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THE RECEIVER OPERATING CHARACTERISTIC

THE RECEIVER OPERATING CHARACTERISTIC. FANTINO SEMINAR APRIL 10, 2013 UCSD STEPHEN LINK. Fechner’s experiments on human sensory discrimination were based on a theory of how two sensory stimuli are compared. W A = Standard weight of say 300g Versus W B = Comparison weight of 320g

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THE RECEIVER OPERATING CHARACTERISTIC

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  1. THE RECEIVER OPERATINGCHARACTERISTIC FANTINO SEMINAR APRIL 10, 2013 UCSD STEPHEN LINK LINK AT THE FANTINO SEMINAR

  2. LINK AT THE FANTINO SEMINAR

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  4. Fechner’s experiments on human sensory discrimination were based on a theory of how two sensory stimuli are compared. WA = Standard weight of say 300g Versus WB = Comparison weight of 320g How does the subject decide that WB is greater in weight than the Standard, WA? LINK AT THE FANTINO SEMINAR

  5. THE THEORY LINK AT THE FANTINO SEMINAR

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  7. Because these are Gaussian (Normal) distributions Fechner could use response probabilities to determine the unknown value of t. LINK AT THE FANTINO SEMINAR

  8. Then knowing that 2t equaled the distance between the two means divided by the standard deviation he determined the unknown variability within the nervous system by computingMean Heaviness(WB) – Mean Heaviness(WA) 2t = ----------------------------------------- s=𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑖𝑣𝑖𝑎𝑡𝑖𝑜𝑛 Mean H(WB)– Mean H(WA) s = ----------------------------------- 2t LINK AT THE FANTINO SEMINAR

  9. Fechner did not know the Heaviness created by a weight but he did know the physical weight. He substituted the known physical weight to obtain a measure of the variability of heaviness in the human nervous system IN UNITS OF THE PHYSICAL STIMULUS. 320g – 300g s = ---------------------------------------- 2t Suppose there were 75% correct responses and 25% errors then t =0.675 and 10g s = ------------------------------------- 0.675 = 14.8g PSYCHOLOGY became a science. LINK AT THE FANTINO SEMINAR

  10. As a measure of the sensitivity of the subject Fechner used 1/s. When the variability was great, s was large and 1/s was small Indicating little sensitivity. But when the variability was small The value of 1/s was large indicating high sensitivity LINK AT THE FANTINO SEMINAR

  11. BUT THERE WAS ANOTHER WAY TO USE THE IDEAS. LINK AT THE FANTINO SEMINAR

  12. 75% Correct responses 75% Correct responses LINK AT THE FANTINO SEMINAR

  13. For a fixed pair of stimuli the difference between the means is fixed. But if the standard deviation changes the number of correct responses will change as shown in this figure. LINK AT THE FANTINO SEMINAR

  14. In order to standardize measures of sensitivity scientists began experiments to determine the comparison stimulus that would generate 75% correct responses which corresponds to a fixed standard deviation and therefore a fixed sensitivity. In this way the 75% threshold was created to measure sensitivity. LINK AT THE FANTINO SEMINAR

  15. The comparison stimulus generating 75% correct responses became a useful criterion, called the 75% threshold, for comparing sensitivities both within and between subjects. LINK AT THE FANTINO SEMINAR

  16. THE 75% THRESHOLD BECAME A UNIVERSAL CRITERION FOR JUDGMENT LINK AT THE FANTINO SEMINAR

  17. EVEN TODAY ONE FINDS EXAMPLES OF THE USE OF THE 75% THRESHOLD The End is Near It looks like the participation in the Greek debt swap has passed the magic 75% threshold. Both Reuters and Dow Jones are reporting that number in the last hour quoting sources in the Greek government. A meeting of the Greek cabinet has just ended with Finance Minister Evangelos Venizelos saying that the debt swap is going well. A 75% participation rate would push the swap above the 75% threshold that the Greek government says is its minimum for proceeding with the offer. A 75% participation rate is also above the 66% level that would let the Greek government invoke collective action clauses on 90% or so of the government’s outstanding debt and force holders of those bonds to participate in the swap. The government has said that it will post the results for the swap offer, which ends tonight, on the website of the Greek Treasury at 6 a.m. Greenwich time tomorrow. LINK AT THE FANTINO SEMINAR

  18. GIVEN THE USEFULNESS OF THIS MEASURE OF SENSITIVITY WHAT IS WRONG WITH USING THE 75% THRESHOLD AS A MEASURE OF SENSITIVITY? LINK AT THE FANTINO SEMINAR

  19. World War II brought about a renewed interest in the abilities of soldiers to discriminate between stimuli. In particular, distinguishing between the noise of the surrounding ocean, as heard over earphones and the sound of the ocean with a nearby submarine lurking within it. Sensitivity became critical to survival. The idea of how to distinguish between the ocean noise and the noise with the submarine somehow adding to the noise became important as the German U2 wolfpacks destroyed vast numbers of ships transporting cargo to Europe from the United States and Canada. The theory of how Sonar Operators could distinguish “Signal” from Noise was the following: LINK AT THE FANTINO SEMINAR

