A Different Loss Function for the Choice between Two Populations

Abstract

SUMMARY In previous discussions of the problem of balancing sampling costs against the cost of choosing the wrong population it has been assumed that the cost of sampling is equal to the sample size multiplied by a constant known unit cost. In the present paper the cost of sampling is assumed to be the cost of an incorrect choice for half of the sample programme (which is divided evenly between the two populations). The resulting loss function is considered when the choice is between two normal populations of known equal variance, the standard of performance being determined by the mean. Wald's (1950) minimax principle is used to determine fixed size and sequential sampling procedures, and the performance of these procedures is examined.