Yates's and Other Sums of Squares

TL;DR

This paper demonstrates the equivalence of Yates's sum of squares method with other approaches in linear models, extending its application and illustrating its use in complex experimental designs.

Contribution

It establishes the equivalence of Yates's sum of squares with other methods and extends its application to more general linear models.

Findings

Yates's sum of squares is equivalent to other numerator sums of squares.

The method can be extended to general linear models.

Illustrations include unequal-subclass-numbers models for two-factor effects.

Abstract

It is shown that the sum of squares by Yates's method of weighted squares of means is equivalent to numerator sums of squares formulated by other methods. These relations are established first for hypotheses about fixed effects in a general linear model, in the process showing how Yates's method can be extended. They are then illustrated in the unequal-subclass-numbers model for main effects and interaction effects of two factors.