ERIC Number: ED365730
Record Type: RIE
Publication Date: 1993-Nov
Reference Count: N/A
The Effects of Single and Compound Violations of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Models.
Johnson, Colleen Cook
This study integrates into one comprehensive Monte Carlo simulation a vast array of previously defined and substantively interrelated research studies of the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) statistical procedures. Three sets of balanced ANOVA and ANCOVA designs (group sizes of 15, 30, and 45) and one set of unbalanced ANOVA and ANCOVA designs (groups of 15, 30, and 45) were simulated. Violations of normal shape and three degrees of heterogeneity of group variances were included. Each set of ANCOVA analyses included ANOVA violations as well. Each data set violation was simulated in isolation and in combination, resulting in 665 unique ANOVA or ANCOVA F sampling distributions. Unbalanced designs almost always produced statistically invalid F ratios in the presence of any data set assumption except those that only involved perturbation of shape. In balanced designs, a degree of robustness beyond that expected was found, even when heterogeneity of variance was coupled with heterogeneous regression slopes and a skewed covariate. Robustness was found even when the ratio of largest to smallest group variance was five. Implications of these findings for educational, social science, and behavioral research are discussed. Three tables are included. (Contains 29 references.) (Author/SLD)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Balanced Designs; Unbalanced Designs; Variance (Statistical); Violation of Assumptions
Note: Paper presented at the Annual Meeting of the Mid-South Educational Research Association (New Orleans, LA, November 10-12, 1993).