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A survey and evaluation of methods for determination of combinatorial equivalence of factorial designs. (English) Zbl 1130.62077
Summary: 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. 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.

MSC:
62K15 Factorial statistical designs
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