Why Covariance? A Rationale for Using Analysis of Covariance Procedures in Randomized Studies

Analysis of covariance is a useful statistical procedure for data analysis even when carefully executed random assignment procedures are employed. Statistically adjusting for the effects of the covariates on the outcome can help account for pretreatment group differences—even with careful sampling. In addition, analysis of covariance can increase statistical power, thus reducing the Type II error rate. This paper uses diagrams to show how analysis of covariance manipulates data under a variety of conditions. Also discussed are the relationship between analysis of covariance and statistical power and issues related to covariate selection. Finally, a simulated data analysis is used to demonstrate the process of selecting covariates and to show the results with and without statistically adjusting for the effects of the covariate.