What is signal detection theory?

Introduction

Signal detection theory is not so much a “theory” in the traditional sense as it is a term used to describe certain types of measurement procedures. Developed by mathematicians and engineers at the University of Michigan, Harvard University, and the Massachusetts Institute of Technology in the 1950s, signal detection theory is based on a method of statistical hypothesis testing and on findings in electronic communication. It provides a method to measure two factors independently: a person’s sensitivity to sound or other stimulation, and any bias (a consistent tendency to respond positively or negatively in a situation) or decision criterion the person might adopt that affects his or her performance during a sensitivity test.

A typical measurement procedure might involve detection of sound in a quiet room. In an acoustically insulated chamber, an individual puts on earphones and is told to pay attention to a small warning light that comes on periodically. The individual is instructed to report, for each occurrence of the warning light, whether a sound is heard through the earphones at that time. The sounds coming through the earphones vary in intensity, though not in frequency; they may initially be of very low amplitude, or they may be readily audible. Indeed, the warning light may come on with no sound at all; this is a “catch” trial—a situation designed to catch someone who simply pretends to hear a sound every time the light comes on. No matter what the sound, the individual being tested must respond with “Yes, I heard a sound” or “No, I heard nothing.”

Much of the time the response is “yes” when a sound is present; this is called a hit, because it is a correct recognition of the stimulus. Often, when no sound is presented, the individual says “no,” giving a correct rejection. Sometimes, however, the response is “yes” when no sound is present, which is a false alarm, and sometimes the individual says “no” when the sound is in fact present, which is a miss. Thus the experimenter collects data showing the number of hits, false alarms, misses, and correct rejections for each individual participant.

Individuals are told exactly what proportion of the trials will be catch trials (in a study measuring sensitivity to certain stimuli, a trial in which no stimulus is presented). This gives them some idea of what to expect. If the experiment were set up with 90 percent catch trials and participants in the study were given no knowledge of this, they might think, hearing so little, that something was wrong with the earphones. These same people would expect a session with 20 percent catch trials, for example, to sound very different. When there is a lower proportion of catch trials, individuals tend to respond “yes” more than when the proportion is higher; thus, they maximize hits and (since there are few catch trials) cannot make many false alarms. If there is a high proportion of catch trials, individuals tend to say “no” more, thus making fewer false alarms, but also making fewer hits. Thus, both hits and false alarms vary depending on the number of catch trials, even though the sound intensities are exactly the same in each of these conditions.

Role of Educated Guessing

If one took part in a trial without putting on the earphones, one could only guess whether a sound is present. In guessing, however, one might guess “yes” more frequently if told there would be few, rather than many, catch trials. This educated guessing is what a normal participant does. When unsure as to the presence of a sound, people guess; the probability of guessing “yes” is given by the proportion of catch trials. The psychologist collecting these data determines the number of hits and false alarms for each individual and compares them with a “guessing line”: the percentage of hits and false alarms for a participant who merely guesses. The degree of difference between these two modes of response is a pure measure of sensitivity; bias has been eliminated with the guessing baseline. Sensitivity is high when the individual hears most of the sounds presented and has to guess on few of them, and it is low when many of the responses are guesses.

Determining Bias and Effect of Personality

The experimenter also determines each person’s bias, or decision criterion, in responding. The decision criterion, which changes whenever the number of catch trials changes, may also be influenced by other factors. For example, there is always some noise going on when a stimulus is received. Even in an acoustically quiet chamber, there are sounds from one’s own heart, blood rushing through vessels, and breathing. These vary from moment to moment, and they influence perception of other sounds, particularly those that may seem very weak. Outside a quiet chamber, there are other noisy background sounds: hums of air conditioners, computers, street traffic, and so on.

In addition, people who participate in these measurement studies bring different decision criteria that are characteristic of their own personalities. For example, a participant may not respond with a “yes” unless absolutely certain that a sound is present, saying “no” otherwise and thus failing to make all the hits—but also making few false alarms. Another might respond with a “yes” whenever it seems as though a sound could conceivably be present and say “no” only when absolutely certain there is no sound. These two people might have the same sensitivity—that is, they could perceive the sounds equally well—but the number of sounds presented that they identify correctly would be different. They would therefore achieve equal measures of sensitivity but very different measures of bias. Signal detection theory, then, provides an ingenious method for the measurement of an individual’s sensitivity to sounds or other stimuli independent of factors that impinge on that individual’s decision.

Perceptual Vigilance

Signal detection methods are applied in studies in which a stimulus or event is to be detected. Used to separate sensation from motivational bias, these methods are most successful with simple stimuli.

One of the earliest and simplest of these studies involves perceptual vigilance. The basic task is to detect a few signals against a background pattern of noise similar to the signal. The best known of these displays is the Mackworth clock, which presents clockwise jumps of a black pointer across a white field. The signal jumps are twice as large as the repetitive background jumps, and they occur at irregular time intervals ranging, for example, from forty-five seconds to ten minutes. The noise occurs at a high rate and is constant, regular, and monotonous.

