Decision making by classical test procedures using an optimal level of significance

This paper expands the decision space of a hypothesis testing situation by including the signficance level as a decision variable along with the sample size and test statistic. It suggests that in cases where hypothesis testing is tantamount to decision making the significance level should be optimally determined based on the consequences of errors of both kinds. To achieve this goal it develops a three stage procedure that minimizes the total costs of sampling and incorrect decisions as a function of the sample size, significance level and the test statistic. The procedure is applied to test the mean of a normal distribution and a bivariate table is prepared to routinise the process. The advantages of using this table instead of the standard normal table are discussed and the benefits of the optimal as opposed to a predetermined significance level are illustrated with the help of a numerical example.