An Asymptotically Efficient, Sequential Equivalent of the t-Test
Lionel E. Weiss, Jacob Wolfowitz · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1972
Summary Let X1, X2, …, be independent, normally distributed chance variables, each with mean μ and variance σ2, both unknown to the statistician. Let it be required to test sequentially the hypothesis that (make a decision between) μ = μ1 against the alternative μ = μ2, μ1 < μ2. When the sample size is fixed the Student t-test is usually used for this purpose. In the present paper we give a sequential procedure for performing this test which is consistent and asymptotically efficient as (μ2 – μ1) approaches zero.