The concept of a power function in statistics often proves rather difficult to absorb. Johnson & Tetley (1950) develop the theory at some length, and Forster (1947) in an admirable article in this Journal provides some extra reading which is of necessity in rather general terms. It is hoped that the problem discussed in this article may prove a useful example of the application of the power concept to a particular problem and clarify the underlying theoretical ideas.

In any statistical test two kinds of error may arise. The first kind of error occurs when the hypothesis tested, usually called the null hypothesis, is rejected when it is in fact true. The second kind of error occurs when the null hypothesis is accepted when it is in fact false. The hypothesis with which the test is concerned will in general be denoted by Hi. In our case simple hypotheses will be considered which are concerned with the value of some parameter defining the probability law of the individuals.