Material Conditions on Tests of Statistical Hypotheses

Abstract

Orthodox statistical theory, which is the theory used by most practicing statisticians, physicists, biologists, and social scientists, assumes there are objective probabilities which are properties of physical systems. Statistical hypothesis testing is a branch of statistical theory concerned with a theory for accepting or rejecting statements which ascribe these objective probabilities to particular physical systems. Since use of the theory of statistical hypothesis testing leads to the acceptance or rejection of a kind of empirical statement, I shall assume that this theory is a part of inductive logic. Recent philosophical inquiries have largely ignored orthodox statistical theory, and personalistic (or Bayesian) statisticians have attacked it. Since the theory is so widely used, it is important to reexamine its foundations and its place in the canon of inductive logic.