A candidate for locally most powerful sequential t test

Abstract

A sequential t test is presented based on a simple function of the usual student t statistic. This function is shown to possess the martingale property that, conditional on previous observations, the expectation of a future increment is zero. This property facilitates calculation of error probabilities and expected sample sizes, so that the resulting test is relatively straightforward to use. It is argued that this test behaves in a manner similar to that of the locally most powerful test for the mean of a normal distribution with variance known against the one-sided alternative, and might be viewed as its logical analogue for a test of the same hypotheses for the case in which the variance is unknown.