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Psychophysics 3

Psychophysics 3. Research Methods Fall 2010 Tamás Bőhm. Signal detection theory. Aka. sensory decision theory (SDT) A model & a data analysis method for decision problems with uncertainty (noise) Originates from World War II: aircraft detection on radar signals

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Psychophysics 3

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  1. Psychophysics 3 Research Methods Fall 2010 Tamás Bőhm

  2. Signal detection theory • Aka. sensory decision theory (SDT) • A model & a data analysis method for decision problems with uncertainty (noise) • Originates from World War II: aircraft detection on radar signals • Today: widely used in psychophysics, medicine, radiology and machine learning

  3. Signal detection theory • Experiment setup: • In some trials a stimulus (signal) is presented, in others there is no stimulus; • Observer reports if she/he saw a signal or not • Calculate how many times the observer detected a signal when she/he was presented one (hit rate) • Is the hit rate all we want to know? Two observers achieved the same hit rate. Are they certainly behaving the same way? • NO, we also need to know how many times the observer said “I see” when there was no signal (false alarm rate)

  4. Signal detection theory • Confusion matrix: contains all the information about the observer’s performance

  5. Signal detection theory • Confusion matrix: contains all the information about the observer’s performance • As columns add up to 100%, it is enough to know one item from each column 40 trials 20 = 100% 20 = 100% 18 = 90% 6 = 30% 2 = 10% 14 = 70%

  6. Signal detection theory • Perfect detection: 100% 0% 0% 100%

  7. Signal detection theory • No detection at all (1st example): always reporting “Seen” 100% 100% 0% 0%

  8. Signal detection theory • No detection (2nd example): always reporting “Not seen” 0% 0% 100% 100%

  9. Signal detection theory • No detection (3rd example): flipping a coin 50% 50% 50% 50%

  10. Signal detection theory • No detection (4th example): reporting “Seen” in 30% of the trials (no matter what is presented) Rows equal  no detection 30% = 30% 70% = 70%

  11. Signal detection theory • Receiver operating characteristic (ROC): 100% hit rate 100% false alarm rate

  12. Signal detection theory • Receiver operating characteristic (ROC): 100% hit rate 90% 30% 10% 70% 100% false alarm rate

  13. Signal detection theory • Receiver operating characteristic (ROC): 100% Perfect detection hit rate 100% 0% 0% 100% 100% false alarm rate

  14. Signal detection theory • Receiver operating characteristic (ROC): 100% No detection: always “yes” hit rate 100% 100% 0% 0% 100% false alarm rate

  15. Signal detection theory • Receiver operating characteristic (ROC): 100% No detection: always “no” hit rate 0% 0% 100% 100% 100% false alarm rate

  16. Signal detection theory • Receiver operating characteristic (ROC): No detection: reporting “yes” in 50% of the trials (flipping a coin) 100% hit rate 50% 50% 50% 50% 100% false alarm rate

  17. Signal detection theory • Receiver operating characteristic (ROC): No detection: reporting “yes” in 40% of the trials 100% hit rate 40% 40% 60% 60% 100% false alarm rate

  18. Signal detection theory • Receiver operating characteristic (ROC): No detection: reporting “yes” in 30% of the trials 100% hit rate 30% 30% 70% 70% 100% false alarm rate

  19. Signal detection theory • Receiver operating characteristic (ROC): No detection: reporting “yes” in 60% of the trials 100% hit rate 60% 60% 40% 40% 100% false alarm rate

  20. Signal detection theory • Receiver operating characteristic (ROC): 100% Diagonal: no detection hit rate 100% false alarm rate

  21. Signal detection theory • SDT model: • No way to remove the noise • But sensation can be separated from decision by using ROCs SL ≥β YES Sensation level (SL) Signal present/absent Sensation Decision NO SL < β Noise Criterion (β)

  22. Signal detection theory SL ≥β YES Sensation level (SL) Signal present/absent Sensation Decision NO SL < β (Noise) Criterion (β) Without noise: perfect detection is possible signal absent criterion signal present probability sensation level

  23. Signal detection theory SL ≥β YES Sensation level (SL) Signal present/absent Sensation Decision NO SL < β (Noise) Criterion (β) signal absent criterion signal present 100% 0% probability 0% 100% sensation level

  24. Signal detection theory SL ≥β YES Sensation level (SL) Signal present/absent Sensation Decision NO SL < β Noise Criterion (β) signal absent(noise only) signal present(signal+noise) criterion Noise: smears the distributions perfect detection is impossible (if the two distributions overlap) probability sensation level online demo

  25. Signal detection theory Sensation level Sensation level http://www-psych.stanford.edu/~lera/psych115s/notes/signal/

  26. Signal detection theory hit rate Sensation level false alarm rate Sensation level

  27. Signal detection theory β = 6 β = 6 ROC curve β = 8 β = 8 hit rate β = 10 β = 10 false alarm rate

  28. Signal detection theory • Criterion (β): specifies where we are on the ROC curve • The ROC curve is specified by sensory capacities only(discriminability) β hit rate false alarm rate probability sensation level

  29. Signal detection theory • Discriminability: how well the observer can separate the presence of signal from its absence~ overlap between the two distributions~ bowing out of the ROC curve • Measured by d’ (discriminability index,also called sensitivity) http://www-psych.stanford.edu/~lera/psych115s/notes/signal/

  30. Signal detection theory d’: selects the ROC curve β: specifies a point on the selected ROC curve • same information as hit rate & false alarm rate, but: hit rate, false alarm rate:both reflect sensation & decision characteristics;cannot separate the two d’: depends only on sensation β: depends only on decision β The two processes are separated http://psych.hanover.edu/JavaTest/Media/Chapter2/MedFig.ROC.html

  31. Fechner’s methods: Is a stimulus detectable? Yes or no? Clear-cut threshold value (with some variability) that can be measured Stimulus intensity > threshold  detectable Stimulus intensity < threshold  not detectable Dichotic outcome, categorical model Signal detection theory: How well is it detectable? How sensitive the observer is to the stimulus? Measured by d’ The higher d’ is, the more the stimulus is detectable d’ = 0  not detectable at all Scalar outcome, dimensional model Signal detection theory

  32. SL ≥β YES Decision NO SL < β Criterion (β) Different task Forced-choice: eliminates the criterion SDT: separates the criterion Correct Incorrect Signal detection theory • Problem with Fechner’s methods: criterion Sensation level (SL) Stimulus Sensation (Noise)

  33. Signal detection theory Psychophysical measurements with SDT: • Create a stimulus set with a range of intensities (like in the method of constant stimuli) • Test each stimulus many times with each observer • On each trial, either present a randomly selected stimulus or do not present anything • Ask the observer if he/she detected the stimulus • Calculate the hit rate and false alarm rate for each observer, for each stimulus intensity • Use the formula/table to calculate d’ for each case • Examine how d’ changes with intensity: the higher d’ is for a stimulus intensity, the greater the observer’s ability to detect this intensity http://psych.hanover.edu/JavaTest/Media/Chapter2/MedFig.SignalDetection.html

  34. Signal detection theory • Main results: changes in d’ values Caudek–Rubin Vision Res. 2001

  35. Signal detection theory • There is also a β value for each d’ value • It can be informative about the decision behavior: • Balanced: false alarm and miss rates are equal • Liberal: the observer says “yes” whenever there may be a signal • Conservative: decision is yes only when it is almost certain that there is a signal balanced conservative liberal probability sensation level

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