Skip to main content
SpringerLink
Log in

The main effect confounding pattern for saturated orthogonal designs

  • Published:
Metrika Aims and scope Submit manuscript

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 \(L_9(3^4)\), \(L_{27}(3^{13})\) 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Box GEP, Hunter WG, Hunter JS (1978) Statistics for experimenters. Wiley, New York

    MATH  Google Scholar 

  • Cheng SW, Ye K (2004) Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. Ann. Stat. 32:2168–2185

    Article  MathSciNet  MATH  Google Scholar 

  • Clark JB, Dean AM (2001) Equivalence of fractional factorial designs. Stat. Sin. 11:537–547

    MathSciNet  MATH  Google Scholar 

  • Elsawah AM, Fang KT, Ke X (2019) New recommended designs for screening either qualitative or quantitative factors. Stat Pap. https://doi.org/10.1007/s00362-019-01089-9

    Google Scholar 

  • Fang KT, Ma CX (2000) The uniformity—a useful criterion in experimental design. In: First midwest conference for new directions in experimental design, May 2000, Columbus, OH

  • Fang KT, Ma CX (2001) Orthogonal and uniform experimental designs. Science Press, Henderson, pp 175–183 (in Chinese)

    Google Scholar 

  • Fang KT, Mukerjee R (2000) Connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika 87:173–198

    Article  MathSciNet  MATH  Google Scholar 

  • Fang KT, Zhang A (2004) Minimum aberration majorization in non-isomorphic saturated designs. J Stat Plan Inference 126:337–346

    Article  MathSciNet  MATH  Google Scholar 

  • Fang KT, Quan H, Chen QY (1988) Practical regression analysis. Science Press, Henderson, pp 348–349 (in Chinese)

    Google Scholar 

  • Fang KT, Tang Y, Yin JX (2008) Lower bounds of various criteria in experimental designs. J Stat Plan Inference 138:184–195

    Article  MathSciNet  MATH  Google Scholar 

  • Fries A, Hunter WG (1980) Minimum aberration \(2^{k-p}\) designs. Technometrics 8:601–608

    MATH  Google Scholar 

  • Hickernell FJ (1998) A generalized discrepency and quadrature error bound. Math Comput 67:299–322

    Article  MATH  Google Scholar 

  • Lam C, Tonchev VD (1996) Classification of affine resolvable \(2-(27, 9, 4)\) designs. J Stat Plan Inference 56:187–202

    Article  MathSciNet  MATH  Google Scholar 

  • Li W, Zhou Q, Zhang RC (2015) Effective designs based on individual word length patterns. J Stat Plan Inference 163:43–47

    Article  MathSciNet  MATH  Google Scholar 

  • Ma CX, Fang KT (2001) A note on generalized aberration in fractional designs. Metrika 53:85–93

    Article  MathSciNet  MATH  Google Scholar 

  • Ma CX, Fang KT, Lin DKJ (2001) On isomorphism of factorial designs. J Complex 17:86–97

    Article  MathSciNet  MATH  Google Scholar 

  • Tang Y, Xu HQ (2014) Permuting regular fractional factorial designs for screening quantitative factors. Biometrika 101(2):333–350

    Article  MathSciNet  MATH  Google Scholar 

  • Tang Y, Xu HQ, Lin DKJ (2012) Uniform fractional factorial designs. Ann Stat 40(2):891–907

    Article  MathSciNet  MATH  Google Scholar 

  • Wang Y, Fang KT (1981) A note on uniform distribution and experimental design. Chin Sci Bull 26:485–489

    MathSciNet  MATH  Google Scholar 

  • Xu H, Wu CFJ (2001) Generalized minimum aberration for asymmetrical fractional factorial designs. Ann Stat 29:549–560

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang RC, Li P, Zhao SL, Ai MY (2008) A general minimum lower-order confounding criterion for two-level regular designs. Stat Sin 18:1689–1705

    MathSciNet  MATH  Google Scholar 

  • Zhou YD, Fang KT, Ning JH (2013) Mixture discrepancy for quasi-random point sets. J Complex 29:283–301

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Division of Science and Technology, BNU-HKBU United International College, Zhuhai, 519085, China

    Yuxuan Lin & Kai-Tai Fang

  2. The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing, China

    Kai-Tai Fang

Authors
  1. Yuxuan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai-Tai Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuxuan Lin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, Y., Fang, KT. The main effect confounding pattern for saturated orthogonal designs. Metrika 82, 843–861 (2019). https://doi.org/10.1007/s00184-019-00713-w

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-019-00713-w

Keywords

Search

Navigation