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Journal of Statistical Theory and Practice

, Volume 1, Issue 1, pp 101–115 | Cite as

On the Geometric Equivalence and Non-equivalence of Symmetric Factorial Designs

  • T. I. Katsaounis
  • C. A. Dingus
  • A. M. Dean
Article

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. In this paper, we compare two known methods for the determination of geometric equivalence and propose a modified method based on the “split weights” of the rows of a design matrix. We also propose and evaluate new screening methods for geometric non-equivalence. Most of the paper concentrates on symmetric designs with factors at three levels, but extensions to designs with factors at four or more levels and to asymmetric designs are indicated.

MSC 2000 subject classification

62K15 

Keywords

Deseq algorithm design equivalence design isomorphism factorial experiment geometric equivalence indicator function 

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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityMansfieldUSA
  2. 2.Battelle Memorial InstituteColumbusUSA
  3. 3.Department of StatisticsThe Ohio State UniversityColumbusUSA

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