportion of p-values sampled from the null hypothesis. A second distribution is also developed to model p-values when the alternative hypothesis is not well understood or, as is often the case, a mixture of many alternatives. Our study of the extreme order statistics allows us to express two types of estimates of the proportion of p-values sampled under the null using relaxed assumptions. Both distributions are fitted to data from a study of breast cancer patients comparing many genetic markers.