A Purely Sequential Selection and Its Acceleration for the Best Treatment Under a New Formulation of the Indifference Zone: Asymptotic Theory and Simulations

A traditional indifference zone (IZ) approach selects the best treatment, with a preset high probability of correct selection when the best one is much better than the second-best in line. Customarily, the effect size is the difference between the best (largest mean) and the second-best treatment under consideration from k(≥2) normal populations with unknown means and equal but unknown variance σ2. We argue that an effect size could involve unknown means, as well as unknown variance σ2, because it is sometimes unrealistic to assess the effect size and preset it in the absence of σ2. Under a new IZ formulation, we rebuild both purely sequential and accelerated sequential selection methodologies for the largest mean and associated first-order (f.o.) and second-order (s.o.) asymptotics. Such a breadth of rich asymptotic theory is supplemented by a thorough discussion of the performance of the two selection strategies from a set of simulations when the sample sizes are small, medium, or large.