The Mechanics Of Signal Detection Theory: A Brief Overview
The basic premise behind SDT is that both signal and noise are represented probabilistically within the decision-maker, and the extent to which those representations overlap can be estimated based on the decision-maker’s responses and whether or not the signal is present . The decision-maker bases their decision relative to their criterion , where a signal will be reported present when the internal signal is stronger than β and absent when the internal signal is weaker than β. A hit represents the probability that the subject reports the signal present when it is and a false alarm represents the probability that the subject reports the signal present when it is absent . Alternatively, a miss represents the probability that the subject reports the signal absent when it is present and a correct rejection represents the probability that the subject reports the signal absent when it is absent . All response probabilities are reflected as a part of the area underneath a normal curve. If the probability of each response type is therefore known, both the signal and the noise distributions can be estimated based on simple statistical principles.
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.
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
Signal Detection Theory And Roc Analysis In Psychology And Diagnostics: Collected Papers
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Signal Detection Theory In Psychology
Signal detection theory acts as a method of assessing the capability to distinguish between data-holding patterns and arbitrary occurrences. Random incidences interrupt the flow of information and are called noise. In line with the theory, there are numerous determinants of the way a person will detect a stimulus and the degree of its threshold. Such determining factors elucidate why the variation of threshold influences the capacity to discern, usually revealing how concerned one is to the task, objective, or issue at hand. Attributes such as experience, anticipation, psychological condition , and other aspects may affect the employed threshold . For example, a guard has the probability of distinguishing weaker stimuli during confrontation than in peaceful conditions attributable to lesser criterion. Nevertheless, in wartime, a guard might also take harmless stimuli as threats. The research question that will guide this study is as follows: how can signal detection theory help in the determination of a persons bias in judgment? Signal detection theory presumes that a person is not an inactive receiver of information but an active verdict maker who can realize intricate judgments under situations of doubt.
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
| Miss | Correct 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
Noise and Signal Plus Noise Distributions
Receiver Operating Characteristic Curve
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Signal Detection: Decision Making In Uncertainty
We all experience uncertainty: How did I do on that test? What do they think of me? Where did I leave my keys? Is my phone ringing? In these and other uncertain situations, we have to take the evidence we have and make our best guess about the answer. Sometimes we’re right, and sometimes we’re wrong. Sometimes how we respond is biased – like assuming every sound or vibration is the phone when you’re waiting for an interview or job offer. Signal detection is a theory, research method, and statistical method for explaining and measuring how we act under uncertainty. Theory:
Under basic signal detection theory there are two situation dimensions, world state and your level of evidence. Take weather forecasts as an example: if the forecast is that it will rain at 4pm , when it gets to 4pm it will be either 100% raining or 100% not, one of two mutually-exclusive world states. We call when the stimulus is present the signal and when it’s absent noise – notice that signal and noise are mutually exclusive categories.
Our other two outcomes add up to 100% of times when there is no signal. The name correct rejection tells us that the level of evidence led to the correct decision: low evidence, such as for rain, correctly predicted the world state, such as not raining. If the level of evidence for rain was high enough to be above threshold leading to the prediction of rain, but it didn’t rain, we call this a false alarm.
Statistical Method:
Research Method:
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.
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Models Of Auditory Detection And Discrimination
Auditory models based on Signal Detection Theory have played a major role in psychoacoustically based theories of hearing . The classic auditory stimulus condition for these models involves the detection of a tonal signal in a background of Gaussian noise. The energy-detection model, as developed by Dave Green and colleagues in the 1960s, was derived from SDT . It assumes that the listener uses the distribution of instantaneous amplitudes of the two sounds for a decision as to whether or not a tone was added to the noise. The instantaneous amplitudes of Gaussian noise are normally distributed with zero mean and a standard deviation equal to the root-mean-square amplitude of the noise. When a sinusoidal tone is added to the noise, the distribution remains normal with a mean equal to the energy of the signal and the same standard deviation. The decision is assumed to be based on the likelihood that a sampled instantaneous amplitude would come from the signal-plus-noise distribution as opposed to the noise distribution. The distributions of the likelihood ratios remain normal and the distance between the two distribution means normalized to the common standard deviation takes the form: d o ) , where E is signal energy and No is noise spectrum level. Thus, as the energy of the signal increases relative to the level of the noise, dâ² increases, suggesting higher signal detectability.
