New heterogeneous test statistics for the unbalanced fixed-effect nested design

Authors


Correspondence should be addressed to Dr Wei-Ming Luh, Institute of Education, National Cheng Kung University, 1 University Road, Tainan City 701, Taiwan (e-mail: luhwei@mail.ncku.edu.tw).

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.

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