Abstract
In this chapter, we introduce three fiducial approaches to heteroscedastic ANOVA and MANOVA. The first approach is that of Li et al. (2011) which was proposed for ANOVA but can be easily generalized to MANOVA. The second approach is that implicit in Behrens (Landw. Jb. 68, 807–837, 1929) paper. The third approach is that implicit in Fisher (Ann. Eugen. 6, 391–398, 1935) paper. As a motivation, we begin with the two-sample ANOVA problem to which all the three approaches are applied. As a further motivation, the k-sample ANOVA problem is presented where k > 2. Finally, we present the heteroscedastic MANOVA problem to which all the three approaches are applied. For the k-sample ANOVA problem, k > 2, and for the heteroscedastic MANOVA problem, we use the FDR algorithm. Type I errors and power for each method are also presented. Finally, two examples are also presented.
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Desai, T. (2013). On Heteroscedastic MANOVA. In: A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem. SpringerBriefs in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6443-3_4
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DOI: https://doi.org/10.1007/978-1-4614-6443-3_4
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