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.
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The research reported herein was performed pursuant to a contract with the United States Office of Education, Department of Health, Education, and Welfare. The assistance of Sister M. Jacinta Mann, S. C., at one stage of this investigation is gratefully acknowledged.
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Stanley, J.C. Analysis of unreplicated three-way classifications, with applications to rater bias and trait independence. Psychometrika 26, 205–219 (1961). https://doi.org/10.1007/BF02289715
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DOI: https://doi.org/10.1007/BF02289715