Signal Detection Theory Psychology: Meaning & Application

In this article, you will learn:

  1. What is Signal Detection Theory in Psychology?
  2. Signal Detection Theory Psychology Example
  3. Signal Detection Theory in Psychology
  4. Limitations of Signal Detection Theory in Psychology
  5. Application of Signal Detection Theory in Psychology
  6. FAQs

We humans come across a host of situations where we need to make a decision despite great uncertainty. 

For instance, a radiologist while examining a CT scan has to make a decision amidst great uncertainty with regards to finding evidence whether there exists a tumor or not.

Likewise, during World War II, a radar operator had to decide whether any of the given signals represented an enemy airplane or not.

As you can see, it is extremely important to make a correct decision in situations like these, otherwise the consequences are certainly going to be extreme.

Researchers or psychologists in the field of psychology face similar situations. They have to analyse a wide variety of psychological and neuroscience experiments where they have to make accurate decisions.

A psychologist may have to decide whether a child he is treating has ADHD or not based on the score that he may get by administering the Child Behavior Checklist (CBCL). 

These are quite ambiguous situations as the researchers and psychologists have to discriminate between the quite faint stimuli and make an accurate decision.

Thus, to enable such professionals to make accurate decisions amidst great uncertainty, a collection of researchers introduced the concept of noise distribution in the early 1950s. 

This led to the development of Signal Detection Theory and Receiver Operating Characteristics (ROC).

What is Signal Detection Theory in Psychology?

As you already know, all reasoning and decision making takes place in the presence of some uncertainty. Such uncertainty may cause challenges in taking accurate decisions.

Therefore, to remove such challenges of ambiguity in decision making, the Signal Detection Theory was introduced.

Thus, Signal Detection Theory is a theory that provides a precise language and graphic notation to analyze decisions in the presence of uncertainty.

It is a theory regarding the ways in which the choices are made. 

Signal Detection Theory Psychology Definition

Signal Detection Theory in Psychology is a theory that determines an individual’s ability to detect, discriminate, recognize, and identify stimuli based on his level of sensitivity and bias.

This theory assumes that an individual’s perception or sensory performance involves decision-making. And such decision-making gets challenging due to the presence of noise as well as stimuli or signals.

Here, the term sensitivity refers to the ability of an individual to determine whether a particular stimulus exists or not. In other words, it is a person’s ability to distinguish the presence of a stimulus from its absence in a given situation.

For example, the ability of a radiologist to examine the existence of a tumor increases when he gets access to more information after undertaking CT scan and an MRI.

Bias refers to the tendency of an individual to use criteria or a parameter in deciding whether a specific signal is present or not.

Thus, Signal Detection Theory is a framework for explaining choice performance.

To understand the Signal Detection Theory in detail, it is important to understand certain components of the decision-making process.

Components of Decision Making Process

The important components of the decision-making process include Information Acquisition, Criterion, Internal Noise, and Internal Response.

However, to understand these components, let’s take the example of a medical practitioner who wants to determine whether there exists a tumor after examining a CT scan.

It is important to note that interpreting CT images is quite challenging as there is too much uncertainty involved in determining whether there exists a tumor or not.

Now, there exists two possibilities for the doctor. Either there exists a tumor (i.e. the signal is present) or there does not exist a tumor (i.e. signal is absent). 

In other words, either the doctor responds ‘yes’ as he sees a tumor or he responds ‘no’ as he does not see a tumor, a task that requires a lot of training and experience.

Accordingly, there exist four possibilities of outcomes:

  • Tumor is present and the doctor says ‘Yes’ – Hit
  • The tumor is present but the doctor says ‘No’ – Miss
  • Tumor is absent and the doctor says ‘Yes’ – False Alarm
  • The tumor is absent and the doctor says ‘No’ – Correct Rejection

It is important to note that the increased number of hits and correct rejections have good consequences for the doctor as well as the patient. Whereas, an increased number of misses and false alarms can have bad consequences for both entities.

Let’s have a look at how the components of the decision-making process help an individual in making a decision.

Signal Detection Theory Psychology Example

Information Acquisition

A CT scan lets the doctor know whether there exist any changes to the shape of the lungs of the patient. Healthy lungs may have a characteristic shape, color, texture, etc. 

So, proper training helps the doctor to look out for things in order to make a decision whether there exists a tumor or not. 

Further, the doctor can also conduct an MRI in order to have more information and to increase the likelihood of getting either a Hit or Correct Rejection.

Criterion

Besides using technologies to access more information, the doctors even make use of their judgment to make a decision.

