On equivalence of fractional factorial designs based on singular value decomposition
Faculty of Applied Economics
Journal of statistical planning and inference. - Amsterdam
, p. 1950-1953
University of Antwerp
The singular value decomposition of a real matrix always exists and is essentially unique. Based on the singular value decomposition of the design matrices of two general 2-level fractional factorial designs, new necessary and sufficient conditions for the determination of combinatorial equivalence or non-equivalence of the corresponding designs are derived. Equivalent fractional 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. Results extend to designs with factors at larger number of levels. (C) 2013 Elsevier B.V. All rights reserved.