Signal detection theory explains how people detect faint stimuli under conditions of uncertainty. It separates true sensitivity from the decision criterion that a person adopts.

On every trial a stimulus may or may not be present. The observer responds “yes” or “no.” Hits, misses, false alarms, and correct rejections are tallied. Sensitivity (d′) reflects how well the signal can be distinguished from noise; the criterion reflects how willing the observer is to say “yes.” A liberal criterion produces more hits and more false alarms; a conservative criterion produces fewer of both.

The theory applies to radar operation, medical diagnosis, eyewitness identification, and any situation in which a weak signal must be distinguished from background noise. It shows that detection is not a simple matter of threshold but a decision process influenced by expectations, payoffs, and experience. Training and feedback can improve both sensitivity and the appropriateness of the criterion.

Whether a faint signal is reported depends on both the strength of the evidence and the observer’s willingness to decide that it is there.