ROC Curve
Definition
Receiver operating characteristic curve: a plot of sensitivity (y-axis) against FPR (x-axis) as the decision threshold is swept from its most lenient to its most stringent value. The area under the ROC curve (AUC) summarises discriminating power, ranging from 0.5 (chance) to 1.0 (perfect).
- Axes
- Sensitivity (y) versus false positive rate (x)
- Generated by
- Sweeping the decision threshold from lenient to stringent
- Summary statistic
- Area under the curve (AUC), 0.5 to 1.0
- AUC 0.5
- Chance-level discrimination
- AUC 1.0
- Perfect discrimination
Common questions
How does an ROC curve help choose an operating threshold, not just report AUC?+
Each point on the curve corresponds to a specific threshold's sensitivity and false positive rate pair, so an analyst can pick a threshold that meets a target false positive rate for a given application rather than relying on AUC alone.
Why is AUC preferred over a single accuracy number for comparing methods?+
A single accuracy figure depends on the threshold chosen, while AUC summarises performance across every possible threshold, making it a fairer basis for comparing two detection systems independent of where each sets its cutoff.
What does a curve that bows toward the top-left corner indicate?+
It indicates the system achieves high sensitivity while keeping the false positive rate low, meaning it separates true and false cases well across a wide range of thresholds.
Related terms
- Decision Threshold
- The cut-off score above which a classification method declares a positive result. Raising the threshold reduces FPR but increases FNR; lowering it...
- False Negative Rate (FNR)
- The proportion of true matches (or true positives) that a classification method fails to detect, declaring them as non-matches. Also called the...
- False Positive Rate (FPR)
- The proportion of true non-matches (or true negatives) that a classification method declares as matches (or positives). Also called the type I...
- Sensitivity (True Positive Rate)
- The proportion of true matches correctly identified as matches. Sensitivity = TP / (TP + FN) = 1 minus FNR. A method...
- Specificity (True Negative Rate)
- The proportion of true non-matches correctly identified as non-matches. Specificity = TN / (TN + FP) = 1 minus FPR. A method...