Abstract
The problem of pairwise comparisons of three parameters is considered. It is assumed that a set of unbiased estimators of these parameters has a trivariate normal distribution with covariance matrix σ2 B, where B is a known positive definite matrix. A probability inequality sharper than that used by Hochberg (1974) is discussed. Based on this inequality it is possible to achieve simultaneous confidence intervals uniformly shorter than those arising from the GT2 method. These new intervals are also generally shorter than the intervals arising from Scheffé's method and from the Bonferroni inequality. In addition, these new intervals are at times shorter than those from Kramer's method, when the latter method is appropriate.
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