The main effect confounding pattern for saturated orthogonal designs

Yuxuan Lin; Kai Tai Fang

doi:10.1007/s00184-019-00713-w

The main effect confounding pattern for saturated orthogonal designs

Yuxuan Lin^*, Kai Tai Fang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

3 Citations (Scopus)

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 L₉(3 ⁴) , L₂₇(3 ¹³) and L₁₆(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.

Original language	English
Pages (from-to)	843-861
Number of pages	19
Journal	Metrika
Volume	82
Issue number	7
DOIs	https://doi.org/10.1007/s00184-019-00713-w
Publication status	Published - 1 Oct 2019

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Centered L-discrepancy
Generalized word-length pattern
Isomorphism
Main effect confounding pattern
Mixture discrepancy
Orthogonal design

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10.1007/s00184-019-00713-w

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title = "The main effect confounding pattern for saturated orthogonal designs",

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 L9(3 4) , L27(3 13) and L16(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 Ln(fs) designs have the same WD/CD/MD discrepancy values.",

keywords = "Centered L-discrepancy, Generalized word-length pattern, Isomorphism, Main effect confounding pattern, Mixture discrepancy, Orthogonal design",

author = "Yuxuan Lin and Fang, {Kai Tai}",

note = "Funding Information: This work was partially supported by the UIC Grants (R201712, R201810 and R201912) and the Zhuhai Premier Discipline Grant. Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",

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T1 - The main effect confounding pattern for saturated orthogonal designs

AU - Lin, Yuxuan

AU - Fang, Kai Tai

N1 - Funding Information: This work was partially supported by the UIC Grants (R201712, R201810 and R201912) and the Zhuhai Premier Discipline Grant. Publisher Copyright: © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - 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 L9(3 4) , L27(3 13) and L16(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 Ln(fs) designs have the same WD/CD/MD discrepancy values.

AB - 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 L9(3 4) , L27(3 13) and L16(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 Ln(fs) designs have the same WD/CD/MD discrepancy values.

KW - Centered L-discrepancy

KW - Generalized word-length pattern

KW - Isomorphism

KW - Main effect confounding pattern

KW - Mixture discrepancy

KW - Orthogonal design

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DO - 10.1007/s00184-019-00713-w

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SN - 0026-1335

VL - 82

SP - 843

EP - 861

JO - Metrika

JF - Metrika

IS - 7

ER -

The main effect confounding pattern for saturated orthogonal designs

Abstract

Scopus Subject Areas

User-Defined Keywords

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