Testing interaction in three-way anova tables with a single observation per cell

Abstract

A common approach in analyzing nonreplicated data is to omit the highest order interaction and regard it as error. This paper discusses the use of a multiplicative model, called a quadrilinear model, in order to separate variability due to the three-factor interaction from random error, and also examines its significance in nonreplicated three-factor experiments. The quadrilinear model is a nonreplicated three-way multiplicative model with quadrilinear terms. These estimated quadrilinear terms can be obtained by performing a three-mode principal component analysis of the residuals. In particular, we derive a criterion to select an appropriate number of multiplicative terms to describe significant three-factor interaction. A table of degrees of freedom associated with the three-factor interaction term is constructed by applying Monte Carlo simulations. An ANOVA table with estimated experimental error variance and