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A diagnostic method of identifying influential observations in performing the Hotelling's T^2 test based on influence function is suggested by defining an appropriate functional whose value at the empirical distribution functions becomes the Hotelling's T^2 statistic. The maximum likelihood estimators are very sensitive to influential observations so that the Hotelling's T^2 statistic would be vulnerable to influential observations. The diagnostic method based on influence function may be useful for measuring the influence of observations on the Hotelling's T^2 statistic and it can be adapted to other statistical problems. A numerical example is provided for illustration.