basic concepts in perception - university of...

Basic Concepts in PerceptionThe Process of Perception &

Methods for Measuring Simple Perceptions

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Basic Concepts in Perception

• Why study perception?

• Methods in perception research

• Measuring perceptions quantitatively

Chapter 1 in Chaudhuri

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Structure of CourseSomato-sensory

ChemosensoryAudition Vision

Smell Taste

Stimulus Pressure, heat/cold, vibration...

Chemical odorants

Chemical tastants Sound waves Light

Sense OrganThe skin (& other

epithelials)

Olfactory mucosa Tongue

Outer, middle, & inner ear Eye, retina.

Sensory Transducer

Mechano/Thermo/Noci

receptors

Olfactory sensory neurons

Taste Buds Hair cells Rods & Cones

Neural Processing

Medial Lemniscal vs. DorsolateraI. VPN, S1, S11, etc.

Olfactory bulb, O1

3 taste-carrying nerves, NoST,

VPM, POC

Auditory NerveCN, SON, IC, MGN, A1, etc.

Optic Nerve,LGN, SC, V1,

etc. etc.

Higher-order perception

Haptic object recognition,

illusions

Pheromonal effects Flavour

Auditory scene analysis, pitch

Object recognition

ModalitiesTouch,

temperature, motion

???Sour, sweet, bitter, salty,

savoury

Pitch, amplitude, source location

Spatial vision, motion, colour,

depth

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Why Study Perception?

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• Future careers: Graduate school work in perception, cognition etc.; clinical areas too.

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• Applies to many other areas (design, graphic arts, intelligent systems programming...)

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• Understanding the immense intricacy of the sensory systems

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• Understanding the immense intricacy of the sensory systems

• Because it is very very cool! (yes, I’m biased)

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Schizophrenia & Smooth Pursuit Eye Movements

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See, e.g., Holahan ALV, O'Driscoll GA.. Schizophrenia Research, 2005, 76, 43-54. http://tinyurl.com/yv4nhy

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Perception & IQ

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Baltes P.B., & Lindenberger, U. (1997). Psychology and Aging, 12, 12-21.

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Perception & IQ

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Perception & IQ

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The Importance of Perception

• “Man is nothing more than a bundle of sensations” --Protagoras, 450 B.C.

• Virtually everything you know, you know ultimately because of a sensory input.

• Scientific knowledge is entirely dependent on the perceptions of scientists.

• Perception seems simple and direct, but it is in fact fiendishly complex and very indirect.

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Naïve Realism• The philosophical POV

that sensation is simple and direct “I see it because it is there”

• Illusions, among other things prove that this is incorrect

• Research has shown that our sensory systems use complex heuristics to give us a percept of the world that is limited.

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• The moon illusion is one example of illusions that we experience around us on an everyday basis.

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• The moon looks bigger on the horizon, even though it is in fact the same size and at the same distance.

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• This is not an atmospheric lensing effect

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• This is not an atmospheric lensing effect

• For more on this and many other illusions:http://www.michaelbach.de/ot/

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Sensation vs. Perception

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Questions

• What are some reasons for studying perception?

• Give an example of how perception applies to other fields.

• Define “naïve realism”. Why is it untenable?

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Methods in Perception Research

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Methods in Perception

• Qualitative: Getting the big picture.

• Quantitative: Understanding the details

• Threshold-seeking methods

• Magnitude estimation

• Many others, often similar to those used in other areas of psych.

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Qualitative Observation

• “Thatcher Illusion”

• Qualitative observation uncovered the phenomenon

• Much quantitative work now trying to find out why it happens & what it means

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Schwaninger, A., Carbon, C.C., & Leder, H. (2003). Expert face processing: Specialization and constraints. In G. Schwarzer & H. Leder (Eds.), Development of Face Processing, pp. 81-97. Göttingen: Hogrefe.

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Qualitative Methods in Perception

• Also called phenomenological or naturalistic observation methods

• Relatively non-systematic observation of a given perceptual phenomenon or environment (e.g., an illusion)

• Yields a verbal description of one’s observations, (possibly with some simple numerical assessment)

• First step in any study of any perceptual phenomenon. Gives the “big picture”

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• Also called phenomenological or naturalistic observation methods

• Relatively non-systematic observation of a given perceptual phenomenon or environment (e.g., an illusion)

• Yields a verbal description of one’s observations, (possibly with some simple numerical assessment)

• First step in any study of any perceptual phenomenon. Gives the “big picture”

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• Example: Famous perception researcher Jan Purkinje noticed that his flower bed looked light red/dark green during the day but dark red/light green at twilight

• This phenomenological observation led to the hypothesis of 2 visual systems, & ultimately to an understanding of the functions of rods and cones

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Quantitative Methods

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Quantitative Methods in Perception

• Threshold seeking methods measure a physical quantity representing a limit of perceptual ability (i.e., a threshold)

• Measured in physical units (meters, decibels, parts-per-million, candelas of light, etc.)

