An Exact Test of Significance for Goodman and Kruslkal's Gamma

Publisher Website
Google Scholar
Abstract
Goodman and Kruskal's gamma is a convenient measure of association between ordered polytomies. It is here proposed to perform an exact test of significance of a given gamma by: (a) setting forth all possible sets of all frequencies of the matrix in question, leaving the marginals fixed; (b) computing gamma for each such arrangement; and (c) computing and sum ming the exact probabilities of all such sets where gamma is at least as great as that observed, with the same sign. The method here proposed thus differs somewhat from that of Freeman and Halton (1951); one example was significant according to their test at the .0024 level, but according to the method here proposed at the .1572 level.