The underlying model of SDT consists of two normal distributions, one representing a signal and another representing noise. In this tutorial, we refer to the signal distribution as “Signal Present” and the noise distribution as “Signal Absent.” How well a person can discriminate between Signal Present and Signal Absent trials is represented by the difference between the means of the two distributions, d’. The willingness of the person to say ‘Signal Present’ in response to an ambiguous stimulus is represented by the criterion.
The logic of the SDT model is very similar to statistical hypothesis testing. The Signal Absent distribution corresponds to the null hypothesized distribution, the Signal Present is the alternative distribution, and the criterion is the alpha error rate set by the analyst.
“Yes-No” paradigms
A research domain where SDT has been successfully applied is in the study of memory. Typically in memory experiments, participants are shown a list of words and later asked to make a “yes” or “no” statement as to whether they remember seeing an item before. Participants may respond “old” or “new” to words they are shown. The outcome of each decision can be portrayed in what is called a decision matrix.
|
Old |
New |
|
|
Say “Old” |
Hit |
False Alarm |
|
Say “New” |
Miss |
Correct Rejection |
The hit rate is defined as the proportion of “old” responses given for items that are Old and the false alarm rate is the proportion of “old” responses given to items that are New.
Does this look familiar? In hypothesis testing, the same decision matrix would have the following labels:
|
Ho False |
Ho True |
|
|
Reject the Null Hypothesis |
Correct Decision |
Type I Error |
|
Fail to Reject the Null Hypothesis |
Type II Error |
Correct Decision |
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