The widespread applicability and use of normal approximations creates a need for methods for assessing their accuracy in an operational fashion. This Note presents two new methods based on a comparison of the level curves of an exact likelihood with the level curves of the usual normal approximation to it and on a comparison of selected line integrals of an exact density and a normal approximation to it. The operational usefulness of these methods is compared with the operational usefulness of two well-known existing approaches to the accuracy of approximations, namely convergence rates and the curvature methods of D.M. Bates and D.G. Watts.
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