The effect of a nonlinear regression term on the behavior of the standard analysis of covariance (ANCOVA) F test was investigated for balanced and randomized designs through a Monte Carlo study. The results indicate that the use of the standard analysis of covariance model when a quadratic term is present has little effect on Type I error rates but produces a substantial power loss compared to theoretically expected values, often in excess of 20%. The extent of the power loss depends on the magnitude of the regression parameter associated with the nonlinear term. This finding appears consistently for varying numbers of groups and sample sizes and for various distributions. These results highlight the importance of plotting data and checking for nonlinearity prior to employing the standard analysis of covariance F test. (Contains 2 tables and 22 references.) (Author/SLD)