A survey and evaluation of methods for determination of combinatorial equivalence of factorial designs

Katsaounis, T.I. and Dean, A.M. (2008) A survey and evaluation of methods for determination of combinatorial equivalence of factorial designs. [in special issue: International Conference on Design of Experiments (ICODOE)] Journal of Statistical Planning and Inference, 138 (1), 245-258. (doi:10.1016/j.jspi.2007.05.008).

Abstract

Equivalent factorial designs have identical statistical properties for estimation of factorial contrasts and for model fitting. Non-equivalent designs, however, may have the same statistical properties under one particular model but different properties under a different model. In this paper, we describe known methods for the determination of equivalence or non-equivalence of two-level factorial designs, whether they be regular factorial designs, non-regular orthogonal arrays, or have no particular structure. In addition, we evaluate a number of potential fast screening methods for detecting non-equivalence of designs. Although the paper concentrates mainly on symmetric designs with factors at two levels, we also evaluate methods of determining combinatorial equivalence and non-equivalence of three-level designs and indicate extensions to larger numbers of levels and to asymmetric designs.

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