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The main effect confounding pattern for saturated orthogonal designs

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  • Yuxuan Lin

    (BNU-HKBU United International College)

  • Kai-Tai Fang

    (BNU-HKBU United International College
    The Chinese Academy of Sciences)

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.

Suggested Citation

  • Yuxuan Lin & Kai-Tai Fang, 2019. "The main effect confounding pattern for saturated orthogonal designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 843-861, October.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:7:d:10.1007_s00184-019-00713-w
    DOI: 10.1007/s00184-019-00713-w
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    References listed on IDEAS

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    1. Yu Tang & Hongquan Xu, 2014. "Permuting regular fractional factorial designs for screening quantitative factors," Biometrika, Biometrika Trust, vol. 101(2), pages 333-350.
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