An area under the ROC curve of 0.5 indicates what?

• A. No discriminative ability; performance equivalent to random chance
• B. Perfect discrimination
• C. Excellent discrimination
• D. Moderate discrimination

Answer: (A)

The key idea is what the area under the ROC curve represents: the model’s ability to distinguish between positives and negatives. An AUC of 0.5 means the model’s scoring is no better than random chance. If you plotted the ROC curve, it would lie on the diagonal from 0,0 to 1,1, indicating that the true positive rate and false positive rate align as they would with a coin flip. In other words, the model has no discriminative power to separate cases from non-cases. For contrast, an AUC of 1.0 would indicate perfect discrimination, while lower values indicate some level of ability.