The robustness of the Johnson-Neyman technique and analysis of covariance (ANCOVA) to violations of assumptions of homoscedasticity and homogeneity of variance was tested through the use of Monte Carlo computer procedures. The study simulated a one-way, fixed-effects analysis with two treatment groups, one criterion, Y, and one covariate, X. Five fixed values of the covariate were selected with zero mean and unit variance, while the values of Y were varied randomly with a constant regression coefficient of .75. Four combinations of group sizes, five combinations of group variances, and five forms of heteroscedasticity were studied. Results indicated that ANCOVA is robust to violations of assumptions of homoscedasticity and homogeneity of variance, both singly and in combination, when group sizes were equal; For cases of different group sizes and heterogeneous variances, a predictable bias was observed. The Johnson-Neyman technique was sensitive to violation of the assumption of homoscedasticity for both equal and unequal group sizes. (Author)