• Absolute threshold - smallest detectable physical quantity (e.g., 2 dB, 3.57 grams...)

• Difference threshold - smallest detectable difference between two physical quantities

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Quantitative Methods in Perception

• Thresholds are defined for a given level of response accuracy

• Typically we speak of the “50% threshold”, meaning the physical quantity detectable (absolute threshold) or the physical difference detectable (difference threshold) 50% of the time

• But a threshold can be defined for any level of accuracy (e.g., 75%, 83.6%...)

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Threshold-seeking Methods

• Classic methods (Fechner, 1850’s)

• Method of adjustment: Quick and dirty

• Method of limits: Easy on observer, fairly fast and accurate

• Method of constant stimuli: Very slow but very accurate

• Adaptive methods: Fast, very accurate, but can be difficult for untrained observers

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Method of Adjustment

• Stimulus intensity is adjusted (usually by the observer) continuously until observer says he can just detect it

• Threshold is point to which observer adjusts the intensity

• Repeated trials averaged for threshold

• Fast, but not always accurate, due to inherently subjective nature of adjustment

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Adjustment Constant Stim.

Collin, C.A., Therrien, M., Martin, C., & Rainville, S.J.M. (2006). Spatial frequency thresholds for face recognition when comparison faces are filtered and unfiltered. Perception & Psychophysics, 68, 879-889.

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0.9Photometer Reading: cd/m2

Instructions: Adjust the intensity of the light using the slider until you can just barely see it

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Points of Subjective Equality (PSEs)

• Threshold-seeking methods can also be used to find PSEs.

• The PSE is the level of a physical characteristic of a stimulus at which it appears similar to another stimulus.

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Method of Adjustment for PSE

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Instructions: Adjust the length of the lower figure until it appears to be the same length as the upper (standard) stimulus

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Points of Subjective Equality (PSEs)

• PSEs can be used to (among other things) quantify the strength of an illusion

• Example: If the lower figure has to be 1.2 times the length of the upper one to appear equal, then we can say that under these circumstances the illusion has a 20% effect.

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Method of Limits• Stimuli of different intensities presented in

ascending and descending order

• Observer responds to whether she perceived the stimulus

• Cross-over point (between “yes, I see it” and “no, I don’t”) is the threshold for a sequence

• Average of cross-over points from several ascending and descending sequences is taken to obtain final threshold.

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Method of Limits (descending sequence)

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Instructions: For each light intensity, indicate whether you can detect it.

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Method of Limits (ascending sequence)

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Example Data FromMethod of Limits

• Why ascending and descending sequences?

• Why different starting points?

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Method of Constant Stimuli

• 5 to 9 stimuli of different intensities are presented many times each, in random order

• The intensities must span the threshold, so must know approx. where it is a priori.

• Multiple trials (often 100’s) of each intensity are presented

• Threshold is the intensity that results in detection in 50% of trials

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QuestionHere are some data from a participant in the MoCS. Can you estimate her 50% threshold?

Stimulus Intensity cd/m % of stims detected

0.2 0

0.3 0

0.4 0.1

0.5 0.4

0.6 0.7

0.7 0.8

0.8 0.9

0.9 0.9

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The Psychometric Function

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.2 .3 .4 .5 .6 .7 .8 .9 (Stimulus Intensity cd/m2)

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Calculating 50% Threshold Intensity

• To calculate thresholds we use curve-fitting techniques to fit a sigmoidal (=s-shaped) function to the data (green dots).

• This is called a psychometric function (grey line). It links physical stimulus intensity to performance

• Debate exists over which kind of function--Cumulative Normal, Weibull, Logistic, etc.--is theoretically best, but in practice differences are minor

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Math Review: Logs

• Remember exponents? 22 = 4

• Logarithms are the opposite log2(4) = 2

• “What exponent will turn the base--usually 2, 10 or e--into the operand?”

• What is the log10(100)? log2(8)?

