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Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions involve many nuisance parameters, an impossible number of tables would be necessary in order to make exact confidence intervals. In the virtual absence of tables, approximations and bounds become important. In this paper, an attempt has been made to investigate the adequacy of certain suggested approximations [2], [5], [8] by computing the exact distributions for some particular cases. These exact distributions have been compared with approximations. This paper is concerned with two-sided confidence intervals, rather than one-sided intervals. [ABSTRACT FROM AUTHOR]

A general method is developed for obtaining confidence limits on the mean of X+ Y where X and Yare two independent random variables whose individual distributions and percentiles are in standard statistical tables. The procedure uses this information to obtain approximations for the percentiles of the sum or approximate confidence limits on the mean of the sum. The method is applied to two problems: approximating the percentiles of the noncentral t distribution, and determining confidence limits for variance components in a one-way classification. Numerical examples compare it to other approximations. [ABSTRACT FROM AUTHOR]