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Problem statement: Hotelling's T2 statistic has been well documented in the existing&#13; literature and exact as well as asymptotic results have been obtained. In the present article, we focus on&#13; an important particular case of T2 and we note that, there is no clear way to show, how univariate&#13; results, used in the theory of Students t statistic, could be used to derive corresponding multivariate&#13; ones, for T2. Therefore, our goal is to find an alternative method, which would be more useful than the&#13; usual one, in order to generalize directly univariate theory. Approach: At first, we used some matrix&#13; tools in order to obtain an equivalent algebraic form for T2 and, then, we applied some univariate&#13; results concerning distributions which arise from the normal distribution. Results: We found an&#13; algebraic representation of T2, which can be conceived as the natural extension of some results&#13; appearing in the literature and, we used our findings to show how standard univariate techniques can&#13; be applied in order to derive the exact and limiting distributions of T2. Conclusion: Using the&#13; proposed representation of T2 gives a better insight on the generalization of univariate results to&#13; multivariate analyses and indicates, at the same time, an alternative way to prove typical multivariate&#13; results. Furthermore, it allows for usual theoretical calculations to simplify

An Application of Univariate Statistics to Hotelling's T<sup>2</sup>