Weighted Optimality in Designed Experimentation

Abstract

An optimality framework is developed for designing experiments in which not all treatments are of equal interest, such as those including an established control. Differential interest in treatments is formalized by assignment of weights, incorporated into optimality measures through a weighted version of the information matrix. All conventional measures of design efficacy are shown to have weighted analogs. The properties of weighted measures are explored, some general theory is developed, and weighted optimal designs are determined for unblocked experimentation. This new approach includes “test treatments versus control” experiments as a special case. Supplementary materials for the article are available online.