On the Distribution of a Weighted Estimate of Variance and on Analysis of Variance in Certain Cases of Unequal Weighting

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Abstract
A proof is given that: [image] and the variates [chi]i(i=12, ..., n) are each normally distributed with variance 1/wi], is distributed as [chi]2 with n[long dash]1 degrees of freedom by use of an orthogonal matrix which is defined. An application, which involves data with equal wts., is given.