DANIEL ZELTERMAN 
School of Public Health, Department of Biostatistics
Yale University
“A Distribution for P-Values”
ABSTRACT
What is the distribution of the p-value under the alternative hypothesis? We describe the properties of the exact answer and an approximate parametric distribution. These distributions include the uniform as special cases. The functional form of the approximation is derived as the distribution of the p-value in a statistical test of a pair of close hypotheses in a variety of settings. The distributional form is retained when it is compounded with a uniform or when the individual p-values are sampled from a variety of different hypotheses. We describe properties of the parameter estimate and the distribution of extreme order statistics. The distribution is fitted to data from a study of breast cancer patients comparing many genetic markers. The motivation for this work is to develop methods to estimate the proportion of p-values sampled from the null hypothesis.
Joint work with Chang Yu of Vanderbilt University.