Now different doctors may hold different views about errors. For instance, some doctors may believe if they miss an opportunity for early diagnosis, it would mean putting the life of the patient in danger.

On the other hand, a few others would believe that even if the outcome is a false alarm, it may just demand from the patient a routine biopsy operation.

Thus, in the above two cases, the doctor’s decision would be inclined towards the existence of a tumor.

However, there may exist a set of doctors who believe that unwanted surgeries are not good as these surgeries involve costs, give unnecessary stress to the patient, and so on.

Thus, the doctors may be more conservative in their approach and would say ‘No Tumor’ more often.

As a result of following this approach, they will miss more tumors. However, such doctors would certainly be preventing unwanted surgeries.

Now, it is important to note that such decisions undertaken by the doctors do not depend on acquiring more information.

It simply depends on the criteria or the approach that the doctor utilizes out of his experience given both sets of doctors are equally trained.

Noise

There are two types of noise that add to the uncertainty in decision-making. These include internal and external noise.

External noise refers to the disturbance caused by external factors while making a decision. In reference to our radiologist example, the external factors may include the existence of inadequacy in the photographic process. Or something in the patient that looks fine but seems like a tumor. 

On the other hand, internal noise refers to the disturbances or distractions that exist within the doctor’s mind. 

Thus, a first glance at the CT scan may indicate that everything seems normal in the patient’s lungs. However, another examination of the same CT scan may lead to generating certain signals in the doctor’s mind indicating that there is a possibility that a tumor exists.

Internal Response

The internal response refers to the neural activity within the doctor’s brain determining his impression about whether there exists a tumor or not.

It is important to note that this internal response is noisy. This means even if there are no signals that indicate the presence of a tumor, there will be some degree of internal response in the sensory system of the doctor.

Now, let’s understand the dynamics of internal response through internal response curves. 

The following image showcases two hypothetical internal response curves. The one to the left represents a curve for noise-alone experimental trials. 

Remember, noise refers to the neural activity inside the radiologist’s brain that gives noisy and variable responses.

This curve represents the trials of healthy lungs or trials without any tumor. However, there is noise inside the radiologist’s brain.

Whereas, the internal response curve to the right demonstrates the signal-plus-noise experimental trials.

That is, this curve represents the trials of unhealthy lungs with tumors combined with the noise inside the radiologist’s brain.

Further, the horizontal axis represents the internal response whereas, the vertical axis of the graph represents the probability. Additionally, the height of each curve indicates the number of times a given level of internal response will occur.

Let’s consider an example in order to understand the internal response curves.

Factors Playing Significant Role in Decision-Making as per Signal Detection Theory Psychology s

Internal Response

Consider the curve representing the noise-alone trials or trials without the tumor in lungs. 

Typically, very little internal response of around 10 units occurs in case the radiologist conducts trials when no tumor is present.  However, there does exist some trials with some internal response because of the internal noise. 

If you carefully notice, the noise is always present given any circumstance. Now, let’s consider the response curve showcasing signal-plus-noise trials.

The internal response is generally greater relative to the response curve indicating noise-alone trials. Further, in this curve, there exists some distribution or spread of possible responses.

Also notice that both the curves overlap. This means that the internal response for a noise-alone trial may exceed the internal response for a signal-plus-noise trial.

Criterion

Then, the next factor that plays an important role in making a decision whether there exists a tumor or not is the criterion that the radiologist chooses.

One criterion is the strength of the tumor and the other is the judgment of the radiologist. The simple strategy that a radiologist can adopt in this case is that he can choose criteria closer to the internal response axis.

So whenever the internal response is greater than this criteria, he can respond ‘Yes’. And whenever the internal response is less than this criteria, the radiologist can respond ‘No’.

Let’s consider the below figure to understand how this happens.

What Does the Above Figure Suggest?

As you can see, the ‘Criterion Line’ is the one that divides the entire graph into four sections namely: Hits, Misses, False Alarms, and Correct Rejections.

On both Hits and False Alarms, the internal response is greater than the criterion as the subject is responding ‘Yes’. Hits refer to signal plus noise trials when the internal response is greater than the criterion.

Whereas, False Alarms refer to the noise-alone trials when the internal response is greater than the criterion.

Say, a subject chooses a low criterion as shown in the figure below. In such a case, the subjects say ‘Yes’ to almost everything. This means a radiologist will never say that the tumor does not exist and thus will have a very high Hit Rate.

But, it is important to note that saying ‘Yes’ to almost everything will greatly increase the number of False Alarm Rates.

