A-Optimal Factorial Designs for Test Versus Control Comparisons

Abstract

The majority of the existing work on factorial designs centers around the well-known orthogonal parametrization. In particular, main-effect plans compare the treatment levels of each factor by means of orthogonal parametrization. In contrast, significant research has been carried out for single-factor experiments for comparing a set of test treatments with a control treatment. Here, the comparison leads to a nonorthogonal parametrization. A-optimal designs for single-factor test-control experiments have been investigated in the literature. In practical situations, however, it is quite common that several factors are under study simultaneously. We study optimal designs for factorial experiments where test-control comparisons are of interest. We adopt a technique for finding A-efficient designs under the test-control parametrization via the approximate theory. We illustrate the procedure for finding A-efficient exact designs through few examples.