| Robustness and power of analysis of covariance applied to small samples of data distorted from normality by floor effects and to ordinal scaled data are investigated through computer simulation. Two treatment groups and a single covariate which reflects a pre-treatment assessment are considered. Six parametric analysis of covariance tests are investigated which vary according to assumptions about the homogeneity of regression slopes. Hierarchical tests are included which involve a preliminary test for the homogeneity of regression slopes prior to the test of adjusted treatment means. All tests are performed using general linear models and ordinary least squares estimation. Situations are considered where regression slopes are homogeneous and non-homogeneous.;Using data generated under the null hypothesis of no difference in adjusted treatment means, significance levels are estimated by comparing observed test statistics to appropriate values from the F distribution tables for nominal significance levels of 0.10, 0.05, 0.02 and 0.01. Power is estimated by comparing observed test statistics to appropriate values from the F distribution tables for nominal significance levels of 0.10, 0.05, 0.02 and 0.01, under various alternative hypotheses.;For small samples of data distorted by floor effects with either homogeneous or non-homogeneous regression slopes, the analysis of covariance test which assumes homogeneous regression slopes and the hierarchical test which includes the specification of the covariate as a deviation from the mean, as opposed to a raw score, are robust in general. In the presence of homogeneous regression slopes, both tests produce power which is higher than expected in the presence of normally distributed data except when the sample sizes are small (n$sb1$ = n$sb2$ = 5). In the presence of non-homogeneous regression slopes, observed power is no more than 15% less than expected.;For small samples of ordinal scaled data with homogeneous regression slopes, the analysis of covariance test which assumes homogeneous regression slopes is robust. The hierarchical test, described above, produces significance levels which are close to the nominal levels, though the preliminary test produces significance levels which are less than the nominal levels. In the presence of 4 and 5 point ordinal scaled data with non-homogeneous regression slopes, tests produce significance levels which exceed the nominal levels. In the presence of 3 and 4 point ordinal scaled data, the test which assumes homogeneous regression slopes and the hierarchical test produce power which is no more than 13% less than expected. |