  20. CORRECT REJECTIONS HITS LINK AT THE FANTINO SEMINAR

  21. Sonar (originally an acronym for SOund Navigation And Ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, communicate with or detect objects on or under the surface of the water, such as other vessels. The problem for the SONAR operator is apparent in our figure of the two distributions of loudness. If the value of t is too high the probability of not detecting a submarine when it is present is very high and the submarine blasts you out of the water. LINK AT THE FANTINO SEMINAR

  22. If the value of t is too low even a passing school of fish may make you believe that a sub is present. You sound the alarm and waste a lot of depth charges only killing fish. You might deplete your store of depth charges to a dangerous level. You must somehow optimize your value of t, your criterion, in making judgments. Now the value of the criterion is not fixed between the two means but may vary according to information available to the SONAR operator. LINK AT THE FANTINO SEMINAR

  23. CORRECT REJECTIONS HITS LINK AT THE FANTINO SEMINAR

  24. CORRECT REJECTIONS HITS In Signal Detection Theory sensitivity is measured by Mean[ Noise + Signal ] - Mean [ Noise ] d’ = ------------------------------------------------------------------------ standard deviation = 2t in Fechner’s terms LINK AT THE FANTINO SEMINAR

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  26. Tanner, Swets and Green (1956) Single subject discriminating between Noise and Noise +Signal LINK AT THE FANTINO SEMINAR

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  31. Data from Tanner Swets and Birdsall 1955 Visual Brightness P(Y|n) P(Y|n) Luce’s Low Threshold Theory Signal Detection Theory LINK AT THE FANTINO SEMINAR

  32. SIGNAL DETECTION THEORY LUCE’S LOW THRESHOLD THEORY Acoustic P(Y|s) P(Y|s) P(Y|n) P(Y|n) LINK AT THE FANTINO SEMINAR

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  35. R. C. Atkinson Theory: Variable Sensitivity ROCs LINK AT THE FANTINO SEMINAR

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  37. !!! YIKES !!! WHERE DO ALL THESE DIFFERENT ROC’S COME FROM? THE STIMULI USED IN THE EXPERIMENTS ARE SIMILAR IF NOT IDENTICAL BUT SOMEHOW THE SUBJECTS GENERATE ALL THESE DIFFERENT PERFORMANCES. LINK AT THE FANTINO SEMINAR

  38. Differences between the sensory values of two stimuli are added together over time until a response threshold is exceeded. Then a response occurs LINK AT THE FANTINO SEMINAR

  39. LINK (1975), LINK & HEATH (1975), LINK (….) LINK AT THE FANTINO SEMINAR

  40. ALL THE VARIOUS ROC’S CAN OCCUR BY ROC FOR SIGNAL DETECTION THEORY A. MOVING THE STARTING AMOUNT FROM A BIAS TOWARD RESPONDING HEAVIER TOWARD A BIAS FOR RESPONDING LIGHTER. THIS AMOUNTS TO REQUIRING DIFFERENT AMOUNTS OF INFORMATION TO DECIDE HAEVIER OR LIGHTER. B. INCREASING THE TOTAL AMOUNT OF INFORMATION REQUIRED TO MAKE A RESPONSE. THE RESPONSE BARRIERS MOVE FURTHER APART. THIS RESULTS IN WHAT APPEARS TO BE AN INCREASE IN SENSITIVITY – BUT IS NOT. IT IS AN INCREASE IN THE AMOUNT OF INFORMATION REQUIRED TO MAKE EITHER RESPONSE. LINK AT THE FANTINO SEMINAR

  41. LUCE’S LOW THRESHOLD THEORY • HOLDING THE STARTING VALUE FIXED AND ONE RESPONSE BARRIER FIXED • BUT VARYING THE OTHER RESPONSE BARRIER. • THIS IS THE SAME AS REQUIRING MORE INFORMATION FOR ONE RESPONSE • THAN THE OTHER. • THIS GENERATES TWO STRAIGHT LINE ROCS DEPENDING ON WHICH • BARRIER IS HELD FIXED. LIKE IN THE LUCE THEORY. LINK AT THE FANTINO SEMINAR

  42. ATKINSON’S VARIABLE SENSITIVITY THEORY • SWITCHING BETWEEN THE TWO STRATEGIES IN THE LUCE MODEL WITH DIFFERENT PROBABILITIES GENERATES THE UNIT SLOPE ATKINSON THEORY. LINK AT THE FANTINO SEMINAR

  43. FORTUNATELY THE CHANGES IN PERFORMANCE DUE TO CHANGES IN SENSITIVITY VERSUS CHANGES IN THE AMOUNT OF INFORMATION REQUIRED FOR A RESPONSE CAN BE DIFFERENTIATED WHEN RESPONSE TIMES ARE COLLECTED WITH THE RESPONSE CHOICES. That is why knowing the correct and error response times is critical to interpreting a subject’s performance especially when examining the ROC. That’s all there is to that. THANK YOU LINK AT THE FANTINO SEMINAR

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