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A Modification of Kendall's Tau for Measuring Association in Contingency Tables

Published online by Cambridge University Press:  01 January 2025

Bertram P. Karon  and
Irving E. Alexander
Bertram P. Karon
Affiliation:
Princeton University
Irving E. Alexander
Affiliation:
Princeton University
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Abstract

A coefficient of association τ′ is described for a contingency table containing data classified into two sets of ordered categories. Within each of the two sets the number of categories or the number of cases in each category need not be the same. τ′=+1 for perfect positive association and has an expectation of 0 for chance association. In many cases τ′ also has a -1 as a lower limit. The limitations of Kendall&s τ′a and τ′b and Stuart&s τ′c are discussed, as is the identity of these coefficients to τ′ under certain conditions. Computational procedure for τ′ is given.

Type
Original Paper
Information
Psychometrika , Volume 23 , Issue 4 , December 1958 , pp. 379 - 383
Copyright
Copyright © 1958 The Psychometric Society

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References

Kendall, M. G. Rank correlation methods, London: Griffin, 1948.Google Scholar
Macht, L. B. An application of the resultant weighted valence theory of level of aspiration to the study of occupational preference. Unpublished undergraduate thesis, Princeton Univ., 1957.Google Scholar
Stuart, A. The estimation and comparison of strength of association in contingency tables. Biometrika, 1953, 40, 105–110.CrossRefGoogle Scholar