The Estimation of Variance Components in Analysis of Variance

Abstract

Two uses of the analysis of variance are distinguished to obtain tests of significance of treatment effects, and to provide estimates of the variance components of the several effects contributing to the total variance. The hypotheses appropriate for each case, based on the same fundamental equation, are described. The author gives a general rule for determining the average values of any mean square from a multiple classification with equal subclass numbers. Rules for the variances of the estimated components are also given. The procedures are illustrated by an example.