# Signal Detection: Summary and Follow Up Questions

Signal Detection Theory (SDT) allows an analyst to separate sensitivity from response bias. Observers are assumed to make decisions based upon information derived from two distributions. The first (Signal Absent) is assumed to represent a background level of “noise.” The second distribution (Signal Present) represents an addition to the background level of noise caused by the introduction of a stimulus. That is why the second distribution is sometimes referred to as the ‘Signal + Noise‘ distribution.

An observer’s sensitivity, as indexed by d’, is how well the observer can differentiate items coming from the Signal Absent and Signal Present distributions. Criterion (i.e., response bias) represents the minimum level of internal certainty needed for the observer to decide that a signal was present. ROCs represent the relationship between hits and false alarms, and can be used to describe performance in terms of d’. SDT has applications in fields such as medical diagnosis, bioinformatics, psychology, and engineering.

#### Follow-up Questions

Use the SDT applet to help you with these questions.

1) Participant A had a hit rate of .82 and a false alarm rate equal to .24. Participant B had a hit rate of .82 and a false alarm rate of .40. Compare these two participants in terms of the d’ and criterion scores.

Participants A and B have the same hit rate (.82), but A has greater sensitivity, as evidenced by a lower false alarm rate (.24 vs. .40). The d’ is 1.62 for Participant A, and 1.17 for Participant B. The criterion values for A and B are .71 and .25, respectively. This means that A is more conservative than B, requiring stronger evidence of a signal before indicating that the signal is present.

2) A construction worker sued his employer over a work-related injury. He contended that loud noises at the construction site ruined his hearing, leaving him totally deaf. The insurance company representing the construction company wanted to find out how damaged his hearing really is. To do so, they constructed a “yes-no” hearing test in which half of the trials contain a signal that is quiet, but is readily perceivable to someone with normal hearing, and half contain no signal. The response rates are listed in the table below. Calculate d’ and give your conclusion as to whether the worker really is totally deaf.

Proportions:

 Signal Present Signal Absent Say “yes” .10 .50 Say “no” .90 .50

What is the Hit rate, False Alarm rate, d’, and Criterion measure?

The construction worker probably is malingering. That is, he is pretending to have a greater hearing deficit than he actually does. How do we know this? If he was actually deaf, his hit rate and false alarm rate would be approximately equal, producing d’ near zero. His false alarm rate is .50, as would be expected if he was guessing, but his hit rate is .10. These hit and false alarm rates yields a d’ value of -1.28.

What’s your conclusion concerning his hearing status? Why?

What this means is that in situations where there was no signal, he was simply guessing (false alarm rate = .50). If he really couldn’t hear any of the test stimuli, then his hit rate should also have been around .50. However, his very low hit rate of .10 suggests that when he heard a signal he was more likely to say “no” than “yes” and that produced a negative d’ value. We can see from this example that Signal Detection Theory can be used to measure sensitivity to different types of items as well as decision strategies of participants.

3) Using the SDT applet, create three situations that yield a d’ of approximately 1.

a) Hit rate = .85, False Alarm rate = ?

b) False Alarm rate = .40, Hit rate = ?

c) Hit rate = .30, False Alarm rate = ?

a) False Alarm rate = .52

b) Hit rate = .77

c) False Alarm rate = .065

#### Selected Books on Signal Detection Theory

Swets, J. A. (1996). Signal detection theory and ROC analysis in psychology and diagnostics: Collected papers. Mahwah, N.J.: L. Erlbaum Associates.

Wickens, T. D. (2002). Elementary signal detection theory. Oxford; New York: Oxford University Press.

This concludes the SDT theory tutorial. Congratulations!

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