A comparison between the <i>U</i> and <i>V</i> tests in the Behrens-Fisher problem

The V test introduced by Welch (1937) seems to have been ignored in later literature, and the U test which is most in use nowadays is compared with the V test, using stochastic simulation.

Abstract

Several statistical methods have been recommended for use in the Behrens—Fisher situation. One of these methods, the V test introduced by Welch (1937), seems to have been ignored in later literature. We have compared the V test with the U test which is most in use nowadays, using stochastic simulation. The comparisons have been carried out for both tests with fixed critical values and for approximate tests. In the former case the V test is highly recommended, and in the latter case also the approximate V test seems to perform better than the U test.