ERIC Number: ED365720
Record Type: RIE
Publication Date: 1993-Nov
Reference Count: N/A
The Effects of Violation of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Procedures.
Johnson, Colleen Cook
The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects analysis of variance (ANOVA) and one concomitant analysis of covariance (ANCOVA) statistical procedure. Methodological and data set statistical assumptions that must be met for ANOVA and ANCOVA are discussed. Research results were obtained from an exploratory study of the effects of single and compound violations of the mathematical conditions (assumptions) underlying use of ANOVA and ANCOVA through Monte Carlo methods using randomly created data for a mathematical simulation (665 data set conditions). For all of the analyses, comparisons were made between the empirical F sampling distributions and the theoretical (i.e., nominal) F distributions expected when one uses normal theory. For balanced designs, the ANOVA and ANCOVA F tests were found to be remarkably robust when faced with most of the violations in the simulation. Research does reaffirm that ANOVA and ANCOVA should be avoided when group sizes are not equal. Specific recommendations are made for checking the ratio of largest to smallest group variances. (Contains 29 references.) (SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Balanced Designs; Violation of Assumptions
Note: Paper presented at the Annual Meeting of the Mid-South Educational Research Association (New Orleans, LA, November 10-12, 1993).