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In this paper an asymptotic formula for the cumulative distribution function (c. d. f. ) of Hotelling's generalized T₀² statistic is derived for general values of the number of dimensions in the non-null case. This result includes as a special case the previous result of the author for the null distribution of T₀² 5, and shows certain properties of T₀² which help determine the power of the test based on the statistic for moderately large samples. Both of the author's results provide an approximate complete analysis of the T₀² test, although the exact null and non-null distributions of T₀² are not available at present.
Koichi Ito (Thu,) studied this question.