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

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 grou...

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Bibliographic Details
Main Author: Shields, Joyce L
Format: Report
Language:English
Subjects:
ANALYSIS OF VARIANCE
BEHAVIORAL SCIENCES
COMPUTERIZED SIMULATION
COVARIANCE
DATA ACQUISITION
GROUP DYNAMICS
HETEROGENEITY
HETEROSCEDASTIC MODELS
HETEROSCEDASTICITY
MONTE CARLO METHOD
PE62722A
Psychology
REGRESSION ANALYSIS
SKILLS
SOCIAL SCIENCES
Sociology and Law
STATISTICAL ANALYSIS
Statistics and Probability
TEST AND EVALUATION
TRAINING
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Summary: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.