Susan C. Weller, in, 2005
Pseudoscience As A Tool For Teaching Signal Detection Theory
Many pseudosciences present excellent examples that can be used to demonstrate the value of SDT to learners. While believers of pseudoscientific principles claim to be sensitive to those principles, sensitivity in these situations is not typically considered with respect to false alarms. For example, the efficacy of homeopathic treatments is typically considered as a placebo effect, which can be understood within the SDT framework . If an individual claimed that a particular homeopathic treatment was effective , but would also be likely to claim that a placebo was effective , the associated d’ for that individual would be low. The value of SDT in this situation is that it provides an objective measure of an individual’s sensitivity outside of subject bias.
Here, I present two examples that can be used as to demonstrate the value of SDT using pseudoscientific principles. These examples can be easily adapted to utilize many pseudoscientific principles that may be taught in undergraduate psychology classes. The only statistical knowledge that is required on behalf of the student is a basic understanding of z-scores and the normal distribution. An alternative exercise for students is to formulate their own research designs that would allow them to investigate pseudoscientific principles using SDT with the following examples as a framework. Either approach would provide students with valuable hands-on experience for using SDT to objectively assess human decision-making.
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What Is The Difference Between Absolute Threshold And Signal Detection Theory
The main difference between absolute threshold and signal detection theory is that absolute threshold is the lowest level of stimuli an organism can detect at least half the time whereas signal detection theory is a theory that states that detection of a stimuli states that both the intensity of the stimuli and physical/psychological state of the organism.
Different people respond to the same signal differently. For example, one person may be able to detect a very low sound, while others are not able to detect this sound. Absolute threshold and signal detection theory are two concepts that explain such situations.
What Is Absolute Threshold
Originally, the absolute threshold was defined as the lowest level of stimuli an organism could detect. However, some modifications had to be made to this theory after the introduction of signal detection theory. After these modifications, the absolute threshold is considered to be the smallest amount of a stimulus we can detect 50% of the time.
In the hearing, the absolute threshold is the smallest level of a tone that a person with normal hearing can detect, especially when there are no other interfering sounds. Moreover, in vision, the absolute threshold is the smallest level of light a participant can detect. Measuring the absolute threshold in vision may involve measuring the distance at which a person can detect the flame of a candle in the dark.
For smell, the absolute threshold involves the smallest concentration a person is able to smell for instance, the smallest amount of perfume a person is able to smell in a large room. When considering touch, an absolute threshold is the amount of force that allows you to detect the feeling of something touching your body as an example, a feather lightly brushing your arm. Besides, its important to note that the absolute threshold for touch varies for different body parts as some body parts are more sensitive than others.
Figure 1: Absolute Thresholds of Hearing
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Learning From The Article
From the article and observation, one can establish that credibility and acceptability occur freely, and the perceptual distance involving the two should not differ since it reveals the ensuing variances. Bias is subject to change because the respondents are prejudiced in their recognition of the suitable stimuli . The manipulation of different aspects in the experiment and observation of how individual sensitivity and bias vary provides a clear depiction of the way credibility interrelates with acceptability.
The Theory Of Signal Detection
A funny thing happened to the concept of threshold on the way to the second half of the 20th Century: it disappeared. Or maybe we should say it became mobile.
Experiments showed there was no magic line which, when crossed, made a stimulus perceivable. Instead, people acted like the threshold was a decision point, variable in nature, that could be adjusted depending upon different circumstances.
This conclusion came from a new field called information theory or communications theory. Information theory started after World War II as scientists tried to improve communication systems such as the telephone.
Information theorists found that detectability of a signal depended upon several factors that could be manipulated independently: the level of background noise, the strength of the stimulus, and the redundancy in the stimulus.
What factors determine the detectability of a signal?
If a person is trying to detect very weak signals in background noise the problem is to pick out the signal from the noise. But if the signal is very faint, or the noise level is very high, the observer might make errors. There are two types of errors a person can make.
1. False positives occur if a person says yes but this is wrong because no signal was presented. A falsepositive response can also be called a false alarm. If you thought you heard somebody call your name, but nobody actually did, that is a false positive.
What are false positives and false negatives?
D-prime
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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.
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 doctors 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.
Noise
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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, lets 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 or there does not exist a tumor .
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.
Lets have a look at how the components of the decision-making process help an individual in making a decision.