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.
In this paper we consider and compare several approximate methods for making small-sample statistical inference on the common mean in the heteroscedastic one-way random effects model. The topic of the paper was motivated by the problem of interlaboratory comparisons and is also known as the (traditional) common mean problem. It is also closely related to the problem of multicenter clinical trials and meta-analysis. Based on our simulation study we suggest to use the approach proposed by Kenward & Roger (1997) as an optimal choice for construction of the interval estimates of the common mean in the heteroscedastic one-way model.
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