Signal Detection Theory Tutorial
 Intro to SDT Tutorial

## Basic Vocabulary of Signal Detection Theory

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

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.