A MONTE CARLO STUDY OF THE EMPIRICAL TYPE I ERROR AND POWER FOR PARAMETRIC AND NONPARAMETRIC ANCOVA INVOLVING VIOLATIONS OF THE NORMALITY ASSUMPTION

Uniform random numbers were generated and transformed into four different sampling distributions: normal, uniform, lambda, and double exponential. A one-factor, two-group parametric analysis of covariance (ANCOVA) and a nonparametric analysis of covariance, Quade\u27s rank analyses of covariance (RANCOVA) were performed on each set of data to compare Type I error rate and power at three different alpha levels: 0.05, 0.01, and 0.001. Variables under investigation were violation of the normality assumption, sample size, degree of correlation between the covariate and the dependent variable, and degree of falsity of the null hypothesis. Violation of the normality assumption involved the use of the three non-normal distributions listed above. The two group sample sizes were equal but could be one of three sizes: 5, 15, or 30. The correlation between the covariate and dependent measure was estimated by rho and was chosen from 0.1, 0.5, or 0.75. The degree of falsity of the null hypothesis was chosen from the interval {0 (1) 4}. Each analysis was done one thousand times for each variable combination. Results of Type I error analysis indicated that both ANOVA and RANCOVA had excellent discrimination for all of the distributions observed and at most of the variable combinations. Power analysis indicated that ANCOVA and RANCOVA were different depending upon the distribution and variable combinations. The Lambda distribution had excellent power when the group sizes were 15 or 30, medium to large difference in Ho, small to large population correlation, and at all three alpha levels. Both ANCOVA and RANCOVA were able to detect large differences between means for an alpha of 0.05 in the Lambda distribution when group size was 5. When considering the Normal, Double Exponential, and Uniform distributions, only ANCOVA was observed to have excellent power and only for sample sizes 15 or 30 and high population correlation. This was observed for alpha levels of 0.05 and 0.01 for sample size 15, while for sample size 30, the alpha values were 0.05, 0.01, and 0.001