## D-prime

In the 1960s, researchers found that they could influence people to move the threshold up or down, in effect, by manipulating the costs of different errors. They did this by arranging a variety of different payoff schemes. For example, a subject could be promised \$10 for every successful act of signal detection but penalized \$1 for every false positive. That would create a response bias for saying Yes.

What did signal detect researchers discover, in the 1960s, which allowed them to calculate "d prime"?

If the experimenter reversed the payoffs, awarding \$1 for each "hit" and taking away \$10 for each "miss" or false positive, the subject became more conservative, adopting a more stringent criterion: a higher threshold for saying Yes. The response bias would then be shifted away from false positives toward false negatives.

What was "the important insight" from early research on signal detection theory?

Researchers in signal detection theory had an important insight. They realized that if they collected signal detection data under a range of biasing conditions, they could do calculations that "filtered out" the effects of bias. The result is d' (d prime): a statistic that gives a relatively pure measure of the observer's sensitivity or ability to detect weak signals.

The fact that d' (d prime) is a bias-free statistic allows researchers to test weak or subtle effects which might otherwise be hard to detect because of the effects of bias. This allows psychologists to test the sensitivity of observers in situations that might be strongly influenced by belief. A researcher who calculates the d prime statistic can measure the effect of different biasing conditions, see how bias influences the resuilts, then remove it statistically from the final results.

When is d' (d prime) especially useful? What did a signal detection analysis of acupuncture reveal?

A bias-free measure of observer sensitivity is a real asset in situations where people might be biased toward a Yes or No answer. For example, Clark and Yang (1974) used signal detection theory to study acupuncture, the Chinese medical treatment in which tiny needles are inserted into the body to relieve pain. Most people who use acupuncture are inclined to believe in it. They show a bias toward reporting less pain after acupuncture treatment. Clark and Yang arranged a variety of biasing conditions and calculated the d' statistic for painful stimulation before and during acupuncture. The results showed no change in sensitivity to pain. Clark and Yang concluded people were "less inclined to report pain" after the acupuncture needles were inserted, but their actual sensitivity to pain was unchanged.

What did signal detection analysis reveal about memory under hypnosis?

Similarly, using the Theory of Signal Detection, researchers were able to study the accuracy of memory under hypnosis . Using signal detection theory, researchers showed that memory is not more accurate under hypnosis. The d prime statistic does not change. What changes is the subject's bias or willingness to say Yes. Under hypnosis more memories (both true and false ones) are accepted as true, resulting in more true memories and also more false positives.

What other applications does the d-prime statistic have?

D-prime is useful when a researcher wishes to find out whether signal detection sensitivity is actually changed or whether a person is simply more willing to say Yes under some conditions than others. Swets, Dawes, and Monahan (2000) argue that the Theory of Signal Detection and its d-prime statistic are useful whenever diagnostic decisions must be made. That includes many situations:

Is a cancer present? Will this individual commit violence? Are there explosives in this luggage? Is this aircraft fit to fly? Will the stock market advance today? Is this assembly-line item flawed? Will an impending storm strike? Is there oil in the ground here? Is there an unsafe radiation level in my house? Is this person lying? Is this person using drugs? Will this applicant succeed? Will this book have the information I need? (Swets, Dawes, & Monahan, 2000, p.1)

What did the Theory of Signal Detection turn into?

If you read that list, it includes some very important decisions! The Theory of Signal Detection has transformed into a general science of decision-making in Yes/No situations. What started as an attempt to refine psychophysical functions turned out to have many applications beyond the exploration of human sensory ability.

Write to Dr. Dewey at psywww@gmail.com.

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