The Efficiency Factors of Particular Effects in Designs with Orthogonal Factorial Structure

Abstract

We investigate partial confounding which is not necessarily orthogonal to blocks. The efficiency factor of a main effect or interaction is related to the numbers of paths of a certain type in the treatment concurrence graph. From this we can derive combinatorial principles that help find designs with large efficiency factor for the effect or interaction. The principles are heuristically cogent and convenient, and are a natural generalisation of existing practice. Some illustration is given of their value in finding good generalised-cyclic designs.