NCJ Number
68158
Journal
Sociological Methods and Research Volume: 8 Issue: 4 Dated: (MAY 1980) Pages: 420-433
Date Published
1980
Length
14 pages
Annotation
AN ASYMPTOTIC METHOD IS DESCRIBED FOR OBTAINING ESTIMATES OF THE GRIZZLE, STARMER, AND KOCH (GSK) TECHNIQUE FOR THE ANALYSIS OF COMPLEX CONTINGENCY TABLES.
Abstract
THE GSK APPROACH HAS THE ADVANTAGE OF YIELDING, IN ADDITION TO THE CORRELATION COEFFICIENTS, ASYMPTOTIC ESTIMATES OF THE VARIANCES AND COVARIANCES OF THE SET OF COEFFICIENTS. THESE VARIANCES AND COVARIANCES MAY THEN BE USED FOR HYPOTHESIS TESTS CONCERNING THE CORRELATION COEFFICIENTS. WHILE THERE ARE OTHER METHODS OF ESTIMATING THE VARIANCES FOR MOST ORDINAL AND NOMINAL CORRELATION COEFFICIENTS, THE COVARIANCES OBTAINED BY THE GSK METHOD ARE NEEDED TO TEST HYPOTHESES INVOLVING NONINDEPENDENT CORRELATION COEFFICIENTS. THE GSK APPROACH MAY BE USED WHENEVER THE COEFFICIENT INVOLVED IS A COMPOUND FUNCTION OF THE PROPORTIONS IN A CONTINGENCY TABLE. SINCE SEVERAL PARTIAL RANK ORDER COEFFICIENTS MEET THIS CRITERION, THE GSK APPROACH MAY BE USED FOR PARTIAL CORRELATION COEFFICIENTS AS WELL. FOLLOWING A REVIEW OF THE APPLICATION OF THE GSK TECHNIQUE TO RANK ORDER MEASURES OF ASSOCIATION, PARTIAL CORRELATION COEFFICIENTS ARE CONSIDERED (PARTIAL GAMMA AND PARTIAL KENDALL'S TAU). SOME DIFFICULTIES IN SUING THE GSK APPROACH ARE NOTED. ALTHOUGH THE ARTICLE DEALS SOLELY WITH FIRST-ORDER PARTIALS, IT IS ADVISED THAT THE SAME PRINCIPLES COULD BE APPLIED TO HIGHER-ORDER PARTIALS. MATHEMATICAL EQUATIONS, NOTES, AND 16 REFERENCES ARE PROVIDED. (AUTHOR ABSTRACT MODIFIED)