Power of the Noncentral F-Test: Effect of Additional Variates on Hotelling's T²-Test

We show that the power of the noncentral F-test increases with the number of denominator d.f. and decreases with the numerator d.f. Hence, increasing the dimension of the observed vectors may decrease the power of Hotelling's T 2-test for means, unless the additional non-centrality provided by the extra variates is sufficiently large. A function determining the exact increase in noncentrality required for increased power is studied and tabulated We present procedures designed to test, on the basis of a preliminary sample, whether the increase in noncentrality is sufficiently large to justify inclusion of the extra variates.