Goodman and Kruskal's Gamma

Goodman and Kruskal's gamma (or gamma, for short) is a symmetric measure of association (correlation) which delivers values in the range of -1.0 to +1.0. The idea behind gamma is to measure the relative difference of concordant and discordant⁽¹⁾ pairs in a sorted list of paired observations (ignoring ties).

If the number of concordant pairs is P, and the number of discordant pairs is denoted by Q, then gamma is calculated according to the following formula:

Goodman and Kruskal's gamma is approximately normally distributed for large samples. Thus it is possible to calculate p-values and/or a level of significance.

Caution:

A zero gamma value obtained for non-dichotomous variables does not necessarily mean that there is no correlation among the two variables. On the other hand, if the two variables are uncorrelated then gamma will be zero in any case.

(1)	Concordant/discordant pairs are defined as follows: if we sort the x/y-pairs according to x in ascending order and look at a particular pair, then this pair is said to be concordant if the y value is higher than the y value of the previous pair. For a discordant pair the y value is lower than the previous y value.