Signal Detection Theory

Signal Detection TheoryResources: Visual Perception

A Clinical Orientation Steven H. Schwartz"Signal detection theory". Encyclopedia of

Psychology. FindArticles.com. 03 Jun, 2010. http://findarticles.com/p/articles/mi_g2699/is_000

3/ai_2699000316/

adapted from Professor David Heeger

Gauri S Shrestha, M.Optom

http://findarticles.com/p/articles/mi_g2699/is_0003/ai_2699000316/

Gauri S. Shrestha, M.Optom

Background

The activity led to the development of the idea of a threshold detection with stimulus

even though the level of stimulation remained constant, people were inconsistent in detecting the stimulus

There is no single, fixed value below which a person never detects the stimulus and above which the person always detects it

An approach to resolving this dilemma is provided by signal detection theory


Back ground

This approach abandons the idea of a threshold.

Instead, the theory involves treating detection of the stimulus as a decision-making process

Determinant of this process the nature of the stimulus, Sensitivity of a person to the stimulus, andcognitive factors


Back ground

in a typical sensory experiment that involves a large number of trials, an observer must try to detect a very faint sound or light that varies in intensity from clearly below normal detection levels to clearly above.

There are two possible responses, "Yes" and "No." There are also two different possibilities for the stimulus, either present or absent.

when stimuli are difficult to detect, cognitive factors are critical in the decision an observer makes



The Human Threshold and Signal detection theory

We do not manifest a perfect thresholdDue to decision criteria, attention, and internal

neural noise What is the Signal Detection Theory?

Decision making takes place in the presence of some uncertainty

A model that addresses the role of these factors in determining a threshold

It provides a precise language and graphic notation for analyzing decision making in the presence of uncertainty

SIGNAL DETECTION THEORY

The precise notion/model of analysis decision making process in the presence of uncertainty



The basic idea behind signal detection theory is that

The level of neural noise fluctuates constantly. When a faint stimulus, or signal, occurs, it creates a neural response.

The brain must decide whether the neural activity reflects noise alone, or whether there was also a signal.


Signal detection theory

Neural Noise: Neurons are constantly sending information to the brain, even when no stimuli are present.

The level of neural noise fluctuates constantly. When a faint stimulus, or signal, occurs, it creates a neural response.

The brain must decide whether the neural activity reflects noise alone, or also a signal

When stimulus is difficult to detect= cognitive factors are critical


Payoff Matrix: combination of rewards and penalties for correct and incorrect decisions

There is always a trade-off between the number of Hits and False Alarms

When a person is very willing to say that the signal was present, that individual will show more Hits, but will also have more False Alarms.

mathematical approaches to determine the sensitivity of an individual for any given pattern of Hits and False Alarms- index of sensitivity (d‘)


contents

Graphic interpretation of signal detection theory

Receiver Operating Characteristics (ROC curve)

Discriminability index (d') Examples


Signal Detection Theory

Assumes there is random, fluctuating level of background neural noise

A stimulus’ signal is superimposed on this noise

This makes the observer’s task to differentiate:A. The signal and noise combinationB. The noise alone


What To Remember…

The noise is random and fluctuatingThe signal is constantThe noise is always present and the signal is

superimposedThe larger the signal, the easier it is for the

observer to detect


Internal response and internal noise

External noise: environmental factor, smugs, light, etc .

Internal noise: Internal noise refers to the fact that neural responses are noisy. A doctor has a set of X detector neurons and

monitor the response of one of these neurons to determine the likelihood that there is a X.

These hypothetical X detectors will give noisy and variable responses


Internal response and internal noise

Internal response: determines the one’s impression about whether

or not a x factor is present. the state of the mind is reflected by neural

activity somewhere in the brain. This neural activity might be concentrated in just

a few neurons or it might be distributed across a large number of neurons.

refer to it as internal response


Detectability

Internal response probability of occurrence curves for noise-alone and for signal-plus-noise trials.

d’


Detectability

Definition: The difference between the means of N and N + S

Detectability increases as the distributions of N and N + S become further apart

With a very large ‘d,’ there is no uncertainty whether the stimulus is present

With a weak stimulus, the ‘d’ becomes much smaller


Where does Confusion Occur?

Since the curves overlap, the internal response for a noise-alone trial may exceed the internal response for a signal-plus-noise trial.

