Algebraic characterization of regular fractions under level permutations
Algebraic characterization of regular fractions under level permutations
In this paper we study the behavior of the fractions of a factorial design under permutations of the factor levels. We focus on the notion of regular fraction and we introduce methods to check whether a given symmetric orthogonal array can or can not be transformed into a regular fraction by means of suitable permutations of the factor levels. The proposed techniques take advantage of the complex coding of the factor levels and of some tools from polynomial algebra. Several examples are described, mainly involving factors with five levels.
23 pages, including two appendices
- University of Genoa Italy
Methodology (stat.ME), FOS: Computer and information sciences, Algebraic statistics, Complex coding, Fractional factorial designs, Indicator function, Isomorphic fractions, Orthogonal arrays, Regular fractions, 62K15, 13P10, FOS: Mathematics, Mathematics - Statistics Theory, Statistics Theory (math.ST), Statistics - Methodology
Methodology (stat.ME), FOS: Computer and information sciences, Algebraic statistics, Complex coding, Fractional factorial designs, Indicator function, Isomorphic fractions, Orthogonal arrays, Regular fractions, 62K15, 13P10, FOS: Mathematics, Mathematics - Statistics Theory, Statistics Theory (math.ST), Statistics - Methodology
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