Signal discovery theory

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The detection theory was developed by John A. Swets and David M. Green and in her book for the first time in 1966 Signal Detection Theory and Psychophysics presented. It analyzes the detection of signals that are difficult to detect and provides a measure of the quality of the person or system responsible for this detection. The response behavior is broken down into the two components sensitivity and response tendency. The sensitivity is a measure of the ability to differentiate between the states "signal present" versus "signal not present", the response tendency is a measure of the extent to which the system is inclined to suspect a signal in the event of uncertainty (and thus to risk "false alarms") ).

The first impetus for this research was provided by the Japanese air raid on Pearl Harbor in December 1941 , which, according to official information, had not been detected by either the radar or the radio surveillance of the US defense. Hence the name receiver operator characteristic (see below).

Original experiment

Green and Swets played many noise samples to their test subjects, some of which only contained noise and some of which also contained a barely audible tone. The test subjects stated whether they heard a tone or just noise. As with most of the earlier psychophysical experiments, it was found that their performance did not only depend on the signal-to-noise ratio (i.e. how clearly the sound stood out from the noise) and their actual detection performance, but was also influenced by many additional factors, including motivation, Vigilance / fatigue, distraction by disturbances, information about the percentage of the noise samples contained tones, etc. Green and Swet's particular interest, however, was in the response tendency that the test subjects showed when they were unsure: some more often opted for “yes, I have one Heard sound ”(so-called liberal criterion), while others answered“ no, I didn't hear a sound ”when in doubt ( conservative criterion). The actual detection performance can only be determined if the response tendency is factored out, as the following example shows:
Two medical students should each examine 20 x-rays, of which, however, they do not know, 10 show a tumor. Student A does not want to overlook anything and decides on 13 images for the diagnosis "tumor". Of these, 9 are recognized correctly and 4 are incorrect. Student B, on the other hand, wants to be absolutely sure and decides on 7 images for "tumor". 6 of them are right and 1 wrong. Both have the same number of correct diagnoses (9 - 4 = 6 - 1), only that student A has a more liberal response criterion than B and therefore a higher number of misdiagnoses (= "false alarms").

Dimensions

The signal may or may not be present and the subject (or detection system) may or may not report a detection, so four combinations are possible:

Signal present no signal available
discovered Hit false alarm ( false positive , English false alarm)
not discovered Missed ( false negative , English miss / false rejection) correct rejection

In order to calculate the sensitivity measure d '(English pronunciation dee prime ), one first determines the relative frequencies of hits and false alarms, carries out a z-transformation with these values and finally forms the difference:
d' = z (hit) - z (false alarm)

Another, less frequently used measure is the tendency to respond (also called the tendency to react):
c = −0.5 * (z (false alarm) + z (hit)).

For example, a young drug detector dog has a relative frequency of hits of 89% (estimate of its probability of hit 0.89) and a relative frequency of false alarms of 59% (estimate of its false alarm probability of 0.59). From the associated z-values ​​z (0.89) = 1.23 and z (0.59) = 0.23, a sensitivity of d '= 1 and a response tendency of −0.73 are calculated. After a few years of “work experience” the dog has a hit rate of 96% and only gives the false alarm in 39% of cases. His detection performance d 'therefore improved to 2.03, while his response tendency c remained the same at −0.74 (which is also to be expected from a dog).

Theoretical assumptions

While originally "noise" actually meant the noise in the headphones of the "receiver operator", today this term encompasses all those internal and external influences that can induce the diagnostician to say "yes" even though there is no signal at all is available. The probability that the noise causes a false alarm is assumed to be normally distributed (the upper bell curve in the figure). Against this background noise, which is always present, the signal must "prevail", ie it is added to the noise. This shifts the probability distribution to the right (the lower bell curve in the picture).
For difficult tasks (low signal-to-noise ratio) the curves are flat and wide and overlap strongly (as in the picture here), for light tasks they are steep and narrow and only slightly overlap.

Normal distributions of signal and noise detection

Whether the “operator” actually says “yes” depends on his answer criterion. In the picture, the threshold is on the right (more "no" than "yes" answers), so he is pursuing a more conservative strategy.

Applications

Signal discovery theory can be used in any type of diagnostics; some of their fields of application are:

In such real situations, there is another important influence on the detection performance, namely how great the benefit of hits and, in particular, how dangerous the consequences of missed ones are.

ROC curve

d 'distribution

A frequently used graphical representation of these metrics is the Isosensitivitäts- or ROC curve ( ROC : English for receiver operating characteristic or German operating characteristic of an observer ). The two medical students from the above example are isosensitive. For this purpose, the relative frequency of hits is plotted against the relative frequency of false alarms. All diagnosticians with the same detection ability are therefore on the same ROC curve: Whoever only guesses (hit rate = miss rate = 0.5, d '= 0) is on a straight line with slope 1.Good (more hits than false alarms, d' > 1) and very good diagnosticians (many more hits than false alarms, d '> 2) lie on more or less strongly convex curves. The ROC curves are therefore independent of the response tendency c. Should our two medical students show their tendency to react, e.g. B. encouraged by a new boss to make a complete change, they would still stay on their ROC curve. This can only be changed through training. On each ROC curve, the conservative respondents (few hits and few false alarms) are in the left (lower) area, the liberal respondents (many hits and many false alarms) in the right (upper) area.

See also

literature

  • Swets, JA (Ed.) (1964) Signal detection and recognition by human observers . New York: Wiley
  • Green, DM, Swets JA (1966) Signal Detection Theory and Psychophysics . New York: Wiley, ISBN 0-471-32420-5
  • Velden, M. (1982) The Signal Discovery Theory in Psychology . Stuttgart: Kohlhammer, ISBN 3-17-004936-4

Web links