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Some Properties of the Correlation Matrix of Dichotomous Guttman Items

Published online by Cambridge University Press:  01 January 2025

Rebecca Zwick
Rebecca Zwick*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Rebecca Zwick, Educational Testing Service, Princeton, NJ 08541.
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Abstract

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 if the score distribution is uniform and there is an equal number of items at each difficulty level. Even when these special conditions do not hold, the correlations can often be expressed in a simple form by assuming a particular score distribution.

Keywords

Guttman scalesperfect scalesdichotomous itemsdifficulty factorsfactor analysiscomponent analysis
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 4 , December 1987 , pp. 515 - 520
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

The author thanks Neil Dorans, Bob Mislevy, Ledyard R Tucker, and Howard Wainer for their comments.

References

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