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In statistics, the BehrensFisher problem is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. In his 1935 paper, Fisher outlined an approach to the BehrensFisher problem. Since highspeed computers were not available in Fishers time, this approach was not implementable and was soon forgotten. Fortunately, now that highspeed computers are available, this approach can easily be implemented using just a desktop or a laptop computer. Furthermore, Fishers approach was proposed for univariate samples. But this approach can also be generalized to the multivariate case. In this monograph, we present the solution to the aforementioned multivariate generalization of the BehrensFisher problem. We start out by presenting a test of multivariate normality, proceed to test(s) of equality of covariance matrices, and end with our solution to the multivariate BehrensFisher problem. All methods proposed in this monograph will be include both the randomlyincompletedata case as well as the completedata case. Moreover, all methods considered in this monograph will be tested using both simulations and examples.
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