Statistical Inference for Best Treatment versus a Control

Abstract

In many experiments researchers are interested in comparing several treatment means with a control mean. When there is a treatment significantly better than the control, their primary interest is to evaluate the difference between the best treatment and the control. In this paper, we investigate simultaneous confidence lower bounds for the aforementioned difference for the case that treatments are at least as good as the control and for the case that no restriction is placed on the treatment means and the control mean. Several test statistics are considered. The evaluation of the simultaneous confidence lower bound for the difference between the best treatment mean and the control mean is a concave programming problem subject to homogeneous linear inequality constraints. Two efficient computation algorithms are derived.