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6. Signal Detection Theory and Threshold Determination.pptx
threshold, Weber's law, decision-making process, neural noise, hits and false alarm, internal noise and response, index of sensitivity, detectability, lax criteria, strict criteria, the ROC curve, methods of threshold determination
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6. Signal Detection Theory and Threshold Determination.pptx
- 1. Signal Detection Theory GauriSr Shrestha MMC, IOM, TU
- 2. Learning objectives • Tounderstand the background of ‘Signal Detection Theory’, noise and noise plus signal. • To understand the type of observations and information acquisition criteria. • Understand the stimulus detectability, criteria of decision process, receiver operating characteristics (ROC). • State methods of threshold determination
- 3. Threshold and Weber’slaw? • Threshold: The minimum amount of energy required to detect a stimulus • Weber’s Law: The just-noticeable difference is a constant proportion of the magnitude of an initial stimulus.
- 4. Select a correctanswer. • According to the Weber’s law, which statement is incorrect? a. it is harder to tell the difference between two stimuli at higher levels of intensity than at lower levels of intensity. b. People don't perceive stimuli in terms of their absolute intensity but rather their intensity relative to other stimuli. c. The just-noticeable difference is a constant proportion of the magnitude of an initial stimulus. d. Two stimuli differing by the same percentage to be perceived as different.
- 5. Background • Human arenot perfect observers. In human, threshold varies on repetition of measurement. • Stimulus results in a neural activities. Signal must be perceived as different than the background neural noise • If this neural activity is sufficiently strong. The stimulus is seen. • In summary, there is no single, fixed value below which a person never detects the stimulus and above which the person always detects it.
- 6. Signal Detection Theory •The signal detection theory involves detection of the stimulus (threshold) in the presence of some uncertainty as a decision-making process. This process is dependent on • nature of the stimulus (intensity) • sensitivity of a person to the stimulus • cognitive factors • Decision criteria • Attention • Internal neural noise
- 7. Signal Detection Theory •The level of neural noise fluctuates constantly. • Neural Noise: Neurons are constantly sending information to the brain, even when no stimuli are present. • The brain must decide whether the neural activity reflects • noise alone, or also a signal • This makes the observer’s task to differentiate: • A. The signal and noise combination • B. The noise alone
- 8. Summary • The noiseis random and fluctuating • The signal is constant • The noise is always present, and the signal is superimposed • The larger the signal, the easier it is for the observer to detect
- 9. Relationship between Hitsand False Alarm • In a threshold detection experiment, there are two possible responses, "Yes" or "No." and two different possibilities for the stimulus, “present” or “absent”.
- 10. Observer Responses • FalseAlarm • An observer reports stimulus when stimulus is absent • Correct Reject • An observer does not report stimulus when stimulus is absent • Hit • An observer reports stimulus when stimulus is present • Miss • An observer does not report stimulus when stimulus is present
- 11. Information acquisition criterion Specificity= Correct rejection (CR) / CR + False alarm Sensitivity = Hit / Hit + Miss •Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive. •Specificity (true negative rate) is the probability of a negative test result, conditioned on the individual truly being negative.
- 12. Internal response and internal noise probability of occurrencecurves for noise- alone (N) and for signal-plus-noise (N+S) trials.
- 13. Internal response andinternal noise • External noise: environmental factors. e.g., smugs, room light, temperature, noise, etc. • Internal noise: background neural responses. • Internal response: • determines the one’s impression whether a stimulus is present. • Is the state of the mind is reflected by neural activity
- 14. Relationship between Hitsand False Alarm • 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. • Index of sensitivity (detectability, d’) : determines the sensitivity of an individual for any given pattern of Hits and False Alarms.
- 15. Detectability • Definition: Thedifference 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 • d' = separation / spread • This 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.
- 16. Where does confusionoccur? • 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
- 17. Subject criterion and Decisionprocess • Lax Criterion • Lax: Indicate a stimulus even with a great deal of uncertainty (e.g., eye screening). • A Lax criterion results in a substantial number of false positives, but very few misses. Lax Criteria (sensitivity) High: Hits, False Positives Low: Misses, Correct Rejects
- 18. Subject Criterion and Decisionprocess • Strict Criterion • Strict: Do not indicate a stimulus until they are certainly present. • A Strict criterion results in fewer hits, but a lower number of false positives. Strict Criterion (specific) High: Misses, Correct Rejects Low: Hits, False Positive
- 19. The Receiver Operating Characteristic • Capturesthe 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. • For any reasonable choice of criterion, the hit rate is always larger than the false alarm rate, so the ROC curve is bowed upward values closer to 1 indicate the reliable screening measure whereas values at .50 indicate the predictor is no better than
- 20. The Receiver OperatingCharacteristic
- 21. 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: Clearly, the signal is much more discriminable when there is less spread (less noise) in the probability of occurrence curves. The separation between the peaks is the same but the second set of curves are much thinner.
