UMPU and alternative tests for association in 2 x 2 tables

The use of the uniformly most powerful among the unbiased (UMPU) test was r ecently suggested for the study of gametic association between two polymorp hic loci as an alternative to the Fishers exact test (Zapata and Alvarez, 1 997, Annals of Human Genetics 61, 71-77). However, the proposed test is not UMPU for two-sided alternatives. In this study, we present the UMPU test, discuss criticisms against the use of randomized tests, and compare the pow er of several tests. We show that, in many practical cases, the use of the UMPU test is less than desirable and propose the alternative adjusted-more extreme tables (A-MET) and the equal-tails (ET) tests. We suggest that some of the general arguments against the use of randomized tests can be allevi ated by a newly proposed extended p-value definition.