Characteristic Polynomial of the Information Matrix of a Balanced Resolution V Design of the 4ⁿ Type Approached Through the 2²ⁿ Factorial

Abstract

We consider 4 ⁿ factorial experiments in which the objective is to estimate all the factorial effects up to 2-factor interactions, assuming the rest of the effects to be negligible. A class of designs is considered where the 4 ⁿ factorial is looked at through a 2²ⁿ factorial by associating the levels of a 4-level factor with 4 treatment combinations of two 2-level factors. We introduce relations of association among the effects and define a balanced design arising from the relations. It is shown that such a balanced design is equivalently derivable from a partially balanced array of strength (4, 4) with (n, n) constraints and 2 symbols due to Nishii (1981). The characteristic polynomial of the information matrix of a balanced design is given using the algebra of association matrices.