Robustness and Power of Analysis of Covariance Applied to Data Distorted from Normality by Floor Effects: Non-Homogeneous Regression Slopes

We investigate through computer simulations the robustness and power of two group analysis of covariance tests applied to small samples distorted from normality by floor effects when the regression slopes are non-homogeneous. We consider four parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regression slopes and two t tests on the dependent variable and on difference scores. Under the null hypothesis of no difference in means, we estimated actual significance levels by comparing observed test statistics to appropriate values from the F and t distributions for nominal significance levels of 0.10, 0.05, 0.02 and 0.01. We estimated power by similar comparisons under various alternative hypotheses. We found that the traditional or textbook approach which first tests for homogeneity of slopes and then tests for equality of treatment means only if slopes are homogeneous, the model which assumes homogeneous regression slopes and the two t -tests are generally robust when the sample sizes are equal. The hierarchical approach, which tests for non-homogeneity in the regression slopes and fits a separate slopes model if found significant, and the separate slopes model are consistently liberal. When the sample sizes are unequal, only the traditional approach and the t test on the dependent variable maintain robustness. For equal sample sizes, the model which assumes homogeneous regression slopes and the two t -tests produce good power. The traditional approach, while conservative, produces good power particularly when the sample sizes are small. For unequal sample sizes, the t test on the dependent variable produces higher power than the traditional approach. The remaining ANCOVA tests and the t test on the difference scores are not robust in the presence of distributions distorted by floor effects and non-homogeneity of regression slopes when the sample sizes are unequal.

Keywords:

• Ancova
• Floor Effects
• Non-homogeneous Slopes