• Khan Academy: http://tinyurl.com/7zy5wu7

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Math Review: e (or “Euler’s Number”)• A mysterious constant that just pops up

everywhere in nature. e ≈ 2.71828...

• loge is called the “natural logarithm”, often symbolized as ln

• One also sees ex, where x can be quite a complex expression. “exp(x)” is also used.

• Learn to use your calculator to do logarithms and work with e

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The Weibull Function

• x is stimulus intensity (in some positive physical unit)

• y is predicted probability of stimulus detection (from 0 to 1)

• a is the “offset” and b is the “slope”

• a and b are free parameters whose values are chosen so that the curve best fits the data. These values are determined by curve-fitting algorithms whose details are beyond the scope of the course.

y = 1.0 - exp(-(x/b)a)

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Math Review: Inverse Functions

• If a function F takes input X and returns Y then inverse F takes input Y and returns X

• Example: Y = 2X inverts to X = ½Y

• The Weibull: y = 1.0 - exp(-(x/b)a)

• The inverse Weibull x = b(-ln(1-y))(1/a)

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Math Review: Free Parameters

• Free parameter: Part of a math function that is adjusted so that the function fits data

• Example: The intercept (a) and slope (b) of a line are free parameters when fitting a regression line:y = a + bx;

y = 0 +1x

y = 10 +1x

y = 0 +2x

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Math Review: Free Parameters

• In the Weibull (and its inverse) a and b are free parameters.

• a is the “offset” (in this example a = 1 in all cases)

• b is the “slope” (here varying from 0.5 to 5.0)

y = 1.0 - exp(-(x/5.0)1.0)

y = 1.0 - exp(-(x/1.5)1.0)

y = 1.0 - exp(-(x/1.0)1.0)

y = 1.0 - exp(-(x/0.5)1.0)

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Calculating 50% Threshold Intensity Via Inverse Weibull

• To figure out the threshold, we need to figure out what the right values of a and b are for the Weibull that best fits our data.

• We will then enter the percentage threshold we are seeking (e.g., .5 for 50% threshold) into the inverse Weibull (above) to determine the associated stimulus intensity x

x = b(-ln(1-y))(1/a)

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Calculating 50% Threshold Intensity• Open the excel file "WeibullFit.xlsx"

• Enter your data in two columns:X (stimulus intensity) in column AY (proportion detected) in column B

• Click the Tools menu and select "Solver…". Note that on a Mac you may have to first activate the solver under Tools>Add-Ins

• Click "Solve" in the window that appears. After a moment, the Fit Parameters will appear in cells G2 (slope, or A) and G3 (offset, or B)

• So for our data, the inverse Weibull isx = .589 (-ln (1-y) )(1/1.678)

• We plug in our desired threshold of 0.5 and get a threshold of 0.47 cd/m2

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0"

0.1"

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0.5"

0.6"

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1"

0.00" 0.20" 0.40" 0.60" 0.80" 1.00"

Y"(Data)"

X"

"Data"

"Fit"

Inverse Weibull step-by-step

x = .589 (-ln (1-0.5) )(1/1.68)

x = .589 (.6931)(1/1.68)

x = .589 (.6931)(.596)

x = .589 (.8038)

x = .47

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Example for Self-TestHere are some data from a participant in the MoCS. What is her 50% threshold? What about her 83% threshold?

Stimulus Intensity % of stims detected

0 0

1 0.05

2 0.15

3 0.45

4 0.75

5 0.85

6 0.95

7 0.95

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50% =c.bf83% = e.fc

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Questions

• What is a “free parameter”?

• What is log10(10000)?

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Adaptive Methods• Examples: Staircase, QUEST, PEST, etc.

• Stimulus first presented at an arbitrary level

• If observer perceives it, intensity is reduced by a predetermined step-size

• If observer does not perceive stimulus, intensity is increased

• This is repeated until several reversals are obtained.

• Threshold is average of reversal points.

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N N N N N N Y Y Y N N N Y Y Y N N Y N N

Observer Response “Do you see it?”

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Threshold = (700 + 400 + 700 + 400 + 600 + 500) / 6 = 550

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Calculate the threshold for this run by this observer.

Example for Self-test

ebh.f

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Adaptive Methods• Similar to method of limits, but we don’t run the same

series of levels each time, instead “adapting” each series based on previous performance.

• A number of specific procedures exist, which modify how the adaptation is done (size of steps, etc.): Staircase, QUEST, PEST, etc.

• Very efficient, because almost all trials are close to the threshold and therefore informative.

