The usual analysis of variance based on ordinary least squares (OLS) may be inappropriate to analyze the crossover designs because of correlations within subjects arising from the repeated measurements. The tests used with OLS are compared with three alternative tests that take into account the structure of the covariance matrix for testing the treatment and carryover effects under the assumption of multivariate normality. A modified F-test approximation and a test derived from a Pearson curve fit are shown to give adequate control over Type I error compared to the OLS tests and to tests following an empirical generalized least squares analysis.