Although analysis of covariance (ANCOVA) is used fairly infrequently in published research, the method is used much more frequently in dissertations and in evaluation research. This paper reviews the assumptions that must be met for ANCOVA to yield useful results, and argues that ANCOVA will yield distorted and inaccurate results when these assumptions are violated. For ANCOVA to provide meaningful statistical control and to not obscure or mislead, it must be ascertained that the data set fulfills several requirements, especially those pertaining to the homogeneity of regression slopes. For ANCOVA to increase power against a Type II error, there must be a high correlation between the covariate and the dependent variable and no correlation between the covariate and the independent variable. ANCOVA practitioners should examine their data sets carefully to insure that ANCOVA is an appropriate analytic method rather than a method that generates more problems for a given data set than it actually solves. Numerous examples, five figures, and one table are provided. (Author/SLD)