• But best used with trained psychophysical observers (can be frustrating for untrained Ss)

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Adaptive Variations

• Interleaved staircases

• 1 up / x down

• Weighted

• All combinations of above are possible.

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Interleaved

• Multiple staircases are run at once (typically 2 or 4)

• On a given trial, we choose a staircase at random and show the intensity from that one.

• Keeps the observer from anticipating the direction of stimulus change, reducing bias.

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1 up / X down

• Move up a step in intensity if stimulus not detected.

• But move down a step only once X stimuli in a row (typically 2 or 3) at that intensity are detected.

• Changing X changes the % threshold that the staircase converges upon.

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Weighted Staircases

• Step size is smaller for down than for up.

• Typically, down step is 1/3rd of up step.

• Changing the ratio of up step to down step changes the % threshold the procedure converges on.

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Forced Choice Variations

• Some threshold-seeking methods can be hampered by response bias.

• Some participants have a lax criterion and tend to say “yes, I see it” a lot.

• Some participants have a strict criterion and tend to say “no, I don’t see it” a lot.

• One way to mitigate this problem is to use forced-choice methods.

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X-Alternative Forced Choice Variations

• In a forced-choice task, a participant is given several options to choose from: One contains the stimulus and the others don’t.

• The participant is asked, for example: “Which of the two boxes has a light in it?”

• Note that a forced choice method is a modification of (addition to) the threshold-seeking methods we’ve looked at so far.

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X-Alternative Forced Choice Variations

• Any number of alternatives can be offered, but usually 2 to 8 are given.

• A “2AFC” is a “two-alternative forced choice” procedure, for example.

• The number of alternatives affects the “chance level performance” (= 100% / A)

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2AFC Method of Limits (descending sequence)

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Instructions: For each light intensity, indicate which side it’s on.

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Threshold-finding With Other Senses

• The same methods can be used with a wide variety of sensory qualities.

• Different physical units are used depending on the modality:

• Sound amplitude (decibels)

• Touch pressure (pascals)

• Smell/Taste intensity (parts-per-billion)

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Questions

• What is an absolute threshold?

• Name several methods for measuring absolute thresholds.

• What are some variants on adaptive methods? Why use them?

• Describe generally how the method of limits works.

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Difference Threshold• Smallest intensity difference between two

stimuli a person can detect

• Produces a “Just Noticeable Difference” (JND) in degree of subjective sensation

• Same psychophysical methods are used as for absolute threshold

• As magnitude of stimulus increases, so does difference threshold (∆I)

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Weber’s Law

• Weber’s Law describes the relationship between stimulus intensity (I) and difference threshold (∆I) as follows ∆I / I = K or ∆I = I × K

• This holds true for many senses and many physical quantities across a wide range of moderate intensity levels (but see Steven’s Power Law)

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Weber’s Law

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Method of Adjustment for Difference Threshold

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cd/m2

Instructions: Adjust the intensity of the test light using the slider until you can just barely see the difference between it and the standard light

0.6 cd/m2Standard Light:

Test Light:

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2AFC Method of Limits for ∆I

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• Q: If your Weber fraction (k) is .05, and the standard light’s intensity (Is) is 20, what level will the test light intensity (It)have to be raised to in order for it to be just noticeably different from the standard?

• A: It will have to be higher by the ∆I; That is,

It = Is + ∆I where ∆I = Is × k

∴ It = Is + (Is × k)

It = 20 + (20 × .05) = 21

20 It

Standard Light(Constant)

Test Light(Adjustable)

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• Q: If your Weber fraction (k) is .20, and the standard light’s intensity (Is) is 50, what level will the test light intensity (It)have to be raised to in order for it to be just noticeably different from the standard?

50 It

Standard Light(Constant)

Test Light(Adjustable)

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Example for Self-Test

fj.j

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Questions

• A participant can just tell the difference between lights of 100 cd/m2 and 112 cd/m2. Therefore, she should be able to just tell the difference between 200 cd/m2 and ____ cd/m2.

• What is this participant’s Weber fraction for light intensity?

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Beyond Thresholds

• What do we know about the relationship between subjective sensation and objective intensity at levels above threshold?

• Classic work done by Fechner, who derived Fechner’s Law from Weber’s work.

• This has since been largely supplanted by Steven’s Power Law.

