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

Abstract

S. Weerahandi [Exact statistical methods for data analysis. (1996; Zbl 0912.62002)] suggested a generalization of Fisher’s solution of the Behrens-Fisher problem to the problem of multiple comparisons with unequal variances by the method of generalized p-values. 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 Scheff´e 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.