Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

Shahjahan Khan; Budi Pratikno; Shafiqur Rahman; M. Zakir Hossain

doi:10.2991/jsta.d.190514.001

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Volume 18, Issue 2, June 2019, Pages 103 - 112

Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

Authors

Shahjahan Khan¹^{, *}, Budi Pratikno², Shafiqur Rahman³, M. Zakir Hossain³

¹School of Agricultural, Computational and Environmental Sciences, University of Southern Queensland, Queensland, Australia

²Department of Mathematics and Natural Science, Jenderal Soedirman University, Central Java, Indonesia

³Department of Operations Management and Business Statistics, Sultan Qaboos University, Muscat, Oman

^*Corresponding author. Email: Shahjahan.Khan@usq.edu.au

Corresponding Author

Shahjahan Khan

Received 11 September 2017, Accepted 4 December 2018, Available Online 18 June 2019.

DOI: 10.2991/jsta.d.190514.001 How to use a DOI?
Keywords: Correlated bivariate noncentral F distribution; factorial experiment; linear regression; pretest test; power and size of tests
Abstract: The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This kind of nonsample prior information (NSPI) can be presented by null hypotheses (cf. T.A. Bancroft, Ann. Math. Stat. 15 (1944), 190–204), and its uncertainty removed through appropriate statistical test. Depending on the level of the NSPI the unrestricted, restricted, and pretest (PTT) tests are defined. The sampling distributions of test statistics and power functions of the three tests are derived. The graphical and analytical comparisons of powers reveal that the PTT dominates over the other tests.
Open Access: This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal: Journal of Statistical Theory and Applications
Volume-Issue: 18 - 2
Pages: 103 - 112
Publication Date: 2019/06/18
ISSN (Online): 2214-1766
ISSN (Print): 1538-7887
DOI: 10.2991/jsta.d.190514.001 How to use a DOI?
Open Access: This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

ris enw bib

TY  - JOUR
AU  - Shahjahan Khan
AU  - Budi Pratikno
AU  - Shafiqur Rahman
AU  - M. Zakir Hossain
PY  - 2019
DA  - 2019/06/18
TI  - Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions
JO  - Journal of Statistical Theory and Applications
SP  - 103
EP  - 112
VL  - 18
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.190514.001
DO  - 10.2991/jsta.d.190514.001
ID  - Khan2019
ER  -

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