Abstract
We show that the properties of stein's(1945) two-stage test conditional on an observed ancillary stastistic are such that one may be concerned aboutt its performance in particular individual experiments. We present a new two-stage t-test which has preferable conditional properties under the null hypothesis and we describe a group sequential Stein-based test with appealing properties under null and alternative hypotheses.Study of our new two-stage test reveals a surprising feature of Stein's original procedure which illustrates how the requirements of conditional acceptability and admissibility may come into conflict.
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