Construction of Confounding Plans for Mixed Factorial Designs

Abstract

This paper extends the use of finite fields for the construction of confounding plans, to include "asymmetrical" or "mixed" factorials. The technique employed is to define addition and multiplication of elements from distinct finite fields, by mapping these elements into a finite commutative ring containing sub-rings isomorphic to each of the fields in question. The standard and relatively simple techniques for symmetrical factorials are then applied in a straightforward manner to the asymmetrical case. The paper is concluded with a numerical example for the case of a $3^2 \times 5$ factorial design, and an outline of some possible confounding plans. Fractional factorials are discussed briefly.