What does a flatter ROC curve indicate about the signal's detectability?

A flatter Receiver Operating Characteristic (ROC) curve indicates less effective signal detection, which translates to reduced detectability of the signal. The ROC curve is a graphical representation that illustrates the trade-off between the true positive rate and the false positive rate for a binary classifier as its discrimination threshold is varied.

When the ROC curve is flatter, it reflects a lower true positive rate (hit rate) for a given false positive rate, meaning that the system is generally less effective at distinguishing between the presence and absence of the signal. This results in a decreased likelihood of correctly identifying true signals when they are present.

Thus, rather than suggesting greater detectability, a flatter ROC curve signifies less accuracy and more difficulty in reliably detecting true positive signals, leading to a suboptimal performance in distinguishing between the two classes. This is why the implication of "greater detectability" is not accurate in this context. Note that the implications of accuracy, hit rate, and false positive rates follow from this same principle of how the ROC curve represents performance.