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Comparison of two measures of association in two‐way contingency tables
Author(s) -
Hamdan M. A.
Publication year - 1977
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314783
Subject(s) - upper and lower bounds , contingency table , mathematics , measure (data warehouse) , variance (accounting) , statistics , combinatorics , association (psychology) , coefficient of variation , mathematical analysis , computer science , accounting , database , business , philosophy , epistemology
Stuart's (1953) measure of association in contingency tables, t C , based on Kendall's (1962) t , is compared with Goodman and Kruskal's (1954, 1959, 1963, 1972) measure G. First, it is proved that |G| ≥ | t C |; and then it is shown that the upper bound for the asymptotic variance of G is not necessarily always smaller than the upper bound for the asymptotic variance of t C . It is proved, however, that the upper bound for the coefficient of variation of G cannot be larger in absolute value than the upper bound for the coefficient of variation of t C . The asymptotic variance of t C is also derived and hence we obtain an upper bound for this asymptotic variance which is sharper than Stuart's (1953) upper bound.