THE EXACT DISTRIBUTIONS OF THE UNIVARIATE AND MULTIVARIATE BEHRENS-FISHER STATISTICS WITH A COMPARISON OF SEVERAL SOLUTIONS IN THE UNIVARIATE CASE

The exact distributions of the univariate- and multivariate Behrens-Fisher statistics are derived. As is well known, these distributions are dependent on the unknown variances or covariance matrices. The critical values of the exact distribution are computed and compared to the critical values of several approximations in the univariate case with the variances replaced by sample estimates. In the multivariate situation it is shown that this distribution is a special case of a generalization of a matrix Beta type II distribution as derived by van der Merwe and Nel (1987). Due to the computational intractability of the density function we could not compare it to an approximation. © 1990, Taylor & Francis Group, LLC. All rights reserved.