Components of Variance Analysis

Abstract

<p> In this thesis a systematic and short method for computing the expected values of mean squares has been developed. One chapter is devoted to the theory of regression analysis by the method of least squares using matrix notation and a proof is given that the method of least squares leads to an absolute minimum, a result which the author has not found in the literature. For two-way classifications the results have been developed for proportional frequencies, a subject which again has been neglected in the literature except for the Type II model. Finally, the methods for computing the expected values of the mean squares are applied to nested classifications and Latin square designs.</p>