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Fechner’s Law

• From Weber’s findings, Fechner derived the idea that subjective sensation (S) related to stimulus intensity according to: S = k × ln(I/I0)

• k = empirically-determined free parameter

• Recall that “ln” means “log to base e”

• I = stimulus intensity

• I0 = stimulus intensity at absolute threshold

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Fechner’s Assumption

• Fechner assumed that each time you went up by one difference threshold (or, subjectively, one JND), that that related to a an equal jump in subjective intensity.

• Intuitively appealing, but turns out to be wrong, as Stevens later showed.

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Subj

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∆I ∆I ∆I

Objective Stimulus Intensity (I)

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Fechner’s Law

• Works fairly well for some modalities (loudness, weight), but not others (electric shock) that show response expansion

• More closely models the response of individual neurones than people.

• Still, your music player’s volume control is modelled after Weber’s and Fecher’s laws

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Magnitude Estimation

• Technique pioneered by Stevens to examine the relationship between subjective perception and objective stimulus intensity at easily perceived levels

• All stimuli are well above threshold

• Observer is given a standard stimulus and a value for its intensity (e.g., “see this light? this is a ‘5’.” )

• Observer assigns numbers to the test stimuli relative to the standard (e.g., “that looks about twice as bright, I’ll call it a ‘10’. ”);

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Magnitude Estimation

• Relationship between intensity and perception usually shows either:

• Response compression: As intensity increases, the perceived magnitude increases more slowly than the intensity

• Response expansion: As intensity increases, the perceived magnitude increases more quickly than the intensity

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Magnitude Estimation• Relationship between

intensity and perceived magnitude is a power function

• Stevens’ Power Law

• S = k × Ib

(amazingly simple!)

• Note how for b < 1, we get an approximation of Fechner’s law (red line)

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Magnitude Estimation• S = k × Ib

• S = perceived magnitude

• I = physical intensity

• k and b are empirically-determined free parameters

• Note that k is not the Weber Fraction

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The 3 Laws of Psychophysics

• Weber’s law relates two physical units: Standard stimulus intensity and difference threshold

• Fechner’s law relates a physical unit (stimulus intensity) with subjective sensation (or so he thought).

• The above two derive from one another directly, and are sometimes called the Weber-Fechner law

• Steven’s Power Law expands on Fechner’s Law, covering stimuli that show response expansion as well as more closely modelling human responses.

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Questions

Steven’s Power Law: S = k × Ib

Given that for bitterness b=2 and k=2, what will sensory magnitude (S) be for stimulus intensity (I) of 2 ppm?What if I is doubled to 4 ppm? What does this mean about the relationship between stimulus intensity and sensory magnitude in this case?

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83

Sensitivity & Signal Detection Theory

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84

85

85-1

Sensitivity & Signal Detection Theory

• Sensitivity (d’)

• Criterion (c)

• Will spend some time on this, as it is used in many fields (though with different jargon): • Diagnostics• Inferential statistics• Human factors engineering

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85-2

Absolute Thresholds Ain’t So Absolute

• Thresholds shift for many reasons unrelated to actual sensitivity.

• An especially problematic factor is criterion (tendency to say “yes” a lot or “no” a lot).

• For example, an individual doing Method of Limits could just say “yes” to all stimuli (lax criterion) and look like he’s incredibly sensitive!

• xAFC methods are one way to deal with this, but another is to measure Sensitivity instead of threshold.

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Sensitivity

• Sensitivity is symbolized d' (“dee-prime”).

• Measure of one’s ability to detect a given signal (= a stimulus), usually at low intensity.

• Arises from Signal Detection Theory (more later)

• How might we measure sensitivity?

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(a bad way of) Measuring Sensitivity

• Present stimulus 100 times and note % of times participant says he detects it?

• Problem: P who says “yes” all the time will do very well. (the very problem we are trying to avoid!)

• Need measure that reflects ability to discriminate between “signal present” and “signal absent”

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(a good way of) Measuring Sensitivity

• Present stimulus (signal) on only half of the trials, (test trials).

• Present no stimulus (noise) on other half of trials, (catch trials).

• Note that unlike threshold experiments, we present only one stimulus at one intensity.

• Many trials are presented. For each, the participant says “yes, the stimulus is there” or “no, it isn’t”.

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89

Four Possible Results on Each Trial

Present Absent

Yes, I see it

Hit False Alarm

No, I don’t

MissCorrect Rejection

The stimulus is really...

Part

icip

ant

says

...

90

90

Also Known As...

Present Absent

Yes, it’s there

True PositiveFalse Positive(type I error)

No, it’s not

False Negative(type II error) True Negative

The difference is really...

Stat

istic

al t

est

says

...

