Basic Concepts in Perception
The Process of Perception & Methods for Measuring Simple Perceptions
1
1
1-1
1-2
Basic Concepts in
Perception
Structure of Course
Smell
Taste
Stimulus
Pressure, heat/
cold, vibration...
Chemical
odorants
Sense Organ
The skin (& other
epithelials)
Sensory
Transducer
Mechano/
Thermo/Noci
receptors
Chapter 1 in Chaudhuri
• Why study perception?
• Methods in perception research
• Measuring perceptions quantitatively
Chemosensory
Somatosensory
Neural
Processing
Audition
Vision
Chemical
tastants
Sound waves
Light
Olfactory
mucosa
Tongue
Outer, middle, &
inner ear
Eye, retina.
Olfactory
sensory
neurons
Taste Buds
Hair cells
Rods & Cones
3 taste-carrying Auditory Nerve
Medial Lemniscal
Olfactory bulb,
vs. DorsolateraI.
nerves, NoST,
CN, SON, IC,
O1
VPN, S1, S11, etc.
VPM, POC
MGN, A1, etc.
Higher-order
perception
Haptic object
recognition,
illusions
Pheromonal
effects
Flavour
Modalities
Touch,
temperature,
motion
???
Sour, sweet,
bitter, salty,
savoury
2
3
2
3
Auditory scene
analysis, pitch
Optic Nerve,
LGN, SC,V1,
etc. etc.
Object
recognition
Spatial vision,
Pitch, amplitude,
motion, colour,
source location
depth
Why Study Perception?
Why Study Perception?
• Future careers: Graduate school work in
perception, cognition etc.; clinical areas too.
4
4
4-1
4-2
Why Study Perception?
Why Study Perception?
• Future careers: Graduate school work in
• Future careers: Graduate school work in
• Applies to many other areas (design, graphic
• Applies to many other areas (design, graphic
perception, cognition etc.; clinical areas too.
arts, intelligent systems programming...)
perception, cognition etc.; clinical areas too.
arts, intelligent systems programming...)
• Understanding the immense intricacy of the
sensory systems
4
4
4-3
4-4
Why Study Perception?
Schizophrenia & Smooth
Pursuit Eye Movements
• Future careers: Graduate school work in
perception, cognition etc.; clinical areas too.
• Applies to many other areas (design, graphic
arts, intelligent systems programming...)
• Understanding the immense intricacy of the
sensory systems
• Because it is very very cool! (yes, I’m biased)
See, e.g., Holahan ALV, O'Driscoll GA.. Schizophrenia
Research, 2005, 76, 43-54. http://tinyurl.com/yv4nhy
4
5
4-5
5-1
Schizophrenia & Smooth
Pursuit Eye Movements
Schizophrenia & Smooth
Pursuit Eye Movements
See, e.g., Holahan ALV, O'Driscoll GA.. Schizophrenia
See, e.g., Holahan ALV, O'Driscoll GA.. Schizophrenia
Research, 2005, 76, 43-54. http://tinyurl.com/yv4nhy
Research, 2005, 76, 43-54. http://tinyurl.com/yv4nhy
5
5
5-2
5-3
Perception & IQ
Baltes P.B., & Lindenberger, U. (1997). Psychology and Aging, 12, 12-21.
Perception & IQ
Baltes P.B., & Lindenberger, U. (1997). Psychology and Aging, 12, 12-21.
6
6
6-1
6-2
Perception & IQ
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.
Baltes P.B., & Lindenberger, U. (1997). Psychology and Aging, 12, 12-21.
6
7
6-3
7
Naïve Realism
Naïve Realism
•
The philosophical POV
that sensation is simple
and direct “I see it
because it is there”
•
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
•
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.
•
Research has shown that
our sensory systems use
complex heuristics to give
us a percept of the world
that is limited.
8
8
8-1
8-2
Naïve Realism
Naïve Realism
•
The philosophical POV
that sensation is simple
and direct “I see it
because it is there”
•
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
•
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.
•
Research has shown that
our sensory systems use
complex heuristics to give
us a percept of the world
that is limited.
8
8
8-3
8-4
•
The moon illusion is one example of
illusions that we experience around us on
an everyday basis.
