We consider the effects of incorrectly assuming a scalar error covariance matrix in a linear regression model in the context of a pre-test for linear restrictions on the coefficients. Because of this misspecification the (true) size and power of the pre-test may differ from their assumed values, distorting the pre-test estimator risk function towards that of one or other of its component estimators. The restricted and pre-test estimators may dominate the unrestricted estimator over a larger, or smaller, part of the parameter space, compared to the case with a correctly specified model.