Confirming Statistical Hypotheses

Summary This paper distinguishes between the acceptability and the confirmation of a statistical hypothesis. A hypothesis is called acceptable if it is accepted by a significance test or some similar procedure and unacceptable if it is rejected. The likelihood ratio criterion of acceptability is discussed. In order to define confirmation, a distance function is introduced in the hypothesis space which reflects the size of the departure of any hypothesis from the null hypothesis. All admissible hypotheses are tested and classified as acceptable or unacceptable. If none of the acceptable hypotheses are “near” the null hypothesis, the latter is disconfirmed; if all the acceptable hypotheses are “near” the null hypothesis, it is confirmed; otherwise the experiment is inconclusive and the null hypothesis is unconfirmed. In the second part of the paper these ideas are applied to some common statistical techniques.