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).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.jspi.2007.05.008
ISSNs: 0378-3758 (print)
1873-1171 (electronic)
Keywords: combinatorial equivalence, deseq algorithm, design isomorphism, factorial experiment, hamming distance, hamming weight, indicator function, j-characteristic
Subjects: H Social Sciences > HA Statistics
Divisions : Faculty of Social and Human Sciences > Mathematical Sciences > Statistics
Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute
ePrint ID: 339782
Accepted Date and Publication Date:
1 January 2008Published
13 May 2007Made publicly available
Date Deposited: 30 May 2012 13:22
Last Modified: 31 Mar 2016 14:29
URI: http://eprints.soton.ac.uk/id/eprint/339782

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