Detection theory, or signal detection theory, is a means to quantify the ability to discern between signal and noise. It has applications in many fields such as quality control, telecommunications, and psychology. The concept is similar to the signal to noise ratio used in the sciences, and it is also usable in alarm management, where it is important to separate important events from background noise.
According to the theory, there are a number of psychological determiners of how we will detect a signal, and where our threshold levels will be. Experience, expectations, physiological state (e.g, fatigue) and other factors affect thresholds. For instance, a sentry in wartime will likely detect fainter stimuli than the same sentry in peacetime.
Outline edit
Detection theory assumes that among a larger pool of events there exist certain target events, and that these targets differ from non-target events on some dimension. Receivers may either detect or not detect a target event (irrespective of whether it was a target event), producing the following Matrix.
| Target | |||
|---|---|---|---|
| Present | Absent | ||
| Receiver Response | "Yes" | Hit | False Alarm |
| "No" | Miss | Correct Rejection | |
There are two correct responses, Hits where the receiver correctly identifies a target, and Correct Rejections where a non-target is correctly not identified as a target. The corresponding errors are False Alarms where non-target events are identified as targets, and Misses where target events are not identified as targets. For example, using a legal analogy, a guilty defendant convicted by a jury would be a hit, but if the defendent were acquitted, it would be miss. Conversely, an innocent defendant who was convicted would be a false alarm, but if they were acquitted, it would be a correct rejection. This analogy also illustrated two important points about detection theory. Firstly, in an ideal world, convictions of the guilty and acquittals of the innocent should be maximised, and concomitantly, as few wrongful convictions and false acquittals should occur. Detection theory is often graphically illustrated with probality distributions presented on a strength of evidence axis. As the figure shows, the distribution for target events has a higher mean (i.e., further right) than the non-target distribution. The decision criterion (c) determines whether each event is detected as a target or not. Events to the right of the criterion are identified as targets (irrespective of whether an event is a target or not), and similarly, events to the left are not identified as targets.
Discriminibility edit
Conceptually, discriminibility refers to how hard or easy it is to detect a target from background events. For example, in a recognition memory paradigm, having longer to learn to-be-remembered words, makes it easier to recognised previously seen words. In contrast, having to remember 30 words rather than 5 makes the discrimination harder.
In a graphical depiction, easier discriminibility usually occurs either where the target distribution is located further from the non-target distribution, where the distributions are narrower, or a combination of the two (with the effects being additive). For example, if the detection rule to separate men and women was 'height greater than 1.7m', the large overlap in height distribution and the relatively small mean difference would make for relatively poor discriminibility. In contrast, distinguishing adults from children with a criterion at 1.4m would have better discriminibility due to a greater mean difference.
Bias edit
Bias is the extent to which one response is more probably than another. For example, requiring a unanimous jury for a conviction produces a conservative bias. That is, there is a lower probability of a "guilty" verdict if the jury must be unanamous, as compared to where there is allowed to be a single dissenter.
Bias is independent of discriminibility. Thus, adopting a more liberal criterion has little effect on accuracy, or on the ease of the task. Thus, accepting jury verdicts with one dissenting juror will increase the number of legitimate convictions, but will also increase the number of false convictions. Similarly, marking an exam more strictly will reduce the number of people passing who should have passed, but will also fail more people who should have passed.
Psychology edit
Signal detection theory (sdt) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions. Sdt assumes that 'the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgements under conditions of uncertainty." In foggy circumstances, we are forced to decide how far an object is away from us based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much further away than it actually is.
In order to measure discriminability (sensitivity) and prejudice, psychologists measure "hits" and "correct negatives" (correctly responding to the presence and absence of stimulus, respectively), as well as "false alarms" (incorrectly responding to the absent stimulus) and "misses." By measuring these variables, psychologists can determine how a person perceives an event under varying conditions
See also edit
References edit
- Coren, S., Ward, L.M., Enns, J. T. (1994) Sensation and Perception. (4th Ed.) Toronto: Harcourt Brace.
- Kay, SM. Fundamentals of Statistical Signal Processing: Detection Theory (ISBN 0-13-504135-X)
- McNichol, D. (1972) A Primer of Signal Detection Theory. London: George Allen & Unwin.
- Van Trees HL. Detection, Estimation, and Modulation Theory, Part 1 (ISBN 0-47-109517-6; website)