ABSTRACT
The hypothesis-testing problem is really a decision problem rather than an inference problem. On occasion an experimenter has a choice among different experiments which the author may conduct before reaching a decision, and he has the problem of which one to choose. Indeed there is a very close connexion between the class of admissible functions and the class of Bayes's functions, a connexion close enough to provide justification, on purely mathematical grounds, for the use of prior distributions in decision problems. For an excellent account of this and other aspects of decision theory the reader is referred to Ferguson. The Neyman–Pearson theory provides an analysis of this problem which is to some extent half hearted. It recognizes that the two possible errors involved in a decision procedure, that is, in a test, are not equally serious and the criteria that it lays down for a 'good' test are based on this notion.