9
9
9-1
9-2
•
The moon illusion is one example of
illusions that we experience around us on
an everyday basis.
•
The moon illusion is one example of
illusions that we experience around us on
an everyday basis.
•
The moon looks bigger on the horizon,
even though it is in fact the same size and
at the same distance.
•
The moon looks bigger on the horizon,
even though it is in fact the same size and
at the same distance.
•
This is not an atmospheric lensing effect
9
9
9-3
9-4
•
The moon illusion is one example of
illusions that we experience around us on
an everyday basis.
•
The moon looks bigger on the horizon,
even though it is in fact the same size and
at the same distance.
•
•
This is not an atmospheric lensing effect
Sensation vs. Perception
For more on this and many other illusions:
http://www.michaelbach.de/ot/
9
10
9-5
10-1
Sensation vs. Perception
Sensation vs. Perception
10
10
10-2
10-3
Questions
Methods in Perception
Research
• What are some reasons for studying
perception?
• Give an example of how perception applies
to other fields.
• Define “naïve realism”. Why is it untenable?
11
12
11
12
Methods in Perception
Qualitative Observation
• 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.
•
•
“Thatcher Illusion”
•
Much quantitative work
now trying to find out why
it happens & what it means
Qualitative observation
uncovered the phenomenon
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.
13
14
13
14-1
Qualitative Observation
Qualitative Observation
•
•
“Thatcher Illusion”
•
•
“Thatcher Illusion”
•
Much quantitative work
now trying to find out why
it happens & what it means
•
Much quantitative work
now trying to find out why
it happens & what it means
Qualitative observation
uncovered the phenomenon
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.
Qualitative observation
uncovered the phenomenon
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.
14
14
14-2
14-3
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”
15
15
15-1
15-2
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”
Qualitative Methods in
Perception
•
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
15
16
15-3
16
Quantitative Methods
17
18
17
18
Quantitative Methods in
Perception
Quantitative Methods in
Perception
• Threshold seeking methods measure a
• Thresholds are defined for a given level of
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
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%...)
19
20
19
20
Threshold-seeking
Methods
Method of Adjustment
• 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
• 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
21
22
21
22
Method of Adjustment
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.
Method of Adjustment
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Photometer Reading: 0.9 cd/m2
23
24
23
24-1
Method of Adjustment
Method of Adjustment
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Photometer Reading: 0.8 cd/m2
Photometer Reading: 0.7 cd/m2
24
24
24-2
24-3
Method of Adjustment
Method of Adjustment
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Photometer Reading: 0.6 cd/m2
Photometer Reading: 0.5 cd/m2
24
24
24-4
24-5
Method of Adjustment
Method of Adjustment
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Photometer Reading: 0.4 cd/m2
Photometer Reading: 0.3 cd/m2
24
24
24-6
24-7
Method of Adjustment
Method of Adjustment
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Instructions: Adjust the intensity of the light
using the slider until you can just barely see it
Photometer Reading: 0.2 cd/m2
Photometer Reading: 0.1 cd/m2
24
24
24-8
24-9
Points of Subjective
Equality (PSEs)
Method of Adjustment
for PSE
• Threshold-seeking methods can also be used
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
to find PSEs.
• The PSE is the level of a physical
characteristic of a stimulus at which it
appears similar to another stimulus.
25
26
25
26-1
Method of Adjustment
for PSE
Method of Adjustment
for PSE
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
26
26
26-2
26-3
Method of Adjustment
for PSE
Method of Adjustment
for PSE
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
26
26
26-4
26-5
Method of Adjustment
for PSE
Method of Adjustment
for PSE
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
26
26
26-6
26-7
Method of Adjustment
for PSE
Points of Subjective
Equality (PSEs)
Instructions: Adjust the length of the lower
figure until it appears to be the same length as
the upper (standard) stimulus
• 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.
26
27
26-8
27
Method of Limits
• Stimuli of different intensities presented in
ascending and descending order
Method of Limits
(descending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
• 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.
