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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
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Gauri S. Shrestha, M.Optom
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.
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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‘)
Gauri S. Shrestha, M.Optom
contents
Graphic interpretation of signal detection theory
Receiver Operating Characteristics (ROC curve)
Discriminability index (d') Examples
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Detectability
Internal response probability of occurrence curves for noise-alone and for signal-plus-noise trials.
d’
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Results of Observers’ Criterion
Lax Criterion (Sensitive)High: Hits, False PositivesLow: Misses, Correct Rejects
Strict Criterion (specific)High: Misses, Correct RejectsLow: Hits, False Positive
Gauri S. Shrestha, M.Optom
Effect of shifting the criterion
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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.
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Gauri S. Shrestha, M.Optom
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.
Gauri S. Shrestha, M.Optom
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)
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
How Do We Determine Thresholds?
Methods:Method of Ascending LimitsMethod of Descending LimitsStaircase MethodMethod of Constant StimuliMethod of AdjustmentForced Choice Method
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Staircase Method Demonstration
Gauri S. Shrestha, M.Optom
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)
Gauri S. Shrestha, M.Optom
Method of Adjustment
Participants adjust intensity until the stimulus is barely visible
Advantage:Relatively quick
Disadvantage:Patient criteria skews results
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
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
Gauri S. Shrestha, M.Optom
Thank you