On the Behrens-Fisher distribution and its generalization to the pairwise comparisons

Witkovský, Viktor

Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 73-104.

Résumé

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.

Détail

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

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