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.
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Katsaounis, T.I., Dingus, C.A. & Dean, A.M. On the Geometric Equivalence and Non-equivalence of Symmetric Factorial Designs. J Stat Theory Pract 1, 101–115 (2007). https://doi.org/10.1080/15598608.2007.10411827
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DOI: https://doi.org/10.1080/15598608.2007.10411827