Optimal Structure (k) Designs for Comparing Test Treatments with a Control

Abstract

Mukerjee (1979) introduced structure (k) property of a factorial design. In this article, we introduce structure (k1), structure (k2) and structure (k1k2) properties of a factorial design. We establish properties of each of these structure designs in terms of the incidence and characteristic matrices of the designs. Furthermore, we develop methods of obtaining optimal R-type structure (k) designs and show that such designs are trace, A- and MV-optimal. The proposed methodologies are easy to follow and the construction of the designs comes out in a simple form.

Keywords

• Factorial design; hypercubic design; R-type structure designs; A-optimality; MV-optimality; trace optimality.