Abstract
Summary The general nonnull distribution of Wilks statistic, the likelihood ratio statistic in MANOVA, can be expressed as a product of conditional beta variables [3]. Making use of this result, in the present paper, an upper bound for the nonnull distribution of Wilks statistic is obtained, which provides a conservative evaluation of the power of the likelihood ratio test for the cases when the alternative hypothesis is of rank 1, 2 or 3. For p=2, where p is the number of variables, and large f2, the degrees of freedom, it has been shown that the results of this paper give a much better approximation to the power of Wilks statistic than Mikhail's approximation [10]. A few percentage points have also been computed for p=3 and selected values of the degrees of freedom and the noncentrality parameters, which in the linear case have been compared with the exact values obtained by the author [7].
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