SOME REMARKS ON SCHEFFE'S SOLUTION TO THE BEHRENS-FISHER PROBLEM
Journal/Book: Reprinted from the JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION December 1969 Vol. 64 pp. 1318-1322. 1969;
Abstract: University of Chicago 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. . . .