The Analysis of Variance of the S-Stage Hierarchal Classification

Abstract

The expectations of the mean squares for the completely nested classification with inequality of numbers of observations at all stages is presented. Although the coefficients of a specific variance component must differ from mean square to mean square in general, there are orderly row and column patterns among the coefficients. Column-wise equality of some coefficients is demonstrated when equality of the number of individuals per sub-class (with or without equality of the numbers of sub-classes at a particular stage) is assumed. A brief discussion of computational methods of calculating these coefficients is given, as well as an example.