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91

Present (n =100)

Absent (n=100)

Yes, I see it 90 20

No, I don’t 10 80


Part

icip

ant

says

...

Present (n =100)

Absent (n=100)

Yes, I see it 80 10

No, I don’t 20 90


Part

icip

ant

says

...

Present (n =100)

Absent (n=100)

Yes, I see it 90 30

No, I don’t 10 70


Part

icip

ant

says

...

Albert Benny

Claire

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Link to Sensitivity Calculations (#98)

Link to Criterion Calculations (#104)

Some Example Results

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Sensitivity• The results of such an experiment yield:

proportion of hits (Ph= Nhits / Ntesttrials)proportion of FAs (Pfa= Nfa / Ncatchtrials)

• For example, for Albert: Ph= 90 / 100 = .9Pfa= 20 / 100 = .2

• Note that we could calc proportions of misses and correct rejections too, but these are redundant (Pm = 1-Ph; Pcr = 1-Pfa)

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Questions

• What is Benny’s proportion of hits (Ph)?

• What is his proportion of FA’s (Pfa)?

• How do sensitivity experiments differ in method from threshold-seeking methods?

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Sensitivity

• Perfect participant: Ph = 1, Pfa= 0

• Participant just guessing: Ph = .5, Pfa= .5

• Worst possible participant (perfectly backwards) : Ph = 0, Pfa= 1

• In calculating sensitivity, we want to reward hits and punish FAs, so we could just use “Basic Sensitivity”: BS = Ph - Pfa

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Sensitivity

• BS equals:

• Perfect participant: Ph of 1 - PFA of 0 = 1

• Participant guessing: Ph of .5 - PFA of .5 = 0

• Backward participant: Ph of 0 - PFA of 1 = -1

• So BS essentially works. However, for obscure statistical reasons, BS is, well, B.S.

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• Instead we calculated' = z(Ph) - z(PFA)

• Converting the proportions of hits and FAs to z-scores yields a more valid result.

• d’ is measured in standard deviation units.

• How to calculate the z scores?

• In Excel, use norminv(P, 0, 1)

• Table A5.1 from MacMillan & Creelman• Or the “unit normal” table from any stats

textbook.

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Normal distribution for finding d' (based on Macmillan & Creelman (2005), Signal Detection: A User’s Guide)

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Sensitivity

• d' = z(Ph) - z(Pfa)

• Albert: Ph = .9 ∴ z = 1.28; Pfa = .2 ∴ z = -0.84 ∴ d’ = 1.28 - (-0.84) = 2.12

• Ben: Ph = .8 ∴ z = 0.84; Pfa = .1 ∴ z = -1.28 ∴ d’ = 0.84- (-1.28) = 2.12

• Claire: Ph = .9 ∴ z = 1.28; Pfa = .3 ∴ z = -0.52 ∴ d’ = 1.28 - (-0.52) = 1.8

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Link back to data (#91)

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Zero and One

• What to do with proportions of 0 and 1?

• These yield z scores of -∞ and ∞• There are many ways of getting around this

(MacMillan & Creelman, 2005, chp. 1). For our purposes, just substitute values of 0.01 and 0.99, respectively.

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100

Present (n =100)

Absent (n=100)

Yes, I see it 0 0

No, I don’t 100 100


Part

icip

ant

says

...

Present (n =100)

Absent (n=100)

Yes, I see it 100 100

No, I don’t 0 0


Part

icip

ant

says

...Present

(n =100)Absent

(n=100)

Yes, I see it 100 0

No, I don’t 0 100


Part

icip

ant

says

...

Easy Eddie

DoubtingDan

FlawlessFran

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101

Sensitivity

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102-1

Sensitivity

• d' = z(Ph) - z(PFA)

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102-2

Sensitivity

• d' = z(Ph) - z(PFA)

• Dan: Ph = 0 ∴ z = -2.33; PFA = 0 ∴ z = -2.33 ∴ d’ = -2.33 - (-2.33) = 0 (usual minimum)

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102-3

Sensitivity

• d' = z(Ph) - z(PFA)


• Eddie: Ph = 1 ∴ z = 2.33; PFA = 1 ∴ z = 2.33 ∴ d’ = 2.33 - 2.33 = 0 (usual minimum)

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102-4

Sensitivity

• d' = z(Ph) - z(PFA)


• Eddie: Ph = 1 ∴ z = 2.33; PFA = 1 ∴ z = 2.33 ∴ d’ = 2.33 - 2.33 = 0 (usual minimum)

• Fran: Ph = 1 ∴ z = 2.33; PFA = 0 ∴ z = -2.33 ∴ d’ = 2.33 - (-2.33) = 4.66 (conventional max.)

