Components of Variance Analysis for Proportional Frequencies

Table of Expectations of Mean Squares in the Analysis of Variance for Crossed Classifications.

“…below) with subscript combinations containing those small Latin letters which correspond to the script letters in the designating symbol of the respective mean square. Thus, for example, the expectation of the mean square for the first order interaction j(H in the five-way classification will contain or 2 …”

Models in the Analysis of Variance

“…The expected mean squares for balanced two-factor classifications, using models with independent interactions, have long been textbook material; and according to Crump (1951) they are available under Model I for several methods of analysing unbalanced designs, although the results do not appear to have been published. When the cell frequencies are proportional and the orthogonal analysis of method I is employed, Bankier and Walpole (1957)…”

Chapter III: Research Methods: Experimental Design and Analysis

“…The components-of-variance model was also considered by Bankier and Walpole (1957) for two-way crossed and nested classifications with proportional subclass frequencies. Useful expected values for various sums of squares were obtained for a variety of models.…”