Variance reduction in the study of a test concerning the behrens-fisher problem

A simulation case study illustrating the implementation of a variance reduction technique appropriate for dichotomous response variables is presented. In this simulation study, concerning the power of the Cochran and Cox test for the equality of means under possibly unequal variances, variance reductions of around 80% or more are obtained. More importantly, a known property of the Cochran and Cox, its conservative character, is detected thanks to the use of variance reduction.