A Comparison of Three Different Procedures for Estimating Variance Components

An analytic procedure for obtaining variances of estimates of variance components in a general multi-way classification is described. As an application, three methods for estimating variance components are compared for a two-way classification. Since the variances of the estimates are affected by the magnitude of the true variance components (parameters) as well as the arrangement of the subclass numbers (n ij 's), a numerical tabulation is necessary in order to make a comparison. Using a UNIVAC 1105, the variances of the estimates of variance components are evaluated over a substantial range of parameters and n ij 's. These results are presented in tabular form for selected sets of parameter values.