Effects of Violations of Data Set Assumptions When Using the Analysis of Variance and Covariance with Unequal Group Sizes.

This research explored the degree to which group sizes can differ before the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are jeopardized. Monte Carlo methodology was used, allowing for the experimental investigation of potential threats to robustness under conditions common to researchers in education. The effects of unequal group sizes were explored under the following data set conditions: (1) heterogeneity of group variances; (2) skew; (3) kurtosis; and (4) in ANCOVA, heterogeneity of regression slopes. Two independent sets of simulations were conducted, one using a total group of 90 and the other a total of 60. Experimentation was limited to simulations using three groups, with the total number divided in a systematic fashion. Results of these studies produced results consistent with previous research. In the analyses having homogeneity of group variances, the only simulations that emerged as statistically significant from the theoretical F test were those that had a large degree of difference in group numbers and unequal regression slopes. No significant differences emerged in simulations with near equal numbers. Tables in this paper document the simulation results, but also offer the research practitioner some idea of the true risk of Type I error in such situations. (Contains 7 tables and 24 references.) (SLD)