On Equivalence of Fractional Factorial Designs Based on Singular Value Decomposition

• Activity Number: 416
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Tena Katsaounis*+
• Companies: Ohio State University
• Keywords: Factorial design ; Combinatorial equivalence ; Design equivalence ; Design isomorphism ; Singular value decomposition

Abstract

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.