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When observers are asked whether they detected a signal, they will respond 'yes' if their neural systems have reached a certain criterion level of intensity. This level can be manipulated by changes in expectancy, which depends on the perceived costs and benefits of various responses, and is affected by the observer's motivation, through such things as attention and effort devoted to the task.
Because noise can sometimes look like a signal, (or vice versa) the responses of the observer fall into four categories. The green area to the right of the criterion line shows the probability (out of 1, because these are normalized curves) that the observer will respond "yes" when a signal is present (a hit). The green area to the left of the criterion is the probability that the observer will respond "no" when a signal is present (a miss). The blue area to the right of the criterion is the probability that the observer will respond "yes" when the target signal is not present (a false alarm). The remaining blue shows the probability that the observer will respond "no" when the signal is not present (a correct rejection). In tabular form:
|State of the world||Yes, there was a signal||No, there wasn't a signal|
Another piece of information that can be useful is the probability of a signal occuring. This probability is one way to influence the observer's expectancy, which will change the pattern of responses. In real situations, the costs and benefits of each of the four possible combinations of signal and response will also influence the observer's responses. Usually the two kinds of errors carry different costs. For example, an air traffic controller's false alarm may lead to rerouting or delaying a flight, while a miss could lead to a crash. In an assembly line, a false alarm may result in additional testing cost or junking a part, while a miss may require later repair or replacement.