The Ratio of Variances in a Variance Components Model

Abstract

Our discussion will concern primarily $\lambda$, the ratio of two variances which arise in discussing the "mixed" incomplete block model. In Section 1 we find first the class of invariant statistics for a test involving this ratio and second the joint distribution of these statistics. In Section 2 we use these statistics to construct a test (with certain optimum properties) of the hypothesis $\lambda < \lambda_0$ versus $\lambda > \lambda_1$.