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On the Geometric Equivalence of Asymmetric Factorial Designs

  • Park, Dong-Kwon (Department of Informations and Statistics, Yonsei University) ;
  • Park, Eun-Hye (Department of Applied Statistics, Yonsei University)
  • Published : 2006.12.31

Abstract

Two factorial designs with quantitative factors are called geometrically equivalent if the design matrix of one can be transformed into the design matrix of the other by row and column permutations, and reversal of symbol order in one or more columns. Clark and Dean (2001) gave a sufficient and necessary condition (which we call the 'gCD condition') for two symmetric factorial designs with quantitative factors to be geometrically equivalent. This condition is based on the absolute value of the Euclidean(or Hamming) distance between pairs of design points. In this paper we extend the gCD condition to asymmetric designs. In addition, a modified algorithm is applied for checking the equivalence of two designs.

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