Tests on a subset of regression parameters for factorial experimental data with uncertain higher order interactions

Khan, Shahjahan and Pratikno, Budi and Rahman, Shafiqur and Hossain, M. Zakir (2019) Tests on a subset of regression parameters for factorial experimental data with uncertain higher order interactions. Journal of Statistical Theory and Applications, 18 (2). pp. 103-112. ISSN 1538-7887

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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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 24 Jun 2019 01:33
Last Modified: 24 Jun 2019 06:44
Uncontrolled Keywords: correlated bivariate noncentral F distribution, factorial experiment, linear regression, pretest test, power and size of tests
Fields of Research : 01 Mathematical Sciences > 0104 Statistics > 010401 Applied Statistics
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.2991/jsta.d.190514.001
URI: http://eprints.usq.edu.au/id/eprint/36608

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