Conclusion

In other words, the radiologist will have to pay a very high price in terms of the number of false alarms.

However, the radiologist responds ‘No’ to everything in case he chooses a high criterion. In such a case, the radiologist will hardly make a false alarm. But, he will miss the maximum number of tumors.

It is important to note that there exist no ways and means using which the radiologist can set the criterion to attain only hits and no misses.

Further, one cannot deny the fact that a subject’s internal responses on noise-alone trials may exceed the internal responses on signal-plus-noise trials, in some instances. 

This means that the subject cannot always be right. Further, the subjects can change the criterion by manipulating it and hence adjust the errors that they make.

Thus, this is the only part of the diagram that is under the control of the subject.

Also Read: Drive reduction theory: Meaning, Examples, & Criticisms

Receiver Operating Characteristic Curve (ROC)

Now a Receiver Operating Characteristic Curve (ROC) describes the complete range of options that a subject has in a single curve.

In other words, this curve captures all the alternatives available to the subject (radiologist in our case) as he moves his criterion to higher or lower levels.

In the graph below, the horizontal axis displays the False Alarm Rate. Whereas, the vertical axis displays the Hit Rate.

As we observe the graph, it is clear that if the criterion is high, both the False Alarm Rate and Hit Rate would be very low.

However, if the criterion is moved lower, both the False Alarm Rate and Hit Rate will increase. 

Thus, a complete ROC curve has an upward sloping shape. Also, it is important to note that the Hit Rate is always larger than the False Alarm Rate for any reasonable choice of criterion.

This is the reason why the ROC curve is sloping upwards. Thus, the subject will have a Hit Rate and a False Alarm Rate somewhere on the ROC curve after setting criteria anywhere.

Strength of the Stimulus

Then comes the strength of the stimulus. In case, the X-Ray of the lungs showcases a prominent patch, then the radiologist’s internal response strength will become stronger.

Therefore, in such a case, the probability density function for signal-plus-noise trials will shift towards the right. That is, slightly away from the noise-alone probability density.

As showcased in the figure below, there is less overlap between the two probability density curves when the signal is stronger. In such a case, it is not that difficult for the subject to make a choice.

Thus, the subjects can choose a criterion that gives them a perfect hit rate with almost no false alarms. And, the ROC curves for stronger signals slope out further than ROC curves for weaker signals.

Then, the next aspect of the probability densities is varying noise that helps in detecting the signal. Such an aspect is represented by the spread of the curves.

Consider the figure below. It showcases two sets of probability densities. As you can see, the separation between the peaks is the same. However, the second set of curves are much thinner.

This clearly distinguishes the signal as there is less spread (less noise) in the probability densities. In this case, it is easy for the subject to set criteria in order to be right nearly all the time.

Separation and Spread

Finally, the discriminability of a signal depends both on the separation and the spread of the noise-alone and signal-plus-noise curves. 

Here separation corresponds to the difference between the means. Whereas, the spread corresponds to the standard deviation of the probability densities. 

Signal Detection Theory in Psychology

Beginnings of Psychology Signal Detection Theory

Signal Detection Theory in Psychology is a framework that was first introduced in the field of Psychology. Then, it was used to study humans’ abilities to detect sensory stimuli as postulated by Green and Swets in 1966.

Accordingly, Green and Swets proposed that the Signal Detection Theory comprises two different processes including detection process and decision process.

Detection Process

The detection or recognition process is the one in which an individual has to identify whether only noise or the signal caused the psychological experience.

Decision Process

The decision process is a process that depends on the required psychological experience of a detector to make an affirmative response.

As per Swets, there exists a complex relationship between detection and decision processes. Further, there are a host of factors that influence such a relationship. These may include expectations, motivation, probability, and so on.

Thus, the Signal Detection Theory distinguishes or separates the detection process from the decision process. And it does this by differentiating between sensitivity and criterion.

As mentioned above, sensitivity and criterion are the independent parameters to measure the capabilities of recognition and decision.

Further, all these traditional methods of SDT are based on the assumption of an absolute sensory threshold. 

Assumption of the Traditional Methods of SDT

As per this assumption, the subjects of an experiment would respond affirmatively only when the intensity of the stimulus was greater than the threshold.

However, Swets argued that the challenge with such methods was that the subject responses were limited to the experimental conditions. 

In other words, such responses did not indicate whether the subjects were truly able to detect the stimulus. In fact, their responses indicated the most appropriate option in terms of yes or no for a given trial.

