title: New heterogeneous test statistics for the unbalanced fixed-effect nested design.
abstract: When the underlying variances are unknown or/and unequal, using the conventional F test is problematic in the two-factor hierarchical data structure. Prompted by the approximate test statistics (Welch and Alexander-Govern methods), the authors develop four new heterogeneous test statistics to test factor A and factor B nested within A for the unbalanced fixed-effect two-stage nested design under variance heterogeneity. The actual significance levels and statistical power of the test statistics were compared in a simulation study. The results show that the proposed procedures maintain better Type I error rate control and have greater statistical power than those obtained by the conventional F test in various conditions. Therefore, the proposed test statistics are recommended in terms of robustness and easy implementation.
authors.affiliation: Department of Applied Mathematics, National Pingtung University of Education, Pingtung City, Taiwan.
authors.forename: Jiin-Huarng
authors.initials: JH
authors.lastname: Guo
authors.forename: L
authors.initials: L
authors.lastname: Billard
authors.forename: Wei-Ming
authors.initials: WM
authors.lastname: Luh
mesh_terms: D003198:Computer Simulation; D004521:Educational Measurement / Q000706:statistics & numerical data; D006801:Humans; D008432:Mathematical Computing; D011336:Probability; D011581:Psychological Tests / Q000706:statistics & numerical data; D011594:Psychometrics / Q000706:statistics & numerical data; D012107:Research Design / Q000706:statistics & numerical data*; D012984:Software