Kruskal's Gamma

Author: Hans Lohninger

Gamma, also called Goodman and Kruskal's gamma, is a symmetric measure which varies from +1 to -1, based on the difference between concordant pairs (P) and discordant pairs (Q). The concept of pairs is discussed separately in the section on association. That is, gamma is computed as (P - Q)/(P + Q).

Gamma is the surplus of concordant pairs over discordant pairs, as a percentage of all pairs ignoring ties. This can be given a PRE (proportionate reduction in error) interpretation. If we ignore tied pairs and are guessing the ranking of two pairs based on knowledge of the independent (column) variable x, then if we are presented with the x values for two randomly selected pairs, we will predict that if the second x is more than the first, then the rank of the second y value will be greater than the rank of the first y value. If gamma is .636, we may say that knowing the the independent variable reduces our errors in predicting the rank (not value) of the dependent variable by 63.6%.

Gamma defines perfect association as weak monotonicity (see discussion in the section on association). Under statistical independence, gamma will be 0, but it can be 0 at other times as well (whenever concordant minus discordant pairs are 0).