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102-5

Questions

• Example for self-test: Zack does a sensitivity experiment with 20 test trials and 20 catch trials. He gets 10 hits and 5 false alarms.

• What are his Ph and Pfa values?

• What is is d’?

103

Ph = .ejPfa= .be

d’ = .fg

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Criterion• The flip side of sensitivity is criterion or

response bias.

• How do we measure a person’s tendency to say yes or no? There are several measures, but the simplest is: c = [z(Ph) + z(Pfa)] / -2

• The lower c, the more a person’s tendency to say “yes”. When c<0, yes > no. When c>0, yes < no.

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Criterion

• c = [z(Ph) + z(PFA)] / -2

• Albert: Ph = .9 ∴ z = 1.28; PFA = .2 ∴ z = -0.84 ∴ c = (1.28 - 0.84) / -2 = -.22 [tends to “yes”]

• Ben: Ph = .8 ∴ z = 0.84; PFA = .1 ∴ z = -1.28 ∴ c = (0.84 -1.28) / -2 = .22 [tends to “no”]

• Claire: Ph = .9 ∴ z = 1.28; PFA = .3 ∴ z = -0.52 ∴ c = (1.28 - 0.52) / -2 = -.38 [tends to “yes”]

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Link back to data (#91)

105

Isosensitivity CurvesA range of Ph and Pfa values can produce the same d’.

P P z(P z(P d’ c

0.8 0.4 0.84 -0.25 1.09 -0.295

0.6 0.2 0.25 -0.84 1.09 0.295

0.35 0.07 -0.39 -1.48 1.09 0.935

This occurs when sensitivity remains the same, but criterion shifts

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(a.k.a. “ROC curves”)

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Isosensitivity CurvesPlotting results for different criterion levels at the same sensitivity yields an isosensitivity curve (aka, ROC curve)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

HitRate

FalseAlarmRate

ROCCurved'=1.09

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107-1


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

HitRate

FalseAlarmRate

ROCCurved'=1.09

d’ = 1.09, criterion = -0.30

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107-2


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

HitRate

FalseAlarmRate

ROCCurved'=1.09

d’ = 1.09, criterion = -0.30

d’ = 1.09, criterion = 0.94

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107-3


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

HitRate

FalseAlarmRate

ROCCurved'=1.09

d’ = 1.09, criterion = -0.30

d’ = 1.09, criterion = 0.94

d’ = 1.09, criterion = 0.30

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Hit

Rat

e (P

h)

False Alarm Rate (Pfa)

Miss R

ate (Pm )

Correct Rejection Rate (Pcr)

1.0

.5

0

0.0

.5

1.00 0.5 1.0

1.0 0.5 0

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Why Does Criterion Shift?

• Many reasons, but an important one is the payoff matrix.

• If the cost of a false alarm, or reward for a correct rejection, is great, one will tend to make one’s criterion stricter (more “no”)

• If the cost of a miss, or reward for a hit, is raised, one will tend to make one’s criterion laxer (more “yes”)

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Example of a Pay-off Matrix Leading to a Lax Criterion

Cancer is...

Present (n =100)

Absent (n=100)

Yes, I see it

Patient Saved Unnecessary Additional Testing

No, I don’t

Patient Dies

Patient Goes Home

Radiologist Says...

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Example of a Pay-off Matrix Leading to a Strict Criterion

Accused person’s guilt is...

Present (n =100)

Absent (n=100)

Yes, I see it

Guilty Man Convicted

Innocent Man

Convicted

No, I don’t

Guilty man Released

Innocent Man Released

Judge Says...

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Present (n =100)

Absent (n=100)

Yes, I see it +100$ -$10

No, I don’t -$10 +10$


Part

icip

ant

says

...

Present (n =100)

Absent (n=100)

Yes, I see it +10$ -$10

No, I don’t -$10 +100$


Part

icip

ant

says

...

Lax Strict

Present (n =100)

Absent (n=100)

Yes, I see it +10$ -$10

No, I don’t -$10 +10$


Part

icip

ant

says

...

Neutral

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Performance vs. Criterion

• This all seems complicated! Why not just use Ph or proportion correct? PC = (Ph + PCR) / 2

• These are sometimes used, but both fail to take into account changes in criterion

• For instance, if one condition yields a higher Ph, it might be that that condition just encourages “yes” answers (i.e., leads to lax criterion), not that it is really easier.