Photometer Reading: 0.9 cd/m2
28
29
28
29-1
Method of Limits
Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.8 cd/m2
Photometer Reading: 0.7 cd/m2
29
29
29-2
29-3
Method of Limits
Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.6 cd/m2
Photometer Reading: 0.5 cd/m2
29
29
29-4
29-5
Method of Limits
Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.4 cd/m2
Photometer Reading: 0.3 cd/m2
29
29
29-6
29-7
Method of Limits
Method of Limits
(descending sequence)
(ascending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.2 cd/m2
Photometer Reading: 0.2 cd/m2
29
30
29-8
30-1
Method of Limits
Method of Limits
(ascending sequence)
(ascending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.3 cd/m2
Photometer Reading: 0.4 cd/m2
30
30
30-2
30-3
Method of Limits
Method of Limits
(ascending sequence)
(ascending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.5 cd/m2
Photometer Reading: 0.6 cd/m2
30
30
30-4
30-5
Method of Limits
Method of Limits
(ascending sequence)
(ascending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Instructions: For each light intensity, indicate
whether you can detect it.
Photometer Reading: 0.7 cd/m2
Photometer Reading: 0.8 cd/m2
30
30
30-6
30-7
Method of Limits
(ascending sequence)
Instructions: For each light intensity, indicate
whether you can detect it.
Example Data From
Method of Limits
•
Why ascending
and descending
sequences?
•
Why different
starting points?
Photometer Reading: 0.9 cd/m2
30
31
30-8
31
Method of Constant
Stimuli
• 5 to 9 stimuli of different intensities are
presented many times each, in random order
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
• 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
cd/m2
32
33
32
33-1
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.4
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-2
33-3
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.7
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-4
33-5
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.4
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-6
33-7
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.9
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-8
33-9
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.4
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-10
33-11
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.2
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-12
33-13
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.5
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
cd/m2
33
33
33-14
33-15
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.5
cd/m2
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Instructions: For each light intensity,
indicate whether you can detect it.
0.5
cd/m2
33
33
33-16
33-17
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Photometer
Readings
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
Method of
Constant Stimuli
Question
Photometer
Readings
Instructions: For each light intensity,
indicate whether you can detect it.
0.5
cd/m2
Here are some data from a participant in the MoCS.
Can you estimate her 50% threshold?
0.4
0.7
0.4
0.9
0.4
0.2
0.5
0.5
0.5
.
.
.
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
33
34
33-18
34
The Psychometric
Function
.2 .3 .4 .5 .6 .7 .8 .9
(Stimulus Intensity cd/m2)
•
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
35
36
35
36
Calculating 50%
Threshold Intensity
Math Review: Logs
• Remember exponents? 2 = 4
• Logarithms are the opposite log (4) = 2
• “What exponent will turn the base--usually 2,
10 or e--into the operand?”
2
2
•
•
What is the log10(100)? log2(8)?
Khan Academy: http://tinyurl.com/7zy5wu7
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
37
38
37
38
The Weibull Function
Math Review: Inverse
Functions
y = 1.0 - exp(-(x/b)a)
• 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.
• 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
y = 1.0 - exp(-(x/b) )
• The Weibull:
• The inverse Weibull x = b(-ln(1-y))
a
(1/a)
39
40
39
40
Math Review: Free
Parameters
Math Review: Free
Parameters
y = 10 +1x
•
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 +2x
y = 0 +1x
y = 1.0 - exp(-(x/5.0)1.0)
•
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/1.5)1.0)
y = 1.0 - exp(-(x/1.0)1.0)
y = 1.0 - exp(-(x/0.5)1.0)
41
42
41
42
Calculating 50% Threshold Intensity
Via Inverse Weibull
Calculating 50% Threshold Intensity
x = b(-ln(1-y))(1/a)
• 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
• Open the excel file "WeibullFit.xlsx"
• Enter your data in two columns:
X (stimulus intensity) in column A
Y (proportion detected) in column B
the Tools menu and select "Solver…". • Click
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 is
x = .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
43
44
43
44
Inverse Weibull
step-by-step
Example for Self-Test
Here 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
1"
0.9"
x = .589 (.6931)(1/1.68)
0.8"
Y"(Data)"
0.7"
x = .589 (.6931)(.596)
x = .589 (.8038)
0.6"
0.5"
"Data"
0.4"
"Fit"
0.3"
0.2"
0.1"
x = .47
0"
0.00"
0.20"
0.40"
0.60"
0.80"
1.00"
X"
45
46
45
46
Questions
• What is a “free parameter”?
