Some sequential analogs of Stein's two-stage test

Abstract

This paper presents several sequential analogs of Stein's two-stage test procedure for testing hypotheses about the mean of a normal population with unknown variance and with specified bounds on the error probabilities. These procedures are modifications of a procedure due to A. G. Baker (1950). When sequential experimentation is feasible, they provide alternatives to the sequential normal test (variance known) or the sequential t -test. If the variance is assumed known, the procedures may still be recommended since the added cost in additional observations may not be large on the average, and the performance of the tests does not depend on the validity of any assumption about the variance. Moreover, unlike the t -test, these procedures do not require that the alternative hypothesis be specified in standard deviation units.