A comparison of two estimators of dispersion effects

Abstract

The applications of this paper is thought to be in screening designs with the purpose of identifying important factors in unreplicated experiments. The primary objective is to study which of the factors that affect the variance of the response when the levels are changed, that is, to study the dispersion effects.

Unbiased estimators of dispersion effects are constructed which are unaffected by location effects. This is done by combining the ordinary estimators of the location interactions. Transforming the original variables into these linear combinations, covariances can be expressed by the dispersion effects and derived using Hadamard products. In some special cases, the distribution of the estimators are derived. The estimators are compared using simulations.

Keywords:

• Variance effects
• Two-level factorial designs
• Main effect model
• Hadamard products