An observer sits in a small cubicle for half-hour periods, watching this moving pointer and responding only when the pointer makes a long jump. At the beginning, attention is high and the observer makes few errors. As time goes on, however, the observer tires, loses concentration, and begins missing signals. The jumps all begin to look alike; after an hour or so, one in every four or five long jumps may be missed. There are few, if any, false alarms.

This vigilance decrement occurs with listening tasks as well. In fact, it is a common observance in nearly all tests of
attention and is applicable to many everyday situations: factory workers monitoring displays on shift, inspectors in industry examining merchandise for flaws, even students sitting in classrooms listening for important points in lectures. Although psychologists were aware of these declines before the theory of signal detection was formulated, their study changed with the method. They began to address new questions. What difference does the nature of the noise make? How might the observer shift the bias, or criterion of response, over time or different situations?

It is perhaps not surprising to find that sensitivity is higher when the signal is most different from the background noise. More interesting is the finding that if there are very few signals, there often is no measurable decline in sensitivity, even if the observers miss more signals over time. This occurs because they also make fewer false alarms over the same time; that is, they become more cautious in their responses—a shift in bias. One sees shifts of bias of this sort in many situations. For example, a physician may diagnose a disease on the basis of insufficient data in cases where failure to detect it would be disastrous and making a false alarm would be relatively insignificant. On the other hand, military personnel would not want to begin sending out retaliatory nuclear weapons against an enemy unless they are absolutely certain that the attack to which they are responding is actually occurring. A false alarm here would be unthinkable, so they exhibit extreme caution—a very high bias against a response.

Use in Human Research and Psychology

Signal detection theory has been helpful in applied human research, perceptual studies, and studies of memory. Measures of sensitivity in memory parallel those in perception. Effects of variables such as aging, brain dysfunctions such as epilepsy, brain insults such as concussions, or periods of oxygen deprivation have been examined more recently for their effects on sensitivity. In a 1977 signal detection study of head-injured patients, Diane McCarthy found that patients recovering from concussions show, during the acute stages of head injury, sensitivity scores similar to an elderly population and considerably lower than normal control subjects. They also show some residual deficit six weeks later, even when the head injury is not severe. Interestingly, this shows a period of reduced sensitivity to stimulation, not merely confusion.

Signal detection theory has provided a routine method in experimental psychology. It is applied in situations where a pure measure of sensitivity, unaffected by changing criteria, is desired. Additionally, it may be used when the target of interest is the criterion or bias itself—for example, in studies of personality factors in response decisions.

Study of Threshold

In the late nineteenth century, experimenters in psychophysics—the study of the relationship between the physical properties of stimuli and the ways in which they are perceived—questioned how accurately people’s perceptions correspond to the physical stimulation they receive. They asked to what extent a person’s reported perception actually reflects the physical changes happening in the real world.

One way of answering this was to try to discover how strong a stimulus needs to be before it is noticed or detected. There are sounds, for example, so soft that they cannot be heard, or can be heard only by a few individuals, and there are sounds so intense that all hearing individuals detect them. At what point in increasingly intense levels is a sound just barely detectable? Psychophysicists called this level the threshold, or limen. They assumed that this level of intensity was like the threshold of a door, in that one is either inside or outside, never in between. They assumed that all sounds less intense than the threshold—all stimulation that is subliminal, or below the limen—would never be detected and that all sounds more intense than the threshold would always be detected.

With this theory in hand, experimental psychologists began measuring thresholds. For example, they determined empirically how much sugar must go into a certain amount of distilled water at a given temperature before it can be tasted, how intensely a 440-hertz sound has to be played under certain acoustical conditions before it is heard, and how intense a spot of white light has to be in a darkened room for a dark-adapted subject to detect it in peripheral vision. However, while making measurements, they ran into difficulties.

Measured thresholds were always imprecise, as the only measurement taken was the occurrence of hits. They were unlike the threshold of a door, a line with no breadth. Sometimes an individual would report hearing a sound that was very weak, then report not hearing a sound that was quite a bit more intense. Most of the time, however, intense sounds were heard and weak ones were not, so that researchers calculated an average—an intensity of sound that a subject reported hearing 50 percent of the time. This they defined empirically as the threshold, assuming that their inability to measure a point perfectly was attributable simply to procedural error or imprecise measurement.

Increasingly, however, researchers began to recognize that threshold measures were contaminated, or confounded, by other factors, such as how important it seemed to a person not to let a sound go unnoticed or not to appear foolish by saying a sound was heard when there was no sound at all. Signal detection theory provided an alternative, a method for determining a person’s sensitivity to a stimulus independent of any bias in response. These methods are now a standard part of experimental psychology, providing another way to determine how perceptions correspond to physical changes in the real world.

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