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New heterogeneous test statistics for the unbalanced fixed‐effect nested design
Author(s) -
Guo JiinHuarng,
Billard L.,
Luh WeiMing
Publication year - 2011
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711010x512688
Subject(s) - statistics , type i and type ii errors , statistical hypothesis testing , robustness (evolution) , mathematics , variance (accounting) , statistical power , test (biology) , f test , computer science , paleontology , biochemistry , chemistry , accounting , biology , business , gene
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.