Multiple Test Functions for Discrete Data

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Josh Habiger*+
• Companies: Oklahoma State University
• Keywords: multiple testing ; fuzzy P-value ; mid-P-value ; randomized P-value ; test function ; decision function

Abstract

In hypothesis testing, a variety of tools have been developed for handling complications arising when test statistics have discrete distributions, such as the mid-P-value, randomized P-value, and the abstract randomized, also sometimes called fuzzy, P-value. However, additional computational issues arise in implementing the latter approach when testing multiple null hypotheses. A unifying framework is provided that facilities a simple solution to this problem and allows for a rigorous assessment of all approaches. In particular, it is demonstrated that utilizing a randomized or mid-P-value amounts to forcing a ``reject'' or ``fail to reject'' decision via the generation or specification of a value u while the use of an abstract randomized P-value is akin to reporting the value of a test function in [0,1], which need not imply a reject or fail to reject decision. It is shown that the test function approach is mathematically superior to other approaches in terms of bias and variance and argued that it is practical in multiple hypothesis testing if inference is exploratory in nature.