• What is log (10000)?
10
50% =c.bf
83% = e.fc
x = .589 (-ln (1-0.5) )(1/1.68)
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.
47
48
47
48
Stimulus Intensity
Stimulus Intensity
Reversal Points
700
600
500
400
300
200
100
0
N
N
N
N
N
N
Y
Y
Y
N
N
N
Y
Y
Y
N
N
Y
N
700
600
500
400
300
200
100
0
N
N
N
N
N
N
N
Y
Y
Y
N
Y
N
N
49
49-1
49-2
500
400
300
200
100
N
N
N
N
Y
Y
Y
N
N
N
Y
Y
Y
N
Y
N
N
Y
N
N
Reversal Points
Stimulus Intensity
Stimulus Intensity
Y
49
600
N
Y
Observer Response “Do you see it?”
700
N
N
Observer Response “Do you see it?”
Reversal Points
0
N
N
Observer Response “Do you see it?”
Y
N
N
700
600
500
400
300
200
100
0
N
N
N
N
N
N
Y
Y
Y
N
N
N
Y
Y
Y
N
N
Observer Response “Do you see it?”
Threshold = (700 + 400 + 700 + 400 + 600 + 500) / 6
= 550
49
49
49-3
49-4
Stimulus Intensity
Example for Self-test
700
600
500
400
300
200
600
500
400
300
200
100
0
100
N
N
N
N
N
N
Y
Y
Y
N
N
N
Y
Y
Y
N
N
Y
N
N
N
N
N
N
N
Y
Y
Y
N
N
N
N
Y
Y
Y
N
N
Y
N
Y
Observer Response “Do you see it?”
Calculate the threshold for this run by this observer.
ebh.f
0
700
50
51
50
51
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)
Adaptive Variations
• Interleaved staircases
• 1 up / x down
• Weighted
• All combinations of above are possible.
52
53
52
53
Interleaved
1 up / X down
• Multiple staircases are run at once (typically
• Move up a step in intensity if stimulus not
• On a given trial, we choose a staircase at
• But move down a step only once X stimuli
• Keeps the observer from anticipating the
• Changing X changes the % threshold that
2 or 4)
random and show the intensity from that
one.
direction of stimulus change, reducing bias.
detected.
in a row (typically 2 or 3) at that intensity
are detected.
the staircase converges upon.
54
55
54
55
Weighted Staircases
Forced Choice
Variations
• Some threshold-seeking methods can be
•
• Typically, down step is 1/3rd of up step.
• Changing the ratio of up step to down step
Step size is smaller for down than for up.
changes the % threshold the procedure
converges on.
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.
56
57
56
57
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.
X-Alternative Forced
Choice Variations
• Any number of alternatives can be offered,
but usually 2 to 8 are given.
• The participant is asked, for example:
• A “2AFC” is a “two-alternative forced
• Note that a forced choice method is a
• The number of alternatives affects the
“Which of the two boxes has a light in it?”
modification of (addition to) the thresholdseeking methods we’ve looked at so far.
choice” procedure, for example.
“chance level performance” (= 100% / A)
58
59
58
59
2AFC Method of Limits
2AFC Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
which side it’s on.
Instructions: For each light intensity, indicate
which side it’s on.
Photometer Reading: 0.9 cd/m2
Photometer Reading: 0.8 cd/m2
60
60
60-1
60-2
2AFC Method of Limits
2AFC Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
which side it’s on.
Instructions: For each light intensity, indicate
which side it’s on.
Photometer Reading: 0.7 cd/m2
Photometer Reading: 0.6 cd/m2
60
60
60-3
60-4
2AFC Method of Limits
2AFC Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
which side it’s on.
Instructions: For each light intensity, indicate
which side it’s on.
Photometer Reading: 0.5 cd/m2
Photometer Reading: 0.4 cd/m2
60
60
60-5
60-6
2AFC Method of Limits
2AFC Method of Limits
(descending sequence)
(descending sequence)
Instructions: For each light intensity, indicate
which side it’s on.
Instructions: For each light intensity, indicate
which side it’s on.
