regression slopes, heteroscedasticity, nonconstant variance, heterogeneity of variance
When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.
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Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Rosopa, Patrick J., "A Comparison Of Ordinary Least Squares, Weighted Least Squares, And Other Procedures When Testing For The Equality Of Regression" (2006). Electronic Theses and Dissertations. 1003.