Discussiones Mathematicae Probability and Statistics 22(1,2) (2002) 73-104

ON THE BEHRENS-FISHER DISTRIBUTION AND ITS GENERALIZATION TO THE PAIRWISE COMPARISONS 

Viktor Witkovský

Institute of Measurement Science
Slovak Academy of Sciences
Dúbravská cesta 9
842 19 Bratislava, Slovak Republic
e-mail:
Witkovsky@savba.sk

Abstract

Weerahandi (1995b) suggested a generalization of the Fisher's solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. In this paper, we present a brief outline of the Fisher's solution and its generalization as well as the methods to calculate the p-values required for deriving the conservative joint confidence interval estimates for the pairwise mean differences, refered to as the generalized Scheffé intervals. Further, we present the corresponding tables with critical values for simultaneous comparisons of the mean differences of up to k = 6 normal populations with unequal variances based on independent random samples with very small sample sizes.

Keywords: Behrens-Fisher distribution, pairwise comparisons, unequal variances, generalized p-values.

2000 Mathematics Subject Classification: 62F04; 62E15.

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Received 5 December 2002