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Abstract The robustness of Hotelling's one- and two-sample tests is investigated by Monte Carlo methods. Samples are presented from uniform, exponential, and lognormal distributions. The results show that the two-sample test is far more robust to departures from normality than the one-sample test, and that the latter may be badly affected by departures due to extreme skewness.
Barry J. Everitt (1979) studied this question.