Critical Values for Bivariate Studentt-Tests

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Abstract
Let t 1 and t 12 be two independent normally distributed random variables with zero means and equal variances, each divided by a common estimate of the standard deviations. The joint distribution of t 1, t 2 is a bivariate Student t-distribution. The integral of the joint frequency function over certain types of critical regions in the (t 1, t 2)-plane may be written as the linear combination of two definite integrals which are easy to compute. Critical values for five alternative hypotheses in simultaneous tests on t 1 and t 2 are presented, and approximations which are asymptotically exact are discussed.