Photometer Reading: 0.3 cd/m2
Photometer Reading: 0.2 cd/m2
60
60
60-7
60-8
Threshold-finding With
Other Senses
Questions
• The same methods can be used with a wide
variety of sensory qualities.
• Different physical units are used depending
on the modality:
•
• Touch pressure (pascals)
• Smell/Taste intensity (parts-per-billion)
Sound amplitude (decibels)
• 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.
61
62
61
62
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)
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)
63
64
63
64
Weber’s Law
65
66
65
66
Method of Adjustment for
Difference Threshold
Method of Adjustment for
Difference Threshold
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
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
Standard Light:
Photometer
Readings
0.6 cd/m2
Standard Light:
Photometer
Readings
0.6 cd/m2
Test Light:
0.9 cd/m2
Test Light:
0.8 cd/m2
67
67
67-1
67-2
Method of Adjustment for
Difference Threshold
Method of Adjustment for
Difference Threshold
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
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
Standard Light:
Photometer
Readings
0.6 cd/m2
Standard Light:
Photometer
Readings
0.6 cd/m2
Test Light:
0.7 cd/m2
Test Light:
0.6 cd/m2
67
67
67-3
67-4
Method of Adjustment for
Difference Threshold
Method of Adjustment for
Difference Threshold
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
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
Standard Light:
Photometer
Readings
0.6 cd/m2
Standard Light:
Photometer
Readings
0.6 cd/m2
Test Light:
0.5 cd/m2
Test Light:
0.4 cd/m2
67
67
67-5
67-6
Method of Adjustment for
Difference Threshold
Method of Adjustment for
Difference Threshold
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
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
Standard Light:
Photometer
Readings
0.6 cd/m2
Standard Light:
Photometer
Readings
0.6 cd/m2
Test Light:
0.3 cd/m2
Test Light:
0.2 cd/m2
67
67
67-7
67-8
Method of Adjustment for
Difference Threshold
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
Standard Light:
Photometer
Readings
0.6 cd/m2
Test Light:
0.1 cd/m2
2AFC Method of Limits
for ∆I
Instructions: For each set of lights, indicate
which pair (right or left) differ.
67
68
67-9
68-1
2AFC Method of Limits
for ∆I
2AFC Method of Limits
for ∆I
68
68
68-2
68-3
Instructions: For each set of lights, indicate
which pair (right or left) differ.
Instructions: For each set of lights, indicate
which pair (right or left) differ.
2AFC Method of Limits
for ∆I
Instructions: For each set of lights, indicate
which pair (right or left) differ.
Standard Light
(Constant)
Test Light
(Adjustable)
20
It
•
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
69
68-4
69
Example for Self-Test
Questions
Standard Light
(Constant)
Test Light
(Adjustable)
50
It
• 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
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?
70
70
for light intensity?
fj.j
•
68
71
71
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.
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
72
73
72
73
Fechner’s Assumption
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.
74
75
74
75-1
Fechner’s Assumption
75
75
75-2
75-3
Fechner’s Assumption
Fechner’s Law
Subjective Sensation (S)
Fechner’s Assumption
• 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.
∆I
∆I
∆I
• Still, your music player’s volume control is
modelled after Weber’s and Fecher’s laws
Objective Stimulus Intensity (I)
76
77
76
77
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 assigns numbers to the test stimuli relative
to the standard (e.g., “that looks about twice as
bright, I’ll call it a ‘10’. ”);
• Relationship between intensity and
perception usually shows either:
• Response compression: As intensity
increases, the perceived magnitude
increases more slowly than the intensity
Observer is given a standard stimulus and a value for
its intensity (e.g., “see this light? this is a ‘5’.” )
• Response expansion: As intensity increases,
the perceived magnitude increases more
quickly than the intensity
78
79
78
79
Magnitude Estimation
Magnitude Estimation
Relationship between
intensity and perceived
magnitude is a power
function
Stevens’ Power Law
•
Magnitude Estimation
S = k × Ib
(amazingly simple!)
Note how for b < 1, we
get an approximation of
Fechner’s law (red line)
•
•
•
•
S = k × Ib
•
Note that k is not the
Weber Fraction
S = perceived magnitude
I = physical intensity
k and b are empiricallydetermined free
parameters
80
81
80
81
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.
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?
