The problems of estimation and hypothesis testing are discussed for the parameters of the simple linear model with replications in the presence of heterogeneous variances. It is argued that guidelines for choosing between ordinary least squares or weighted squares procedures with estimated weights should be partially based on a measure of the severity of the variance heterogeneity. Furthermore, Monte Carlo results are used to provide such guidelines. Several procedures fortesting the general linear hypothesis are compared, with the ordinary least squares procedures demonstrating a surprising degree of robustness with respect to their power and distributional properties. A modified test which accounts for the presence of variance heterogeneity is proposed, and is found to be less powerful than the ordinary least squares test in many cases.