Complex linear models and cyclic designs

Abstract

Many orthogonal factorial designs can be defined by abelian group morphisms. By juxtaposition of such designs, useful nonorthogonal designs can also be obtained, including the classical generalized cyclic designs, as well as a new kind of one replicate factorial block designs. Their efficiencies are easily computed by means of a complex reparametrization based on the irreducible characters of the groups involved. The theory extends to the “group generated” designs defined by Bailey and Rowley, in which the group is not necessarily abelian. In some cases, we give explicit formulas for the efficiencies of these latter designs.