Design and analysis for a two-level factorial experiment in the presence of variance heterogeneity

Abstract

With heterogeneous variance, the standard factorial designs are not optimal for estimation of a mean model. A sequential two-stage experimental design procedure is proposed that first allows estimation of the variance structure, and then uses the variance estimates and the Q-optimality criterion to develop a second stage design that efficiently estimates the mean model. Other procedures considered include the “equal replicate” design analyzed by ordinary least squares, and the same design analyzed by weighted least squares. Finally, the three procedures are compared for various models and variance structures, and for each case a recommendation is made as to which procedure is preferred.