A Monte Carlo Study: Robustness of Analysis of Covariance to Violation of Selected Assumptions
Thomson, David Samuel
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Permalink
https://hdl.handle.net/2142/66019
Description
Title
A Monte Carlo Study: Robustness of Analysis of Covariance to Violation of Selected Assumptions
Author(s)
Thomson, David Samuel
Issue Date
1980
Department of Study
Education
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
It was the purpose of this study, through the use of a Monte Carlo simulation, to investigate the robustness of the analysis of covariance (ANCOVA) model relative to violations of some of the model's assumptions, and to various experimental conditions. In particular, the effect of violating the following assumptions was examined: (1) homgeneity of within-cell population regression coefficients (i.e., slopes), and (2) homogeneity of within-cell population error variances. In addition, the effect of having a contaminated sampling distribution from which the within-cell population error variances were generated (i.e., 10 or 20% of the sampling distribution has a proportionally larger variance) was examined as an experimental condition. The effects of the violations of these assumptions and of the above mentioned experimental condition were considered for equal, as well as unequal, sample sizes. The actual Analysis of Covariance F distribution generated by using (i) different sample sizes, (ii) heterogeneous within-cell regression coefficients, (iii) heterogeneous within-cell error variances, and/or (iv) a contaminated sampling distribution for the within-cell error variances, was compared to the theoretical F distribution under the null hypothesis, when all assumptions of the ANCOVA model have been met. In addition, analysis of variance was used to analyze the results of the Monte Carlo simulation with heterogeneous within-cell regression coefficients, and heterogeneous within-cell error variances for the two and three group cases. The power of the statistical tests used to detect heterogeneous within-cell error variances and heterogeneous within-cell regression coefficients (slopes) were also examined.
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