Vertical lines correspond to the criterion response


Information acquisition criterion

HITHIT

Correct rejectionCorrect rejection

False alarmFalse alarm

RESPONSE

SIGNAL

YES

Present Absent

NO MissMiss

Sensitivity= hit/hit+missSpecificity= Correct rejection/CR+False alarm


Observer Responses

False Positive (False Alarm) Observer reports stimulus when stimulus is not present

Correct Reject Observer does not report stimulus when stimulus is absent

Hit Observer reports stimulus when stimulus is present

Miss Observer does not report stimulus when stimulus is

present


Subject Criterion

Lax Criterion vs. Strict CriterionLax: Indicate a stimulus even with a great deal of

uncertainty (example: optometrist)Strict: Do not indicate a stimulus until they are

certain one is present (Example: hunter)A Lax criterion results in a substantial number

of false positives, but very few missesA Strict criterion results in fewer hits, but a

lower number of false positives


Results of Observers’ Criterion

Lax Criterion (Sensitive)High: Hits, False PositivesLow: Misses, Correct Rejects

Strict Criterion (specific)High: Misses, Correct RejectsLow: Hits, False Positive


Effect of shifting the criterion


The Receiver Operating Characteristic

captures the various alternatives that are available to the examiner in a single graph

ROC curves are plotted with the false alarm rate on the horizontal axis and the hit rate on the vertical axis.

if the criterion is high, then both the false alarm rate and the hit rate will be very low. If we move the criterion lower, then the hit rate and the false alarm rate both increase.

For any reasonable choice of criterion, the hit rate is always larger than the false alarm rate, so the ROC curve is bowed upward


A measure of goodness-of-fit is based on the simultaneous measure of sensitivity (True positive) and specificity (True negative) for all possible cutoff points.


Receiver Operating Characteristic (ROC)

a generalization of the set of potential combinations of sensitivity and specificity possible for predictors

AUC values closer to 1 indicate the reliable screening measure whereas values at .50 indicate the predictor is no better than chance



Varying the noise

For stronger signals, the probability of occurrence curve for signal-plus-noise shifts right and detection is easier

The spread of the curves: The separation between the peaks is the same but the second set of curves are much skinnier. Clearly, the signal is much more discriminable when there is less spread (less noise) in the probability of occurrence curves.


When Does Criterion Not Effect?

d' = z(FA) - z(H) d’ = 0

Stimulus is so weak, no signal is producedRegardless of criteria, the proportion of hits

will match the proportion of false positivesd’ = infinity

Stimulus is easily distinguished and will always be seen by the observer (No false positives)


Discriminability index (d'):

d' = separation / spreadThis number, d', is an estimate of the

strength of the signal. its value does not depend upon the criterion

the subject is adopting, it is a true measure of the internal response


How Do We Determine Thresholds?

Methods:Method of Ascending LimitsMethod of Descending LimitsStaircase MethodMethod of Constant StimuliMethod of AdjustmentForced Choice Method


Method of Ascending Limits

Stimulus is initially presented below threshold Stimulus is presented at increasingly intense levels from

presentation to presentation until visible by observer Advantage:

Relatively quick method Disadvantage:

Participant Anticipation How to Avoid: Start each trial with stimulus of a different

intensity


Method of Descending Limits

Reverse of Ascending Limits MethodStimulus initially presented clearly visible and

reduced until no longer seenExample: Visual Acuity Disadvantage:

Patient AnticipationHow to Avoid: start each trial a different level of

visibility


Staircase Method

Combination of Ascending and Descending How Does It Work?

Stimulus starts below threshold Presented in discrete steps of increasing visibility until observer

reports stimulus Visibility is reduced in discrete steps until stimulus can no longer be

detected Staircase is again reversed

Threshold is defined after three or four reversals Advantage: Quick and Reliable Example: Frequently used in Visual Field Testing


Staircase Method Demonstration


Method of Constant Stimuli

Stimulus is randomly varied from presentation to presentation

Large number of stimuli presented at each level of visibility

Advantage: No Patient Anticipation

Disadvantage: Time Consuming (not typically used

clinically)


Method of Adjustment

Participants adjust intensity until the stimulus is barely visible

Advantage:Relatively quick

Disadvantage:Patient criteria skews results


Forced Choice Method

Minimizes the role of individual’s criterionPatient is forced to choose between several

alternative choices (one contains the stimulus)A Different Number of Choices Can Be Given:

2 Alternative Choice Method4 Alternative Choice Method

Typically results in lower thresholds


Threshold Determination

Threshold = Midway between 100% correct and ‘chance’ Chance=percentage we expect observer to guess correctly

2 Alternative Choice Method ‘Chance’ performance=50% correct Threshold=75% correct

4 Alternative Choice Method ‘Chance’ Performance=25% correct Threshold=62.5% correct


Thank you

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Signal Detection Theory

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