Monte Carlo simulation with parametric and nonparametric analysis of covariance for nonequivalent control groups
There are many parametric statistical models that have been designed to measure change in nonequivalent control group studies, but because of assumption violations and potential artifacts, there is no one form of analysis that always appears to be appropriate. While the parametric analysis of covariance and parametric ANCOVAS with a covariate correction are some of the more frequently completed analyses used in nonequivalent control group research, comparative studies with nonparametric counterparts should be completed and results compared with those more commonly used forms of analysis.
The current investigation studied and compared the application of four ANCOVA models: the parametric, the covariate-corrected parametric, the rank transform, and the covariate-corrected rank transform. Population parameters were established; sample parameter intervals determined by Monte Carlo simulation were examined; and a best ANCOVA model was systematically and theoretically determined in light of population assumption violations, reliability of the covariate correction, the width of the sample probability level intervals, true parent population parameters, and results of robust regression.
Results of data exploration on the parent population revealed that, based on assumptions, the covariate-corrected ANCOVAS are preferred over both the parametric and rank analyses. A reliability coefficient of ṟ=.83 also indicated that a covariate-corrected ANCOVA is effective in error reduction. Robust regression indicated that the outliers in the data set impacted the regression equation for both parametric models, and deemed selection of either model questionable.
The tightest probability level interval for the samples serves to delineate the model with the greatest convergence of probability levels, and, theoretically, the most stable model. Results of the study indicated that, because the covariate-corrected rank ANCOVA had by far the tightest interval, it is the preferred model. In addition, the probability level interval of the covariate-corrected rank model is the only model interval that contained the true population parameter.
Results of the investigation clearly indicate that the covariate-corrected rank ANCOVA is the model of choice for this nonequivalent control group study. While its use has yet to be reported in the literature, the covariate-corrected rank analysis of covariance provides a viable alternative for researchers who must rely upon intact groups for the answers to their research questions.