A Partial Coefficient for Goodman and Kruskal's Gamma

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Abstract
Following Goodman and Kruskal's interpretation of their coefficient, γA,B, a partial coefficient, γA, B|C is defined as “how much more probable it is to get like than unlike orders in measures A and B when pairs of individuals differing on A and on B and tied on C but unselected on any other measure are chosen at random from the population.” It is shown that this coefficient is a weighted sum of the values of γ in the various strata defined by categories of C, where the weight in stratum i is its proportion of the total pairs which differ on A and B and are tied on C. An empirical example illustrates the calculation of the co-efficient.

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