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Some Properties of the Pearson Correlation Matrix of Guttman-Scalable Items

Zwick, Rebecca J.
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Correlation, Guttman, Louis, Item Analysis, Scaling, Statistical Analysis


Although perfectly scalable items rarely occur in practice, Guttman's concept of a scale has proved to be valuable to the development of measurement theory. If the score distribution is uniform and there is an equal number of items at each difficulty level, both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous Guttman-scalable items can be expressed as simple functions of the number of items. Even when these special conditions do not hold, the values of the correlations can be computed easily by assuming a particular score distribution. These findings are useful in conducting research on the properties of scales. (27pp.)

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