Abstract
The asymptotic sampling theory discussed in our 1963 article [3] for measures of association presented in earlier articles [1, 2] turns on the derivation of asymptotic variances that may be complex and tedious in specific cases. In the present article, we simplify and unify these derivations by exploiting the expression of measures of association as ratios. Comments on the use of asymptotic variances, and on a trap in their calculation, are also given.
This research was supported in part by National Science Foundation Research Grants Nos. NSF GS 2818 and NSF GP 16071. Some of the second author’s work on the article was done while he was a Fellow at the Center for Advanced Studies in the Behavioral Sciences and holding a National Science Foundation Senior Post-doctoral Fellowship. The authors are grateful to Stephen Fienberg (University of Chicago) and to Robert Somers (University of California, Berkeley) for helpful suggestions.
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References
Goodman, Leo A. and Kruskal, William H., “Measures of Association for Cross Classifications,” Journal of the American Statistical Association, 49 (December 1954), 732–64.
Goodman, Leo A. and Kruskal, William H., “Measures of Association for Cross Classifications, II: Further Discussion and References,” Journal of the American Statistical Association, 54 (March 1959), 123–63.
Goodman, Leo A. and Kruskal, William H., “Measures of Association for Cross Classifications, III: Approximate Sampling Theory,” Journal of the American Statistical Association, 58 (June 1963), 310–64.
Rosenthal, Irene, “Distribution of the Sample Version of the Measure of Association, Gamma,” Journal of the American Statistical Association, 61 (June 1966), 440–53.
Somers, Robert H., “A New Asymmetric Measure of Association for Ordinal Variables,” American Sociological Review, 27 (December 1962), 799–811.
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© 1979 Springer-Verlag New York
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Goodman, L.A., Kruskal, W.H. (1979). Measures of Association for Cross Classifications. IV: Simplification of Asymptotic Variances. In: Measures of Association for Cross Classifications. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9995-0_4
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DOI: https://doi.org/10.1007/978-1-4612-9995-0_4
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