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The analysis of linear models is supported by a rigorous mathematical development, but there appear to be serious gaps between theory and practice. In this article we compare, for a number of examples, the classical non-full rank analysis with the full rank analysis, or analysis of means. We find that the latter analysis eliminates much of the confusion, particularly in the area of hypothesis testing with unbalanced data.
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Hocking et al. (1975) studied this question.
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