Signal Detection Theory Explained

Green and Swets took this fact into consideration and proposed the yes-no task as a substitute method for evaluating humans’ ability to detect stimuli.

Accordingly, the experimenters provided a clue to the participants in the yes-no task. Such a cue was provided so that the participants knew when the stimulus was going to be presented. 

For instance, the subjects were given the task of detecting an auditory stimulus. Besides this, the experimenters flash a light to let the participants know that the stimulus was about to be presented. 

In addition to this, the experimenters instructed the participants to respond to the stimulus either in “yes” or “no”. And the ‘yes or no’ response would depend on whether or not they were able to interpret the stimulus. 

Besides this, the participants were exposed to either white noise or the target stimulus on each trial in the “yes” or “no” task. 

Now, there were two possible conditions for each of the trials. These included either just noise or signal plus noise. 

Similarly, each trial led to two possible responses. These included either yes or no.

Thus, the following table represents all the possible outcomes of an experiment.

Two-By-Two Contingency Table

ResponseSignal Plus NoiseNoise
YesHitFalse Alarm
NoMissCorrect Rejection

Green and Swets emphasized that one must consider each of the cells in the above table as conditional probabilities.

Hit Rate and False Alarm Rate in SDT Model

Further, such probabilities must be considered based on the two possible states of the world. This is because it would allow the researchers to draw comparisons irrespective of the given probabilities of each of the events.

Besides this, Green and Swets suggested that of all the probabilities, only two probabilities are mandatory to evaluate the overall performance. This is because the other two probabilities are complementary to the two primary probabilities.

Accordingly, the first conditional probability is that a subject will give an affirmative response, that is a ‘Yes’, in the presence of a signal. Signal here means signal plus noise. Thus, such a response is commonly called Hit Rate or p(H1).

The second conditional probability is that the subject will give an affirmative response, that is ‘Yes’, in the absence of a stimulus. Stimulus here means noise. Thus, such a response is commonly called the False Alarm Rate or p(FA).

Noise and Signal Plus Noise Distributions 

It is important to note that as per the traditional SDT Model, the two possible states of the world, that is noise and signal + noise, have a varying impact on the subject’s psychosocial experiences.

Such effects can be represented in the form of two probability density functions overlapping each other.

As per the above figure, Sensitivity (d’) is nothing but the mean difference between the means of the two probability density functions. 

Whereas, Criterion (c) is defined as the point along the psychophysical continuum above which a participant will make an affirmative response.

It is important to note that the traditional psychophysical theories were based on absolute assumptions. As per this assumption, the subjects in a noise trial would respond affirmatively only by chance.

In fact, the early studies revealed that noise trials resulted in a significant proportion of affirmative responses.

Receiver Operating Characteristic (ROC) Curve 

However, in 1961, Swets emphasized that the subject responses were impacted by a number of non-sensory variables. These may include the prior probability of signal trials and different payoffs associated with different responses.

Further, Swets argued in 1996, that different response criteria of the subjects enabled researchers to attain a host of hit and false alarm rate combinations.

In addition to this, Swets emphasized that one could plot such combinations in the form of a curve called the Receiver Operating Characteristic (ROC) Curve.

What Does the Above Diagram Say?

As showcased in the diagram above, the hit rate values are plotted along the ordinate.  Whereas, the false alarm rates are plotted along the abscissa.

However, the straight line that cuts across the bottom left vertex and the top-right vertex represents a sensitivity value at chance performance.

Accordingly, the curved line showcases a sensitivity value greater than chance performance. Whereas, the line that connects the center of the straight line with the center of the curved line represents the exact sensitivity value.

Now, Swets (1961) argued that traditional psychophysical methods were not able to differentiate between sensitivity and criterion setting. These methods included the method of adjustment, the method of limits, and the method of constant stimuli.

He held this view because of the fact that sensitivity could impact performance only if the setting of the criterion was constant. Whereas, changes in criterion setting could impact performance only if sensitivity was constant.

According to Swets and Green, SDT provided a means for distinguishing sensitivity level from criterion setting.

Thus, the Signal Detection Theory is used in a host of domains outside the realm of psychophysics. These include pilot weather judgments, air traffic control, driver decision-making performance, group decision-making, automated speech recognition system performance, etc.

Traditional SDT Model

Under this model, the researchers have proposed the following as sensitivity measures:

  • ​​Degree of separation between signal and signal-plus-noise probability density functions or 
  • Area underneath the ROC space  

Additionally, there are a number of SDT models and measures. However, the most commonly used and widely accepted measures of sensitivity and criterion setting are d ’and c, respectively.

