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Association Coefficients of Identity and Proportionality for Metric Scales

Published online by Cambridge University Press:  01 January 2025

Robert F. Fagot  and
Robert M. Mazo
Robert F. Fagot*
Affiliation:
University of Oregon
Robert M. Mazo
Affiliation:
Institute of Theoretical Science, University of Oregon
*
Request for reprints should be sent to Robert F. Fagot, Department of Psychology, University of Oregon, Eugene, Oregon, 97403.
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Abstract

Zegers' (1986) chance-corrected coefficients of association are derived by alternative methods. A different definition of chance correction is used. It is shown that our correction and that of Zegers are identical for large samples. Three possible assumptions for the derivation of metric coefficients are examined. The first, variable reflection, formulated by Zegers and ten Berge (1985), leads to coefficients that require chance-correction. Two other assumptions, zero covariance and covariance reflection, are proposed and it is shown that the latter two assumptions lead directly to coefficients of identity and proportionality that do not require chance correction (i.e., are identical to the Zegers, 1986, corrected coefficients).

Keywords

association coefficientmetric scalesPearson rproduct-moment correlation
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 1 , March 1989 , pp. 93 - 104
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

We are indebted to Robyn M. Dawes, Carnegie-Mellon University, for stimulating our interest in this project, and for helpful suggestions.

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