• Behrens;
  • Fisher problem, equivalence test, heterogeneous variances, partial differential equation, seriessolution

Abstract.  A test for two-sided equivalence of means has been developed under the assumption of normally distributed populations with heterogeneous variances. Its rejection region is limited by functions ±h that depend on the empirical variances. h is stated implicitly by a partial differential equation, an exact solution of which would provide a test that is exactly similar at the boundary of the null hypothesis of non-equivalence. h is approximated by Taylor series up to third powers in the reciprocal number of degrees of freedom. This suffices to obtain error probabilities of the first kind that are very close to a nominal level of α = 0.05 at the boundary of the null hypothesis. For more than 10 data points in each group, they range between 0.04995 and 0.05005, and are thus much more precise than those obtained by other authors.