# ROC

In signal detection theory, a receiver operating characteristic (ROC), or ROC curve, is a graphical plot that illustrates the performance of a binary classifier system as its discrimination threshold is varied.

ROC graphs are two-dimensional graphs in which true positive rate is plotted on the Y axis and false positive rate is plotted on the X axis. An ROC graph depicts relative tradeoffs between benefits (true positives) and costs (false positives).

The true positive rate, also known as the **hit rate** or **recall**, is calculated as *positives correctly identified* / *total positives*. If all positives are correctly identified, we will have a perfect hit rate.

The false positive rate, also known as the **false alarm rate**, is calculated as *negatives incorrectly classified* / *total negatives*. If all negatives were correctly identified, our false alarm rate is zero.

The sensitivity is also known as the true positive rate.

The specificity is calculated as

(*True negatives*) / (*False positives* + *True negatives*)