Multiple Comparisons with the Best Control in a One-Way Layout

In many settings, one wishes to show that one or more experimental treatments are better than the best of more than one control or standard treatments in a one-way layout. One-sided, normal theory and distribution-free, single-step and step-down simultaneous testing procedures are developed in this article. These tests are intersection-union tests and hence use existing critical points. The single-step tests are inverted to form simultaneous lower confidence bounds on the amount of improvement that each experimental treatment offers relative to the best control or standard treatment. The single-step, normal theory procedures can be improved if one assumes that the control expectations do not differ by more than a predetermined number of standard deviations.