Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions
- 10.2991/jsta.d.190514.001How to use a DOI?
- Correlated bivariate noncentral F distribution; factorial experiment; linear regression; pretest test; power and size of tests
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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Cite this article
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 -