Title: A fresh look at effect aliasing and interactions: some new wine in old bottles,
Abstract: Interactions and effect aliasing are among the fundamental concepts in
experimental design. In this paper, some new insights and approaches are
provided on these subjects. In the literature, the "de-aliasing" of aliased
effects is deemed to be impossible. We argue that this "impossibility" can
indeed be resolved by employing a new approach which consists of
reparametrization of effects and exploitation of effect non-orthogonality. This
approach is successfully applied to three classes of designs: regular and
nonregular two-level fractional factorial designs, and three-level fractional
factorial designs. For reparametrization, the notion of conditional main
effects (cme's) is employed for two-level regular designs, while the
linear-quadratic system is used for three-level designs. For nonregular
two-level designs, reparametrization is not needed because the partial aliasing
of their effects already induces non-orthogonality. The approach can be
extended to general observational data by using a new bi-level variable
selection technique based on the cme's. A historical recollection is given on
how these ideas were discovered.