A Monte Carlo Study of Three Approaches to Nonorthogonal Analysis of Variance

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3 approaches to nonorthogonal ANOVA, sensitivity & error rates

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Several alternative procedures have been advocated for analyzing nonorthogonal ANOVA data. Two in particular, J. E. Overall and D. K. Spiegel's (see record 1970-01534-001) Methods 1 and 2, have been the focus of controversy. A Monte Carlo study was undertaken to explore the relative sensitivity and error rates of these 2 methods, in addition to M. I. Applebaum and E. M. Cramer's (see record 1974-28956-001) procedure. Results of 2,250 3 × 3 ANOVAs conducted with each method and involving 3 underlying groups of population effects supported 3 hypotheses raised in the study: (a) Method 2 was more powerful than Method 1 in the absence of interaction; (b) Method 2 was biased upwards in the presence of interaction; and (c) Methods 1 and 2 both had Type I error rates close to those expected in the absence of interaction. In addition, it was found that in the absence of interaction, the Appelbaum and Cramer procedure was more powerful than Method 2 but slightly increased the Type I error rate.

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Journal of Applied Psychology, v. 66, issue 5, p. 535-540