An Empirical Investigation of the Effect of Heteroscedasticity and Heterogeneity of Variance on the Analysis of Covariance and the Johnson-Neyman Technique.

摘要

The robustness of the Johnson-Neyman technique and analysis of covariance (ANCOVA) to violations of assumptions of homoscedasticity and homogeneity of variance was tested through the use of Monte Carlo computer procedures. The study simulated a one-way, fixed-effects analysis with two treatment groups, one criterion, and one covariate. Five fixed values of the covariate were selected with zero mean and unit variance, while the values of Y were varied randomly with a constant regression coefficient of .75. Four combinations of group sizes (10,10;10,20;20,10;20,20), five combinations of group variances (1,1;1,2;2,1;1,5;5,1), and five forms of heteroscedasticity (combined in 18 different pairs), were studied. These conditions were combined to produce 186 different simulated experimental conditions. For each simulated condition 3000 pseudo-random samples were generated and sampling distributions relevant to the Johnson-Neyman technique and ANCOVA were compiled.