Measures of association for Analyze Binary Response for Factorial Design

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

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.

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