• This is one major reason to measure criterion.

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Questions

Dr. X tests a new field diagnostic procedure by applying it to 50 individuals known to have an illness. He finds that it correctly labels all 50 of them as ill, whereas his old procedure labeled only 40 of them as such. He concludes that the new procedure is better. Is his conclusion sound? Why or why not?

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Questions

• Why would one be interested in measuring changes in criterion?

• True or False: As one travels up and to the right along an isosensitivity curve, criterion rises.

• True or False: A higher criterion value indicates a stronger tendency to say “yes, the stimulus is present”

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Signal Detection Theory

• The concepts of sensitivity and criterion arise out of Signal Detection Theory (SDT)

• SDT suggests that any attempt at detecting a signal (stimulus) has to contend with competing noise

• Noise in this sense is random variations from the environment (e.g., literal noise) or from within the detector (e.g., neuron chatter)

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SDT

• Example: You’re in the shower and expecting a call.

• Signal: Phone ringing

• Noise: Sound of shower (plus all other sources of sound), as well as your own internal neuron chatter.

• If the phone isn’t ringing, you have just noise. If the phone is ringing, you have signal+noise.

• d’ is essentially a measure of how similar the signal is to the noise for you subjectively.

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How much it sounds subjectively like a phone

unmistakablynot at all

noise only

Prob

abili

ty

a bit a lotkinda

Probability Distributions of Noise and Signal+Noise

Link back to matrix

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118-1

phone + noise


unmistakablynot at all

noise only

Prob

abili

ty

a bit a lotkinda

Probability Distributions of Noise and Signal+Noise

Link back to matrix

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118-2

phone + noise


completelynot at all

noise only

Prob

abili

ty

a bit a lotkinda

Probability That a Given Perceptual Effect is Due to N or S+N

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119-1

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


119

119-2

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


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119-3

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


119

119-4

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Different Criteria One Can AdoptResult: Pfa = .50 Ph = .95 d' = 1.64

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120-1

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Different Criteria One Can Adopt

Lax

Result: Pfa = .50 Ph = .95 d' = 1.64

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120-2

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Lax

Result: Pfa = .50 Ph = .95 d' = 1.64

120

120-3

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Lax

Result: Pfa = .50 Ph = .95 d' = 1.64

120

120-4

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Lax

Result: Pfa = .50 Ph = .95 d' = 1.64

120

120-5

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Lax

Result: Pfa = .50 Ph = .95 d' = 1.64

120

120-6

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Lax

Result: Pfa = .50 Ph = .95 d' = 1.64

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120-7

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Different Criteria One Can AdoptResult: Pfa = .05 Ph = .50 d' = 1.64

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121-1

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-2

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-3

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-4

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-5

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-6

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-7

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda


Strict

Result: Pfa = .05 Ph = .50 d' = 1.64

121

121-8

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Increasing d’ means increasing the distance betwen the probability distributions. Note how, with a greater d’, a criterion somewhere in the neutral area will produce very few misses or false alarms.

d’ (large)

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122-1

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Increasing d’ means increasing the distance betwen the probability distributions. Note how, with a greater d’, a criterion somewhere in the neutral area will produce very few misses or false alarms.

d’ (large)

122

122-2

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Decreasing d’ means decreasing the distance between the probability distributions. Note how, with a smaller d’, many misses and/or false alarms result, regardless of where the criterion is placed.

d’ (small)

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123-1

phone + noise



noise only

Prob

abili

ty

a bit a lotkinda

Decreasing d’ means decreasing the distance between the probability distributions. Note how, with a smaller d’, many misses and/or false alarms result, regardless of where the criterion is placed.

d’ (small)

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123-2

Questions

• In terms of the SDT, what would be the effect of turning up the phone volume on the probability curves? What effect would this have on d’? What about turning down the shower?

• A guard is watching the woods for visible signs of intruders. What are some likely sources of “noise” in his situation?

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For More Info...

A nice primer: Stanislaw, H., & Todorov, N. (1999). Calculation of signal detection theory measures. Behavioral Research Instruments, Methods and Computers, 31, 137-149.

The bible of SDT: Macmillan, N. A., & Creelman, C. D. (2005). Detection Theory: A User's Guide (2nd ed.). Mahwah, N.J.: Lawrence Erlbaum Associates.

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basic concepts in perception - university of...

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