Question

Assignment

Sensation and Perception: Signal Detection

Psychologists have always been interested in the relationship between physical stimuli and the cognitive interpretations of the sensations and perceptions these stimuli produce. This field of study is called psychophysics. One of the major contributions of psychophysics is signal detection theory (SDT). The concepts behind SDT had a very practical beginning. They were first developed as a way to help the military pick the best sonar and radar operators during World War II. For example, detection of an enemy plane on a radar screen requires picking a target “signal” (the enemy plane) among lots of other extraneous signals (called “noise”) that may show up on the screen. Humans vary in their ability to do this, and SDT provides a way to analyze this variability.

From a psychological perspective, SDT is really a way to factor a human’s decision-making behavior (called “criteria” or “bias”) into a perception activity that involves sensitivity to a stimulus. Consider a lab experiment in which a subject wears headphones and is asked to indicate whether or not a very weak sound has been presented on a given experimental trial. Typically, there is ambient background noise (called “white noise”) present on every trial, so the subject must pick out the sound within the context of the background noise. The subjects respond “Yes” if the sound is heard or “No” if it isn’t. The sound could either have been present on the trial or not. If the sound is present and the subject decides “Yes”, this is a correct response, called a Hit. If the sound is present and the subject decides “No”, this is an incorrect response, called a Miss. If the sound is absent on the trial and the subject decides “Yes”, this is what is called a False Alarm. If the sound is absent on the trial and the subject decides “No”, this is a Correct Rejection.

We could arrange the possibilities from our example in a simple chart, which is called an SDT table:

Stimulus (Sound) Actually Present?

Subject’s Response

Yes (Signal + Noise)

No (Noise Only)

“Yes, I hear it”

Hit

False Alarm

“No, I don’t hear it”

Miss

Correct Rejection

Now, let’s put some real numbers into our example. Suppose that there are 100 trials in our experiment, with 50 trials, randomly selected, in which the sound is present (called a Signal + Noise trial, because the stimulus sound is presented “on top of” the background noise) and 50 trials on which the sound is not present (called a Noise only trial, because the only thing present is general background white noise). If, on the 50 Signal + Noise trials, the subject said “Yes” on 40 trials and “No” on 10 trials, then that subject got 80% (40/50) Hits and 20% (10/50) Misses. Note that the Hits and Misses are complementary, so if we know the Hit percentage, we can find the Miss percentage by subtracting the Hit percentage from 100%. Similarly, if on the 50 Noise only trials, the subject said “Yes” to 20 trials and “No” to 30 trials, then that subject made 40% (20/50) False Alarms and 60% (30/50) Correct Rejections. Once again, the percentages are complementary.

Now let’s see how we can use these concepts to differentiate the detection abilities of humans. Assume we run both Subject A and Subject B through our above example of 100 trials, 50 with the sound present and 50 with it absent. Let’s say Subject A correctly detects the target sound 25 times, and Subject B correct detects it 17 times. The question is: “Who is doing better?” You might want to say Subject A since he got more Hits, but the frequency of False Alarms clearly needs to be factored in. If Subject A has 20 False Alarms and Subject B has 5 False Alarms, then B is better at distinguishing the trials in which the sound is present from the trials in which the sound is absent. Specifically, these results would seem to indicate that A is pretty much guessing that the sound is present but is wrong (i.e., exhibits a False Alarm) as often as right. Subject B is more selective about saying the sound is detected but rarely says the target sound is there when it is not. Thus, it could be argued that B is in actually doing better at the task.

This example suggests that we need a measure of performance that includes both Hit rates and False Alarm rates in order to successfully differentiate among the signal detection abilities of different people. To this end, researchers have developed a measure of signal detection sensitivity called d’ (pronounced d-prime) that can be computed for an individual who has participated in an SDT task. While the derivation of this measurement is well beyond the scope of PSYC, it is important to understand that the larger the value of d’ the better the subject is at distinguishing the target signal from the noise.

The computation of d’ is fairly complex, but I have provided an Excel spreadsheet for the calculation given Hit and False Alarm rates. To continue with our example above, Subject A has a calculated d’ = 0.253. Subject B has a calculated d’ = 0.869. (You can verify these numbers using the spreadsheet.) This shows that Subject B, while having a lower Hit rate, is actually the better overall performer in our SDT task.

The experiment you are to conduct for Assignment #1 (with you as the subject) measures face recognition abilities of people using these same SDT principles. Humans have an uncanny ability to recognize faces of people they have previously seen, and SDT is a good tool to investigate individual differences in this ability.

Procedure

Questions/Tasks

1. Explain in a paragraph or two the concept of signal detection.

2. What is the independent variable(s) in this experiment?

3. What is the dependent variable in this experiment?

4. Define “Hit”, “Miss”, “False Alarm” and “Correct Rejection” in the context of this experiment.

5.Using your scored results, construct an SDT table that summarizes your performance. Your table should have the same format as the table on the top of page 2 in this handout with the only difference being that you are to put your performance percentages in each cell of the table.

6. Using the “d’ Calculator” Excel spreadsheet, find your d’ value and record it here. This is a measure of your “sensitivity” (i.e., skill) in the face recognition task. While a higher value is associated with greater sensitivity and skill, it is more useful for comparative purposes, so you might want to ask your fellow students in PSYC what their d’ values were – and, of course, brag if yours is higher than theirs!

7. Consider a radiologist who is in charge of reading lung x-rays to detect possible cancerous tumors. Using the Presence of Stimulus as the Presence of Cancer in this case, build an SDT table (like the one above) that shows the four possible outcomes in response to reading a patient’s x-ray. Consider the two possible errors (False Alarm and Miss) that the radiologist could make. In the context of the task, explain these two errors and comment on the ramifications of each one. Many medical people would argue that one of the mistakes has more serious consequences than the other. Which one? From an SDT perspective, how might you “coach” or “train” a radiologist in order to minimize the more consequential mistake?

Answer 1

Sol.1. Concept of Signal Detection: Signal-detection theory provides a general framework to describe and study decisions that are made in an uncertain or ambiguous situation. It is most widely applied in psychophysics the domain of study that investigates the relationship between a physical stimulus and its subjective or psychological effect but the theory has implications about how any type of decision under uncertainty is made. It is among the most successful of the quantitative investigation of human performance, with both theoretical and practical applications.

Here we discuss the study of signal detection theory is with an example of detection situations. Consider a very common situation: an individual must decide whether or not some condition is present. Such decisions are easy to make when the alternatives are obvious and the evidence is clear. However, there are many tasks that are not so simple. Often, the alternatives are distinct, but the evidence on which the decision is to be based is ambiguous. Here is an example:

• A doctor physician, psychologist, or whoever is examining a patient and trying to make a diagnosis. The patient shows a set of symptoms, and the doctor tries to decide whether a particular disorder is present or not. To complicate the problem, the symptoms are ambiguous, some of them pointing in the direction of the disorder, other pointing away from it; moreover, the patient is a bit confused and does not describe the symptoms clearly or consistently. The correct diagnosis is not obvious.