Analysis of Unreplicated Three-Way Classifications, with Applications to Rater Bias and Trait Independence

Abstract

The seven analysis-of-variance mean squares for an unreplicated three-way classification may be written as linear combinations of a mean variance and three mean covariances. Formulas are presented for computing the mean variances and mean covariances from linear combinations of mean squares. The relevance of these formulas for assessing rater biases and trait independence is discussed, a numerical example is provided, and proposed extensions are briefly noted.