An Empirical Investigation of the Effects of Heterogeneous Regression Slopes in Analysis of Covariance

Abstract

The effects of violation of the assumption of homogeneity of regression on the Type I error rate and on the power of analysis of covariance (ANCOVA) were investigated. The data situations included in the study involved two groups with one covariate and one criterion, with varying equal and unequal group sizes, and varying degrees of violation of the assumption of homogeneity of regression. Results indicated that ANCOVA appeared robust to the violation of the assumption of homogeneity of regression when group sizes were equal; the technique appeared not to be robust for unequal group sizes. For equal group sizes and all slope combinations, the empirical alpha levels were near the corresponding nominal alpha levels. For unequal group sizes and unequal regression slopes, however, large discrepancies were observed between the empirical alpha levels and the corresponding nominal alpha levels. Results also indicated that the power of ANCOVA was not severely altered by heterogeneous regression slopes as long as the group sizes were equal.