Nitis Mukhopadhyay

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 $k(\ge 2)$ normal populations with unknown means and equal but unknown variance ${\sigma }^2$. We argue that an effect size could involve unknown means, as well as unknown variance ${\sigma }^2$, because it is sometimes unrealistic to assess the effect size and preset it in the absence of ${\sigma }^2$. 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.