The sensitivity measured ’is defined as the difference between the mean of the signal-plus-noise distribution and the mean of the noise distribution.

Sensitivity

d’=  φ-1[p(HI)]- φ-1[p(FA)] 

where,

d ’= sensitivity

φ-1[p(HI)] = z score corresponding to the point below which the area under the standard normal distribution equals the proportion of hits

φ-1[p(FA)] = z score corresponding to the point below which the area under the standard normal distribution equals the proportion of false alarms

On the other hand, the criterion-setting measure c is defined as the point along the psychophysical continuum above which an observer makes an affirmative response.

c = (-1)*{0.5*φ-1[p(HI)]+0.5*φ-1[p(FA)]}

where,

c = criterion setting

φ-1[p(HI)] = z score corresponding to the point below which the area under the standard normal distribution equals the proportion of hits

φ-1[p(FA)] = z score corresponding to the point below which the area under the standard normal distribution equals the proportion of false alarms

Now, the major advantage of these measures is that one can estimate these from a single combination of Hits and False Alarms proportions.

But as per research, both sensitivity and criterion setting have arguable properties when considering extreme responses. This is quite evident in real-life scenarios like traffic- collision warning systems, monitoring complex cockpit display, and luggage screening.

The reason for such a doubt is that the φ-1function is not defined for values of 0 and 1. Therefore, if an observer has a perfect hit rate of 1 or a false alarm rate of 0, the original hit and false alarm rates need to be transformed first. The problem is that transformations may lead to biased estimates.

Limitations of the Signal Detection Theory in Psychology

It is quite doubtful to apply the traditional SDT model for a variety of domains. 

Firstly, the SDT model is based on the assumption that there exist two probability density functions. And these are associated with signal and signal-plus-noise trials along a continuum. 

According to Swets, the challenge was that the sensory excitation varies from one trial to the other. This is despite the fact that the magnitude of the stimulus is constant.

Further, he even argued that the sensory excitation can be quantified in terms of a single continuous variable, which could be thought of as the decision variable. 

Thus, in most applied settings, this argument is questionable.

Secondly, in the SDT model, one of the criteria to assess the adequacy of measures is the capability to assign scores even when observers do not commit any errors. However, there are limitations related to traditional SDT measures in the presence of extreme responding.

Application of Signal Detection Theory in Psychology

The following are the areas where signal detection theory in psychology is applied in the real world:

  • Eyewitness identification
  • Speech or Language perception
  • Weather forecasting
  • Engineering
  • Psychophysical research
  • Recognition Memory
  • Attention
  • Audiometry
  • Medical Forensic Science
  • Paediatric Audiology
  • Differential Diagnostic Audiometry
  • Auditory Brainstem Response 
  • OtoAcoustic Emissions
  • Acceptability Judgments

FAQs

1. What is signal detection theory in psychology?

Ans: Signal Detection Theory is a theory of understanding human detection performance which is based on a sensory process and a decision process.

2. What is the approach of signal detection theory in psychology?

Ans: Signal detection theory is that nearly all reasoning and decision-making takes place in the presence of some uncertainty. 

It provides precise language and graphic notation for evaluating decision-making in the presence of uncertainty. 

Such an approach helps in a lot of domains like pilot weather judgments, air traffic control, driver decision-making performance, group decision-making, automated speech recognition system performance, etc.

3. What is a miss in signal detection theory psychology?

Ans: It is one of the conditional probabilities regarding the subject that he will give an affirmative response, that is ‘No’, in the presence of a signal. 

The signal here means signal plus noise. Thus, such a response is commonly called the Miss or p(MI). 

For instance, a set of doctors believe that unwanted surgeries are not good as these surgeries involve costs, give unnecessary stress to the patient, and so on. 

Thus, such doctors may be more conservative in their approach and would say ‘No Tumor’ more often. 

As a result of following this approach, they will miss more tumors. However, such doctors would certainly be preventing unwanted surgeries.

4. What does it mean to make a Miss in signal detection theory psychology?

Ans: A Miss in Signal Detection Theory refers to a decision-making scenario where an individual says ‘No’ or rejects the probability of an alternative as he is more conservative in his approach. 

Thus, by adopting this approach, he misses the opportunity to consider the possibility of occurrence or existence of the rejected alternative. 

5. Which of the following is not part of the signal detection theory psychology quizlet?

A. Adaptation 

B. Motivation 

C. Decision-Making 

D. Sensitivity

Ans: A. Adaptation

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