The Measures of Association table contains the following:

·    Pairs information, which contains the number and percent of pairs of observations with different response values that are concordant pairs, discordant pairs, and tied pairs.

·    Somers' D, which shows how many more concordant than discordant pairs exist divided by the total number of pairs.

·    Goodman-Kruskal Gamma, which shows how many more concordant than discordant pairs exist divided by the total number of pairs excluding ties.

·    Kendall's Tau-a, which shows how many more concordant than discordant pairs exist divided by the total number of pairs of observations including pairs with the same response value.

To create the pairs used in these statistics, each observed "success" is paired with every "failure." It is then noted whether the probability of success predicted from the model is higher for the actual "success."

·    If the predicted probability of success is higher for the observation corresponding to a "success," the pair is considered concordant.

·    If the predicted probability of success is higher for the observation corresponding to a "failure," the pair is considered discordant.

·    If the predicted probability of success is the same for both the observed "success" and the observed "failure," the pair is considered tied.

Larger values for Somers' D, Goodman-Kruskal Gamma, and Kendall's Tau-a indicate that the model has better predictive ability.

For the cereal data, 72.9% of the pairs were concordant, while 26.3% of the pairs were discordant. Thus, there is almost a 50% better chance for a pair to be concordant than discordant.

Somers' D (0.47) and Goodman-Kruskal Gamma (0.47) are very close to one another because there are very few tied pairs. They tell you how many more concordant pairs exist as a percentage of the total number of pairs. Somers' D includes tied pairs in this calculation, Goodman-Kruskal Gamma does not.