- 22. When does criterionnot affect? • d' = z(FA) - z(H); • Where, FA = false alarm, H = hit • d’ = 0 • Stimulus is so weak, no signal is produced • Regardless of criteria, the proportion of hits will match the proportion of false positives. • d’ = infinity • Stimulus is easily distinguished and will always be seen by the observer (No false positives) d’ = 0
- 23. How do wedetermine thresholds? •Method of Ascending Limits •Method of Descending Limits •Staircase Method •Method of Constant Stimuli •Method of Adjustment •Forced Choice Method
- 24. Method of AscendingLimits • 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
- 25. Method of DescendingLimits • Stimulus initially presented clearly visible and reduced until no longer seen • Example: Visual Acuity • Disadvantage: • Patient Anticipation • How to Avoid: start each trial a different level of visibility
- 26. Staircase Method • Acombination of Ascending and Descending method • 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
- 27.
- 28. Method of ConstantStimuli • Stimulus is randomly varied from presentation to presentation • Large number of stimuli presented at each level of visibility • Advantage: • No patient anticipation how should they respond • Disadvantage: • Time Consuming (not typically used clinically)
- 29. Method of Adjustment •Participants adjust intensity until the stimulus is barely visible • Advantage: • Relatively quick • Disadvantage: • Patient criteria skews results
- 30. Forced Choice Method •Minimizes the role of individual’s criterion • Patient is forced to choose between several alternative choices (one contains the stimulus) • A different number of choices can be given: • 2 Alternative Choice Method • 4 Alternative Choice Method • Typically results in lower thresholds
- 31. 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
- 32. Summary • Signal DetectionTheory (SDT) explains stimulus detection amidst noise, influenced by stimulus intensity, observer sensitivity, cognitive factors, and decision criteria. • Observers make decisions resulting in outcomes: hit, miss, false alarm, or correct rejection based on signal and noise differentiation. • Internal noise and fluctuating neural activity affect detection; higher signal strength improves detectability (d’), plotted using ROC curves to show the trade-off between hits and false alarms.
- 33. Summary • Observer decisioncriteria impact outcomes: lax criteria increase hits and false alarms, while strict criteria reduce both; d’ measures sensitivity independent of the criterion. • Threshold determination methods include Ascending/Descending Limits, Staircase Method, Constant Stimuli, Method of Adjustment, and Forced Choice Method to establish detection thresholds. • Threshold is defined as the midpoint between chance level and perfect detection; for 2-alternative forced choice, threshold is 75% correct (chance = 50%)
- 34. Reference 1. Resources: VisualPerception, A Clinical Orientation Steven H. Schwartz 2. Professor David Heeger. "Signal detection theory". Encyclopedia of Psychology. FindArticles.com. 03 Jun, 2010.
- 35.
- 36. Probability of chanceguessing • p=(p'-C)/(1-C) Where, p=corrected probability p'=raw probability C=probability of chance success (For 2AFC, C = 0.5, so p'= 0.75 leads to a p = 0.5.)
Editor's Notes
- #4 A
- #5 They are complex biological system. Random neural noise is inherent within the visual system. This idea has led to the development of signal detection theory During a psychophysical trial, the SAME stimulus strength will cause different answers from the same participant; what explains why our threshold detections are not discrete? Signal detection theory Noise detection theory Stimulus discrimination theory Judgemental bias
- #6 In other words, a person will be able to detect more intense sounds or lights more easily than less intense stimuli. Further, a more sensitive person requires less stimulus intensity than a less sensitive person would. Finally, when a person is quite uncertain as to whether the stimulus was present, the individual will decide based on what kind of mistake in judgment is worse: to say that no stimulus was present when there actually was one or to say that there was a stimulus when, in reality, there was none. An example from everyday life illustrates this point. Suppose a person is expecting an important visitor, someone that it would be unfortunate to miss. As time goes on, the person begins to "hear" the visitor and may open the door, only to find that nobody is there. This person is "detecting" a stimulus, or signal, that is not there because it would be worse to miss the person than to check to see if the individual is there, only to find that the visitor has not yet arrived.
- #9 If a person participates in an experiment and receives one dollar for each Hit and there is no penalty for a False Alarm, then it is in the person's best interest to say that the stimulus was present whenever there is uncertainty. On the other hand, if the person loses two dollars for each False Alarm, then it is better for the observer to be cautious in saying that a stimulus occurred. This combination of rewards and penalties for correct and incorrect decisions is referred to as the Payoff Matrix. If the Payoff Matrix changes, then the person's pattern of responses will also change. This alteration in responses is called a criterion shift. 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
- #19 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. 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.