Analysis of covariance (ANCOVA) is a data analysis method that is often used to control extraneous sources of variation in non-equivalent group designs. It is commonly believed that as long as the covariate is highly correlated with the dependent variable there is nothing to lose in using ANCOVA, even in non-randomized studies. This paper examines some of the conditions that lead to successful and unsuccessful criterion source adjustments, and demonstrates that under certain circumstances, ANCOVA may perform in a manner that is antithetical to its intended purpose. Several hypothetical data sets were constructed, each with 70 observations, to illustrate two examples of appropriate ANCOVA use and two examples of inappropriate results. ANCOVA may serve to introduce confounding variables into the analysis when covariates represent differences between groups that are unrelated to outcome measures. Two tables present information from the analyses. A 26-item list of references is included. (Author/SLD)