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

LINK AT THE FANTINO SEMINAR 1

THE RECEIVER OPERATINGCHARACTERISTIC

FANTINO SEMINARAPRIL 10, 2013

UCSD

STEPHEN LINK

4/10/2013

LINK AT THE FANTINO SEMINAR 24/10/2013



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?

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THE THEORY

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Because these are Gaussian (Normal) distributions Fechner could use response probabilities to determine the unknown value of t.

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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(WB) – Mean Heaviness(WA)

2t = ----------------------------------------- s= 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑖𝑣𝑖𝑎𝑡𝑖𝑜𝑛

Mean H(WB)– Mean H(WA)s = -----------------------------------

2t

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Fechner did not know the Heaviness created by a weightbut 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 responsesand 25% errors

then t =0.675 and

10gs = -------------------------------------

0.675

= 14.8g

PSYCHOLOGY became a science.4/10/2013


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 smallIndicating little sensitivity. But when the variability was smallThe value of 1/s was large indicating high sensitivity

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

2

4

6

8

10

12

Sensitivity

sensivity

Standard deviation

Sens

itivi

ty


BUT THERE WAS ANOTHER WAY TO USE THE IDEAS.


75% Correct responses

75% Correct responses


0.00 0.50 1.00 1.50 2.00 2.50 3.000.500

0.750

1.000

PROBABILITY CORRECT

P(Correct)

75% Correct Threshold

Standard deviation

P(Co

rrec

t)

For a fixed pair of stimuli the difference between the meansis fixed. But if the standard deviation changes the number of correct responses will change as shown in this figure.


0.00 0.50 1.00 1.50 2.00 2.50 3.000.500

0.750

1.000

P(Correct)

75% Correct Threshold

sd|Threshold

Standard deviation

P(Co

rrec

t)

In order to standardize measures of sensitivity scientistsbegan experiments to determine the comparison stimulusthat 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.


290 300 310 320 330 340 350 3600.50

0.75

1.00

P(Correct|Comparison stimulus)

COMPARISON STIMULI

P(Co

rrec

t)

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


THE 75% THRESHOLD BECAME A UNIVERSAL CRITERION

FOR JUDGMENT


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


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, distinguishingbetween the noise of the surrounding ocean, as heard over earphonesand 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 noisewith the submarine somehow adding to the noise became important asthe German U2 wolfpacks destroyed vast numbers of ships transportingcargo to Europe from the United States and Canada.

The theory of how Sonar Operators could distinguish “Signal” fromNoise was the following:

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HITS

CORRECTREJECTIONS

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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.

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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 wastea 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 informationavailable to the SONAR operator.

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CORRECTREJECTIONS

HITS

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HITS

CORRECTREJECTIONS

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In Signal Detection Theory sensitivity is measured by

Mean[ Noise + Signal ] - Mean [ Noise ]d’ = ------------------------------------------------------------------------

standard deviation

= 2t in Fechner’s terms



Tanner, Swets and Green (1956)Single subject discriminating between Noise and Noise +Signal

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Visual Brightness

P(Y|n) P(Y|n)

Data from Tanner Swets and Birdsall 1955

Signal Detection Theory Luce’s Low Threshold Theory

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Acoustic

P(Y|s) P(Y|s)

P(Y|n) P(Y|n)

SIGNAL DETECTION THEORY LUCE’S LOW THRESHOLD THEORY

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R. C. Atkinson Theory: Variable Sensitivity ROCs

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LINK AT THE FANTINO SEMINAR4/10/2013 36


!!! 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.

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Differences between the sensory values of two stimuliare added together over time until a response thresholdis exceeded. Then a response occurs


LINK (1975), LINK & HEATH (1975), LINK (….)

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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.

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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.


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 RESPONSECAN BE DIFFERENTIATED WHEN RESPONSE TIMES ARE

COLLECTED WITH THE RESPONSE CHOICES.

That is why knowing the correct and error response timesis critical to interpreting a subject’s performance especially when examining the ROC.

That’s all there is to that.

THANK YOU

4/10/2013

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

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