Some Remarks on Scheffé's Solution to the Behrens-Fisher Problem
Morris L. Eaton · Journal of the American Statistical Association · 1969
The problem considered here is a multivariate generalization of the classical Behrens-Fisher problem. Based on samples of size ni , i = 1, …, k, from k multivariate normal populations (of perhaps different dimension), a test statistic is proposed to test null hypotheses about linear relationships between components of the mean vectors of the k populations. Under the null hypothesis, the test statistic has a central F distribution and under alternatives, a non-central F distribution. For three different specializations of the above problem, the proposed test statistic reduces to tests proposed by Scheffé, Bennett, and Anderson respectively.