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.

Signal Detection Theory and Hypothesis Testing

"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. Alternatively, participants make
"old" or "new" responses. The results of the experiment
can be portrayed in what is called a decision matrix.

Old

New

Say "Old"

Hit

False Alarm

Say "New"

Miss

Correct Rejection

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

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.

Example of an Application to a Memory Experiment

Below is a decision matrix filled in with the frequencies of each response
for a hypothetical memory experiment with 50 Old items and 50 New items.

Old

New

Say "Old"

40

5

Say "New"

10

45

TOTAL

50

50

The hit rate (say "Old" for Old items) is 40/50 or as a proportion .80.

The false alarm rate (say "Old" for New items) is 5/50 or .10.

Note that Misses and Correct Rejections are redundant with Hits and False Alarms.
The miss rate is 10/50 which is .20 or simply (1 - "hit rate") and the Correct Rejection
rate is 45/50 or .90 or (1 - "false alarm rate"). Therefore, you can perfectly describe
all four measures of a person's performance in a signal detection experiment through their Hit and False Alarm rates.