Measures of association for Analyze Binary Response for Response Surface Design

Find definitions and interpretation guidance for every statistic in the Measures of association table.

In This Topic

Pairs
Somers' D
Goodman-Kruskal Gamma
Kendall's Tau-a

Pairs

For binary logistic regression, each observed event is paired with each non-event. These categories describe the pairs:

Concordant: The predicted probability that the event occurs is higher for the observation where the event occurred.
Discordant: The predicted probability that the event occurs is lower for the observation where the event occurred.
Tie: The predicted probability that the event occurs is the same for the observation where the event occurs and the observation where the non-event occurred.

Interpretation

Use the numbers of pairs to compare the predictive performance of models. The higher the percentage of concordant pairs, the better the model performs.

Somers' D

Somers' D is the proportion difference between concordant and discordant pairs, including ties.

Interpretation

Use Somers' D to compare the predictive performance of models. Higher values indicate better predictive performance. For example, if 75% of the pairs are concordant and 25% are discordant, then Somers' D is 0.5.

Somers' D and the Goodman-Kruskal Gamma statistic are identical when the model predicts 0 tied pairs. The more tied pairs, the more the Goodman-Kruskal Gamma statistic exceeds Somers' D.

Goodman-Kruskal Gamma

Goodman-Kruskal Gamma is the proportion difference between concordant and discordant pairs, excluding ties.

Interpretation

Use the Goodman-Kruskal Gamma to compare the predictive performance of models. Higher values indicate better predictive performance. For example, if 75% of the non-tied pairs are concordant and 25% are discordant, the Goodman-Kruskal Gamma is 0.5.

Somers' D and the Goodman-Kruskal Gamma statistic are identical when the model predicts 0 tied pairs. The more tied pairs, the more the Goodman-Kruskal Gamma statistic exceeds Somers' D.

Kendall's Tau-a

Kendall's Tau-a is the proportion difference of concordant and discordant pairs out of all possible pairs, including pairs with the same response value.

Interpretation

Use Kendall's Tau-a to compare the predictive performance of models. Higher values indicate better predictive performance. Kendall's Tau-a is always lower than Somers' D and the Goodman-Kruskal Gamma statistic because those two statistics do not include pairs with the same response value.