Sequential Selection of the Larger of Two Normal Means
Abstract Sequential tests for deciding which of two normal means is larger are considered in situations, such as clinical trials, where it is desirable to reduce the number of observations made on the population with the smaller mean. We propose and study an extension to unknown variances of a test proposed by Flehinger et al. (1972) for known variances. This involves replacing the unknown variances by estimates and replacing parallel stopping boundaries (-b, b) by moving boundaries that decrease to (-b, b). The proposed test is shown to be asymptotically optimal, and simulation results show that it performs satisfactorily for small sample sizes.