Matrix Representation of Models for the Analysis of Variance and Covariance

Extract

Beginning students of analysis of variance frequently find that the explanations concerning numbers of degrees of freedom are rather more mystical than explanatory, and that the dependencies and independencies among parameters and linear restraints are not systematically covered or explicitly presented. It is the purpose of this paper to set forth the simple matrix representation of these models in a way which has been found useful for teaching purposes, and may be found of some value in the setting up of mathematical models for experimental designs calling for the analysis of variance or the analysis of covariance.

The system I shall portray is a more or less natural outgrowth of suggestions made by Dr. R. C. Bose, with whom I have discussed some of the features very slightly. I am also indebted to Professor Frederick Mosteller for assistance with the mechanics of some of the models. Any deficiencies which the system may have are not to be laid to the doors of these gentlemen, however, as they have not had any opportunity to go over the material at any length.