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A Family of Association Coefficients for Metric Scales

Published online by Cambridge University Press:  01 January 2025

Frits E. Zegers  and
Jos M. F. ten Berge
Frits E. Zegers*
Affiliation:
University of Groningen
Jos M. F. ten Berge
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Frits E. Zegers, University of Groningen, Dept. of Psychology, Grote Markt 31-32, 9712 HV Groningen, The Netherlands.
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Abstract

Four types of metric scales are distinguished: the absolute scale, the ratio scale, the difference scale and the interval scale. A general coefficient of association for two variables of the same metric scale type is developed. Some properties of this general coefficient are discussed. It is shown that the matrix containing these coefficients between any number of variables is Gramian. The general coefficient reduces to specific coefficients of association for each of the four metric scales. Two of these coefficients are well known, the product-moment correlation and Tucker's congruence coefficient. Applications of the new coefficients are discussed.

Keywords

association coefficientmetric scaleproduct-moment correlation
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 1 , March 1985 , pp. 17 - 24
Copyright
Copyright © 1985 The Psychometric Society

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