Which of the following is NOT true regarding a ROC curve?

The statement that is NOT true regarding a ROC (Receiver Operating Characteristic) curve is that if a signal has greater detectability, there will be a flatter ROC curve. In fact, a signal with greater detectability would result in a ROC curve that is steeper and more towards the upper left corner of the graph. This pattern reflects a higher true positive rate (sensitivity) relative to the false positive rate, indicating a better ability to distinguish between signal and noise.

In contrast, a flatter ROC curve indicates poorer detectability, as it suggests a higher likelihood of false positives relative to true positives. Greater detectability enhances the discriminative ability of the test, emphasizing the importance of the area under the ROC curve, which quantifies the overall performance. A larger area under the curve signifies better test performance, leading to a steeper curve, while a flatter curve corresponds to less effective signal detection.