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

Published online by Cambridge University Press:  01 January 2025

Julian C. Stanley
Julian C. Stanley*
Affiliation:
University of Wisconsin
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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.

Type
Original Paper
Information
Psychometrika , Volume 26 , Issue 2 , June 1961 , pp. 205 - 219
Copyright
Copyright © 1961 The Psychometric Society

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Footnotes

*

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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