Robustness and power of analysis of covariance applied to data distorted from normality by floor effects: homogeneous...

We investigate through computer simulations the robustness and power of two group analysis of covariance test applied to small samples distorted normality by floor effects when the regression slopes are 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 unadjusted means 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 hypothesis. The hierarchical approach (that adjusts for non-homogeneous slopes if found significant), the test that assumes homogeneous regression slopes, and the test that estimates separate regression slopes in each treatment were robust. In general, each test produced power at least equal to that expected from normal theory. The textbook approach, which does not test for mean differences when there is significant non-homogeneity, was conservative but also had good power. The t-tests were robust but had poorer power properties than the above procedures.