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Title: An approximate degrees of freedom test for heteroscedastic two-way ANOVA
Authors: Zhang, J.-T. 
Keywords: Approximate degrees of freedom test
Tests of linear hypotheses
Two-way ANOVA under heteroscedasticity
Wald-type statistic
Issue Date: Jan-2012
Citation: Zhang, J.-T. (2012-01). An approximate degrees of freedom test for heteroscedastic two-way ANOVA. Journal of Statistical Planning and Inference 142 (1) : 336-346. ScholarBank@NUS Repository.
Abstract: Heteroscedastic two-way ANOVA are frequently encountered in real data analysis. In the literature, classical F-tests are often blindly employed although they are often biased even for moderate heteroscedasticity. To overcome this problem, several approximate tests have been proposed in the literature. These tests, however, are either too complicated to implement or do not work well in terms of size controlling. In this paper, we propose a simple and accurate approximate degrees of freedom (ADF) test. The ADF test is shown to be invariant under affine-transformations, different choices of contrast matrix for the same null hypothesis, or different labeling schemes of cell means. Moreover, it can be conducted easily using the usual F-distribution with one unknown degree of freedom estimated from the data. Simulations demonstrate that the ADF test works well in various cell sizes and parameter configurations but the classical F-tests work badly when the cell variance homogeneity assumption is violated. A real data example illustrates the methodologies. © 2011 Elsevier B.V.
Source Title: Journal of Statistical Planning and Inference
ISSN: 03783758
DOI: 10.1016/j.jspi.2011.07.023
Appears in Collections:Staff Publications

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