The theory of signal detectability consists of statistical decision theory and the theory of ideal observers. At the heart of TSD is the fundamental detection problem, which is the task of discriminating between two events. One event is a signal added to noise and the other event is noise alone. The observer never has access to the events directly, only access to some evidence, which has a probability conditional on either event. This evidence is weighed up, along with the prior probabilities of the events, to form a decision as to which event occurred.

The evidence is a result of some sort of transformation of the original stimuli, this transformation may be due to physiological and psychological processes in a real observer, electronic or electrical processes in a electric-analog-model, and mathematical transformations in an ideal observer.

Receiver-Operating Characteristic (ROC) analysis is performed to measure how well the observer discriminates between the two events. An ROC curve is a simply a graph of the observers' Hit Rate versus the False Alarm Rate for all possible response criteria. Or in other words, the Hit Rate is the proportion of correct Yes decisions and the False Alarm Rate is the proportion of incorrect Yes decisions. The further the ROC curve is away from the chance line, thebetter the performance. The area under the ROC curve is a useful measure of detectability. It varies between 0 and 1 with 0.5 being chance performance.