A decoupling method for analyzing foldover designs

Abstract

Foldover designs often have attractive properties. Among these is that the effects can be divided into two orthogonal subspaces, one for odd effects and one for even effects. In this paper, we introduce a new method for analyzing foldover designs called the decoupling method that exploits this trait. Utilizing mirror image pair runs, two new responses are created, where each of them is only affected by effects in one of the orthogonal subspaces. Thereby the analysis of odd and even effects can be performed in two independent steps, enabling use of standard statistical procedures and formal testing of the presence of higher‐order interactions. The method is demonstrated on real data from a foldover of a 12‐run Plackett‐Burman (PB) design, and further evaluated through a simulation study, in which the decoupling method is compared to existing analysis methods. To get a thorough understanding of the properties, both a PB design and an OMARS design are used, and different design sizes and heredity scenarios considered. The method is especially suited for screening, as it yields high power for detecting the active effects.