Signal detection theory

A psychological theory regarding a threshold of sensory detection.

One of the early goals of psychologists was to measure the sensitivity of our sensory systems. This activity led to the development of the idea of a threshold, the least intense amount of stimulation needed for a person to be able to see, hear, feel, or detect the stimulus. Unfortunately, one of the problems with this concept was that even though the level of stimulation remained constant, people were inconsistent in detecting the stimulus. Factors other than the sensitivity of sense receptors influence the signal detection process. There is no single, fixed value below which a person never detects the stimulus and above which the person always detects it. In general, psychologists typically define threshold as that intensity of stimulation that a person can detect some percentage of the time, for example, 50 percent of the time.

An approach to resolving this dilemma is provided by signal detection theory. This approach abandons the idea of a threshold. Instead, the theory involves treating detection of the stimulus as a decision-making process, part of which is determined by the nature of the stimulus, by how sensitive a person is to the stimulus, and by cognitive factors. In other words, a person will be able to detect more intense sounds or lights more easily than less intense stimuli. Further, a more sensitive person requires less stimulus intensity than a less sensitive person would. Finally, when a person is quite uncertain as to whether the stimulus was present, the individual will decide based on what kind of mistake in judgment is worse: to say that no stimulus was present when there actually was one or to say that there was a stimulus when, in reality, there was none.

An example from everyday life illustrates this point. Suppose a person is expecting an important visitor, someone that it would be unfortunate to miss. As time goes on, the person begins to "hear" the visitor and may open the door, only to find that nobody is there. This person is "detecting" a stimulus, or signal, that is not there because it would be worse to miss the person than to check to see if the individual is there, only to find that the visitor has not yet arrived.

In a typical sensory experiment that involves a large number of trials, an observer must try to detect a very faint sound or light that varies in intensity from clearly below normal detection levels to clearly above. The person responds positively (i.e., there is a stimulus) or negatively (i.e., there is no stimulus). There are two possible responses, "Yes" and "No." There are also two different possibilities for the stimulus, either present or absent. The accompanying table describes the combination of an observer's response and whether the stimulus is actually there. The table refers to a task with an auditory stimulus, but it could be modified to involve stimuli for any sense.

Psychologists have established that when stimuli are difficult to detect, cognitive factors are critical in the decision an observer makes. If a person participates in an experiment and receives one dollar for each Hit and there is no penalty for a False Alarm, then it is in the person's best interest to say that the stimulus was present whenever there is uncertainty. On the other hand, if the person loses two dollars for each False Alarm, then it is better for the observer to be cautious in saying that a stimulus occurred. This combination of rewards and penalties for correct and incorrect decisions is referred to as the Payoff Matrix. If the Payoff Matrix changes, then the person's pattern of responses will also change. This alteration in responses is called a criterion shift.

There is always a trade-off between the number of Hits and False Alarms. When a person is very willing to say that the signal was present, that individual will show

more Hits, but will also have more False Alarms. Fewer Hits will be associated with fewer False Alarms. As such, the number of Hits is not a very revealing indicator of how sensitive a person is; if the person claims to have heard the stimulus on every single trial, then the person will have said "Yes" in every instance in which the stimulus was actually there. This is not very impressive, however, because the person will also have said "Yes" on every trial on which there was no stimulus. Psychologists have used mathematical approaches to determine the sensitivity of an individual for any given pattern of Hits and False Alarms; this index of sensitivity is called d' (called d-prime). A large value of d' reflects greater sensitivity.

The basic idea behind signal detection theory is that neurons are constantly sending information to the brain , even when no stimuli are present. This is called neural noise. The level of neural noise fluctuates constantly. When a faint stimulus, or signal, occurs, it creates a neural response. The brain must decide whether the neural activity reflects noise alone, or whether there was also a signal.

For very intense signals, there is no problem in deciding if there was a stimulus because the neural effect of the signal far outweighs the neural effect of the noise. Similarly, when there is no signal, the nervous system does not respond as it does when an outside signal is present, so decisions are easy. On the other hand, for near-threshold signals, it can be difficult to know whether neural activity results from noise alone or from a signal plus noise. At this point, the observer makes a decision based on the payoff matrix.

Further Reading

Goldstein, E.B. Sensation and Perception, 3rd ed. Belmont, CA: Wadsworth Publishing Company, 1989.