The main effect confounding pattern for saturated orthogonal designs

Yuxuan Lin () and Kai-Tai Fang ()
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Yuxuan Lin: BNU-HKBU United International College
Kai-Tai Fang: BNU-HKBU United International College

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 7, No 5, 843-861

Abstract: Abstract In this paper, we propose a criterion “the main effect confounding pattern (MECP)” for comparing projection designs based on saturated symmetric orthogonal designs. Some studies for $$L_9(3^4)$$ L 9 ( 3 4 ) , $$L_{27}(3^{13})$$ L 27 ( 3 13 ) and $$L_{16}(4^5)$$ L 16 ( 4 5 ) are given. They show that the new criterion MECP is mostly consistent with the criteria: the generalized word-length pattern and the discrepancies CD and MD. Moreover, the MECP can provide more information about statistical performance in the classification for projection designs than the other criteria. Hence, designs with the best projection MECP may perform better in the view of confounding. The MECP provides a way to find the best main effect arrangement for the experimenter. We also prove that all the geometrically equivalent $$L_n(f^s)$$ L n ( f s ) designs have the same WD/CD/MD discrepancy values.

Keywords: Main effect confounding pattern; Orthogonal design; Generalized word-length pattern; Centered $$L_2$$ L 2 -discrepancy; Mixture discrepancy; Isomorphism (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00184-019-00713-w

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