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Various methods to control the influence of a covariate on a response variable are compared. In particular, ANOVA with or without homogeneity of variances (HOV) of errors and Kruskal-Wallis (K-W) tests on covariate-adjusted residuals and analysis of covariance (ANCOVA) are compared. Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set ignoring the treatment levels. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and means are equal for treatment factors. Empirical size and power performance of the methods are compared by extensive Monte Carlo simulations. We manipulated the conditions such as assumptions of normality and HOV, sample size, and clustering of the covariates. Guidelines on which method to use for various cases are also provided.