Sequential Multiple Comparisons with the Best

Abstract

In this article we give a method of designing and analyzing an experiment for comparing k (≥ 2) treatments such that (a) a treatment is terminated as soon as there is (statistical) evidence that it is not the best treatment; and (b) at the conclusion of the experiment, one can assert at some prespecified confidence level simultaneously that those terminated treatments are not the best and those remaining treatments are respectively within certain (small) distances of the unknown best treatment. The inference given by our method is stronger than existing sequential elimination selection inference.