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In this paper we consider the comparison of alternative size corrections of the t and F tests in the normal linear model with unknown error covariance matrix. Rothenberg (I984b) has derived corrected critical values for the F test from a chi-square Edgeworth approximation. Similar corrected critical values for the t test can be derived from a normal Edgeworth approximation. Alternative critical values can be obtained by using Edgeworth approximations based on the F or t distributions respectively. These corrections are locally exact, i.e. they reduce to the exact critical values when the error covariance matrix is known up to a multiplicative factor. Moreover, instead of correcting the critical values, we may use a Cornish-Fisher correction of the test statistic. Thus we avoid the problem of negative "probabilities" in the tails of an Edgeworth "distribution". The relative performance of these corrections is examined in the linear regression model with heteroscedastic errors. A simulation study supports the theoretical considerations in favor of the locally exact Cornish-Fisher corrections. Due to their moderate computational requirements and the simplicity of their use, the Cornish-Fisher corrections can be a useful tool in applied statistical and econometric work.