Balanced factorial designs with two-way elimination of heterogeneity

Abstract

Balanced factorial designs which permit two-way elimination of heterogeneity are defined, and the combinatorial conditions for such designs are derived. Methods of constructing two-way balanced factorial designs are given. In particular, for 5 a prime power and ≥ 3, a method is given to construct an s×s balanced factorial design with s(s-1) columns and s(s-1) rows such that none of the main effects is confounded with either row effects or column effects.