The Effects of Heterogeneous Regression Slopes on the Robustness of Two Test Statistics in the Analysis of Covariance

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Abstract
The present study compares the robustness of two different one way fixed-effects analysis of covariance (ANCOVA) models with respect to the effects of unequal regression slopes. The purpose of this study is to investigate whether the model which uses a test statistic incorporating estimates of the separate slopes will be more robust than the conventional model which assumes the slopes are equal. A Monte Carlo simulation technique was employed to generate data under 64 different situations. Two treatment groups, five different sample sizes and twenty pairs of regression slopes were used. The number of replications in each simulation was 1827 to enable 0.95 confidence that each actual alpha value did not differ from the estimated alpha by more than .01. Both equal and unequal error variance were examined. A different random number seed was used for each of the 64 simulations. The results indicate that when the two standardized regression slopes differed by less than .4, both models were robust. When the difference exceeded .4 and the sample sizes were equal, the model which incorporated estimates of individual regression slopes was more robust than the conventional model which used a pooled within regression coefficient. When the difference between slopes exceeds .4 and unequal sample sizes were associated with unequal error variance, neither of the models were robust.