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Title: CV, ECV, and robust CV designs for replications under a class of linear models in factorial experiments Authors:  Subir Ghosh - University of California (United States) [presenting]
Abstract: A class of linear models is considered for describing the data collected from an experiment so that any two models have some common and uncommon parameters. The uncommon parameters play a significant role in discriminating between any two models. We propose a common variance (CV) design for collecting the data so that all the uncommon parameters are estimated with as similar variances as possible in all models. We get the variance equality for a CV design when there is one uncommon parameter for any two models within the class. We introduce a new concept, Robust CV designs for replications, having the possibility of replicated observations. We present the conditions for a CV design having no replicated observations to be robust for general replicated observations. A CV design having no replicated observations is always robust for equally replicated observations. In the class of linear models considered for factorial experiments, the common parameters for all models correspond to the general mean and main effects, and the other parameters correspond to two-factor interactions. We present two general CV designs for three-level factorial experiments. We also present examples of Efficient CV (ECV) designs and Robust CV designs for general replicated observations.