Sufficient Statistics, Similar Regions and Distribution-Free Tests

Abstract

Thispaper is mainly an elementary exposition (in §1) of the ideas of Lehmann and Scheffé (1950) concerning sufficient statistics and similar regions. One of the virtues of this elegant theory is the way in which it incorporates some distribution-free tests into the general body of tests based on similar regions—this is described in §3. In §2, its bearing on the Fisher-Behrens and related problems is discussed and a class of problems where it is of no use is suggested. In §4, several new distribution-free tests are given.