THE RECEIVER OPERATING CHARACTERISTIC FANTINO SEMINAR APRIL 10, 2013 UCSD STEPHEN LINK 4/10/2013LINK AT THE FANTINO SEMINAR1

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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 How does the subject decide that W B is greater in weight than the Standard, W A ? 4/10/2013LINK AT THE FANTINO SEMINAR4

THE THEORY 4/10/2013LINK AT THE FANTINO SEMINAR5

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Because these are Gaussian (Normal) distributions Fechner could use response probabilities to determine the unknown value of t. 4/10/2013LINK AT THE FANTINO SEMINAR7

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 computing Mean Heaviness(W B ) – Mean Heaviness(W A ) 2t = s= Mean H(W B )– Mean H(W A ) s = t 4/10/2013LINK AT THE FANTINO SEMINAR8

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 = t Suppose there were 75% correct responses and 25% errors then t =0.675 and 10g s = = 14.8g PSYCHOLOGY became a science. 4/10/2013LINK AT THE FANTINO SEMINAR9

4/10/2013LINK AT THE FANTINO SEMINAR10 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

4/10/2013LINK AT THE FANTINO SEMINAR11 BUT THERE WAS ANOTHER WAY TO USE THE IDEAS.

4/10/2013LINK AT THE FANTINO SEMINAR12 75% Correct responses 75% Correct responses

4/10/2013LINK AT THE FANTINO SEMINAR13 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.

4/10/2013LINK AT THE FANTINO SEMINAR14 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.

4/10/2013LINK AT THE FANTINO SEMINAR15 The comparison stimulus generating 75% correct responses became a useful criterion, called the 75% threshold, for comparing sensitivities both within and between subjects.

4/10/2013LINK AT THE FANTINO SEMINAR16 THE 75% THRESHOLD BECAME A UNIVERSAL CRITERION FOR JUDGMENT

4/10/2013LINK AT THE FANTINO SEMINAR17 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. EVEN TODAY ONE FINDS EXAMPLES OF THE USE OF THE 75% THRESHOLD

4/10/2013LINK AT THE FANTINO SEMINAR18 GIVEN THE USEFULNESS OF THIS MEASURE OF SENSITIVITY WHAT IS WRONG WITH USING THE 75% THRESHOLD AS A MEASURE OF SENSITIVITY?

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: 4/10/2013LINK AT THE FANTINO SEMINAR19

HITS CORRECT REJECTIONS 4/10/2013LINK AT THE FANTINO SEMINAR20

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. 4/10/2013LINK AT THE FANTINO SEMINAR21

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. 4/10/2013LINK AT THE FANTINO SEMINAR22

CORRECT REJECTIONS HITS 4/10/2013LINK AT THE FANTINO SEMINAR23

HITS CORRECT REJECTIONS 4/10/2013LINK AT THE FANTINO SEMINAR24 In Signal Detection Theory sensitivity is measured by Mean[ Noise + Signal ] - Mean [ Noise ] d’ = standard deviation = 2t in Fechner’s terms

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Tanner, Swets and Green (1956) Single subject discriminating between Noise and Noise +Signal 4/10/2013LINK AT THE FANTINO SEMINAR26

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Visual Brightness P(Y|n) Data from Tanner Swets and Birdsall 1955 Signal Detection Theory Luce’s Low Threshold Theory 4/10/2013LINK AT THE FANTINO SEMINAR31

Acoustic P(Y|s) P(Y|n) SIGNAL DETECTION THEORYLUCE’S LOW THRESHOLD THEORY 4/10/2013LINK AT THE FANTINO SEMINAR32

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R. C. Atkinson Theory: Variable Sensitivity ROCs 4/10/2013LINK AT THE FANTINO SEMINAR35

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!!! 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. 4/10/2013LINK AT THE FANTINO SEMINAR37

4/10/2013LINK AT THE FANTINO SEMINAR38 Differences between the sensory values of two stimuli are added together over time until a response threshold is exceeded. Then a response occurs

LINK (1975), LINK & HEATH (1975), LINK (….) 4/10/2013LINK AT THE FANTINO SEMINAR39

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. 4/10/2013LINK AT THE FANTINO SEMINAR40

4/10/2013LINK AT THE FANTINO SEMINAR41 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.

4/10/2013LINK AT THE FANTINO SEMINAR42 ATKINSON’S VARIABLE SENSITIVITY THEORY SWITCHING BETWEEN THE TWO STRATEGIES IN THE LUCE MODEL WITH DIFFERENT PROBABILITIES GENERATES THE UNIT SLOPE ATKINSON THEORY.

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 4/10/2013LINK AT THE FANTINO SEMINAR43