期刊名称：Journal of Statistical Theory and Applications (JSTA)
电子版ISSN：1538-7887
出版年度：2019
卷号：18
期号：2
页码：105-114
DOI：10.2991/jsta.d.190514.001
语种：English
出版社：Atlantis Press
摘要：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.
关键词：Correlated bivariate noncentral;
F distribution;
factorial experiment;
linear regression;
pretest test;
power and size of tests
