pp 1–19 | Cite as

The main effect confounding pattern for saturated orthogonal designs

  • Yuxuan LinEmail author
  • Kai-Tai Fang


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 \(L_9(3^4)\), \(L_{27}(3^{13})\) and \(L_{16}(4^5)\) 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 \(L_n(f^s)\) designs have the same WD/CD/MD discrepancy values.


Main effect confounding pattern Orthogonal design Generalized word-length pattern Centered \(L_2\)-discrepancy Mixture discrepancy Isomorphism 



This work was partially supported by the UIC Grants (R201712, R201810 and R201912) and the Zhuhai Premier Discipline Grant. The authors thank Dr. A. M. Elsawah and two reviewers for their valuable comments and suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Science and TechnologyBNU-HKBU United International CollegeZhuhaiChina
  2. 2.The Key Lab of Random Complex Structures and Data AnalysisThe Chinese Academy of SciencesBeijingChina

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