Signal Detection Theory


Published on

  • Be the first to comment

No Downloads
Total views
On SlideShare
From Embeds
Number of Embeds
Embeds 0
No embeds

No notes for slide
  • 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.
  • 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.
  • For very intense signals, there is no problem in deciding if there was a stimulus because the neural effect of the signal far outweighs the neural effect of the noise. Similarly, when there is no signal, the nervous system does not respond as it does when an outside signal is present, so decisions are easy. On the other hand, for near-threshold signals, it can be difficult to know whether neural activity results from noise alone or from a signal plus noise. At this point, the observer makes a decision based on the payoff matrix.
  • Signal Detection Theory

    1. 1. Signal Detection Theory Resources: Visual Perception A Clinical Orientation Steven H. Schwartz "Signal detection theory". Encyclopedia of Psychology. 03 Jun, 2010. 3/ai_2699000316/ adapted from Professor David Heeger Gauri S Shrestha, M.Optom
    2. 2. 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
    3. 3. 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  thenature of the stimulus,  Sensitivity of a person to the stimulus, and  cognitive factors Gauri S. Shrestha, M.Optom
    4. 4. 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
    5. 5. Gauri S. Shrestha, M.Optom
    6. 6. The Human Threshold and Signaldetection theory  We do not manifest a perfect threshold  Due 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 Gauri S. Shrestha, M.Optom
    7. 7. SIGNAL DETECTION THEORY  The precise notion/model of analysis decision making process in the presence of uncertainty Gauri S. Shrestha, M.Optom
    8. 8. The basic idea behind signal detectiontheory 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
    9. 9. 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
    10. 10. Payoff Matrix: combination of rewards andpenalties 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
    11. 11. contents  Graphic interpretation of signal detection theory  Receiver Operating Characteristics (ROC curve)  Discriminability index (d)  Examples Gauri S. Shrestha, M.Optom
    12. 12. 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 combination  B. The noise alone Gauri S. Shrestha, M.Optom
    13. 13. What To Remember…  The noise is 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 Gauri S. Shrestha, M.Optom
    14. 14. 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
    15. 15. 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
    16. 16. Detectability d’ Internal response probability of occurrence curves for noise-alone and for signal-plus-noise trials. Gauri S. Shrestha, M.Optom
    17. 17. 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
    18. 18. 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 M.Optom Gauri S. Shrestha, the criterion response
    19. 19. Information acquisition criterion SIGNAL R Present Absent E S YES HIT False alarm HIT False alarm P O N NO Correct rejection S Miss Correct rejection E Sensitivity= hit/hit+miss Specificity= Correct rejection/CR+False alarm Gauri S. Shrestha, M.Optom
    20. 20. 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
    21. 21. Subject Criterion  Lax Criterion vs. Strict Criterion  Lax: 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 misses  A Strict criterion results in fewer hits, but a lower number of false positives Gauri S. Shrestha, M.Optom
    22. 22. Results of Observers’ Criterion  Lax Criterion (Sensitive)  High:Hits, False Positives  Low: Misses, Correct Rejects  Strict Criterion (specific)  High:Misses, Correct Rejects  Low: Hits, False Positive Gauri S. Shrestha, M.Optom
    23. 23. Effect of shifting the criterion Gauri S. Shrestha, M.Optom
    24. 24. 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
    25. 25. Gauri S. Shrestha, M.Optom
    26. 26. 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
    27. 27. 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
    28. 28. 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
    29. 29. When Does Criterion Not Effect?  d = z(FA) - z(H)  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) Gauri S. Shrestha, M.Optom
    30. 30. Discriminability index (d):  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 Gauri S. Shrestha, M.Optom
    31. 31. How Do We DetermineThresholds?  Methods:  Method of Ascending Limits  Method of Descending Limits  Staircase Method  Method of Constant Stimuli  Method of Adjustment  Forced Choice Method Gauri S. Shrestha, M.Optom
    32. 32. 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
    33. 33. Method of Descending Limits  Reverse of Ascending Limits Method  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 Gauri S. Shrestha, M.Optom
    34. 34. 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  Thresholdis defined after three or four reversals  Advantage: Quick and Reliable  Example: Frequently used in Visual Field Testing Gauri S. Shrestha, M.Optom
    35. 35. Staircase Method Demonstration Gauri S. Shrestha, M.Optom
    36. 36. 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
    37. 37. 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
    38. 38. 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 Gauri S. Shrestha, M.Optom
    39. 39. 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
    40. 40. Thank you Gauri S. Shrestha, M.Optom