Nonorthogonal Analysis of Variance: Putting the Question before the Answer

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Abstract
There has been considerable debate in the literature concerning the "appropriate" method for calculating least squares analysis of variance with unequal sample sizes. It is argued here that the choice of the appropriate method depends upon the question the experimenter wants to answer about the data. The different questions reflect different null hypotheses. An example is presented to demonstrate the practical effects of using two alternative methods of analysis (weighted and unweighted means) and the null hypotheses tested under each method. It is shown that the different methods address substantially different experimental questions. Procedures advocated by Appelbaum and Cramer (1974) are challenged on several grounds. An argument is also presented against use of Overall and Spiegel's Method II, based on the general uninterpretability of the hypotheses tested.