Tests of Hypotheses for Unbalanced Factorial Designs Under Various Regression/Coding Method Combinations

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Abstract
The controversy surrounding regression methods for unbalanced factorial designs is well known and well documented in articles by Overall and Spiegel (1969), Rawlings ( 1972), Gocka (1973), Overall and Spiegel (1973a), Overall and Spiegel (1973b), Appelbaum and Cramer (1974), Overall, Spiegel and Cohen (1975), and Rock, Werts and Linn (1976) to name just a few. Since it is possible to use any one of several popular systems for coding independent classification variables (Kerlinger and Pedhazur, 1973) with any one of the proposed regression methods, it is not surprising that some controversy has arisen concerning these coding schemes as well (Wolf and Cartwright, 1974; Bogartz, 1975; Overall, Spiegel, and Cohen, 1975). To add to the confusion of the applied researcher, "canned" computer programs employ different regression methods (Golhar and Skillings, 1976) in conjunction with different coding schemes with little (or even worse, incorrect) documentation (Francis, 1973). This is important because, as will be shown below, different regression methods when used in combination with different coding schemes yield tests of different hypotheses. Some of these hypotheses seem quite useful, while others do not. Noteworthy also is the fact that these hypotheses as functions of regression/coding method combinations have not been explicitly delineated in the educational literature. Implicit in this paper then is the assumption that researchers assessing unbalanced factorial designs should be aware of the statistical hypotheses which they are bringing under test. This is true when the researcher designs his or her own regression model as well as when packaged computer programs are being used. In order to aid the applied researcher through this maze, then, the purposes of this paper are as follows: (1) to present the statistical

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