82
83
82
83
Sensitivity & Signal
Detection Theory
84
85
84
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
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.
85
86
85-2
86
Sensitivity
• Sensitivity is symbolized d' (“dee-prime”).
• Measure of one’s ability to detect a given signal
(= a stimulus), usually at low intensity.
•
• How might we measure sensitivity?
Arises from Signal Detection Theory (more later)
(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”
87
88
87
88
Four Possible Results on Each Trial
(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”.
Participant says...
•
The stimulus is really...
Hit
False Alarm
No, I don’t
Miss
Correct
Rejection
89
90
Some Example Results
Absent
True Positive
False Positive
(type I error)
Present
(n =100)
Absent
(n=100)
Yes, I see it
90
20
No, I don’t
10
80
Present
(n =100)
Absent
(n=100)
Yes, I see it
80
10
No, I don’t
20
90
The stimulus is really...
Participant says...
Claire
False Negative
True Negative
(type II error)
Benny
Participant says...
Present
The stimulus is really...
The stimulus is really...
Participant says...
The difference is really...
Statistical test says...
Yes, I see it
90
Albert
No, it’s not
Absent
89
Also Known As...
Yes, it’s there
Present
Present (n =100)
Absent
(n=100)
Yes, I see it
90
30
Link to Sensitivity
Calculations (#98)
No, I don’t
10
70
Link to Criterion
Calculations (#104)
91
92
91
92
Sensitivity
Questions
•
The results of such an experiment yield:
proportion of hits (Ph= Nhits / Ntesttrials)
proportion of FAs (Pfa= Nfa / Ncatchtrials)
•
For example, for Albert: •
Note that we could calc proportions of
misses and correct rejections too, but these
are redundant (Pm = 1-Ph; Pcr = 1-Pfa)
h
fa
Ph= 90 / 100 = .9
Pfa= 20 / 100 = .2
method from threshold-seeking methods?
93
94
93
94
Sensitivity
Sensitivity
• Perfect participant: P = 1, P = 0
• Participant just guessing: P = .5, P = .5
• Worst possible participant (perfectly
h
fa
h
fa
backwards) : Ph = 0, Pfa= 1
•
• What is Benny’s proportion of hits (P )?
• What is his proportion of FA’s (P )?
• How do sensitivity experiments differ in
In calculating sensitivity, we want to reward
hits and punish FAs, so we could just use
“Basic Sensitivity”: BS = Ph - Pfa
•
•
•
•
•
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.
95
96
95
96
Normal distribution for finding d'
(based on Macmillan & Creelman (2005), Signal Detection: A User’s Guide)
we calculate
• Instead
d' = z(P ) - z(P )
h
FA
• 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.
97
98
97
98
Sensitivity
Link back to data
(#91)
•
•
d' = z(Ph) - z(Pfa)
•
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
Albert: Ph = .9 ∴ z = 1.28; Pfa = .2 ∴ z = -0.84
∴ d’ = 1.28 - (-0.84) = 2.12
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.
99
100
99
100
Present
(n =100)
Absent
(n=100)
Yes, I see it
0
0
No, I don’t
100
100
Flawless
Fran
•
Participant says...
The stimulus is really...
Participant says...
Participant says...
Doubting
Dan
Easy
Eddie
Sensitivity
The stimulus is really...
Present
(n =100)
Absent
(n=100)
Yes, I see it
100
100
No, I don’t
0
0
The stimulus is really...
Present (n =100)
Absent
(n=100)
Yes, I see it
100
0
No, I don’t
0
100
101
102
101
102-1
Sensitivity
Sensitivity
•
•
d' = z(Ph) - z(PFA)
d' = z(Ph) - z(PFA)
Dan: Ph = 0 ∴ z = -2.33; PFA = 0 ∴ z = -2.33
∴ d’ = -2.33 - (-2.33) = 0 (usual minimum)
102
102
102-2
102-3
Sensitivity
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)
Dan: Ph = 0 ∴ z = -2.33; PFA = 0 ∴ z = -2.33
∴ d’ = -2.33 - (-2.33) = 0 (usual minimum)
•
•
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.)
Dan: Ph = 0 ∴ z = -2.33; PFA = 0 ∴ z = -2.33
∴ d’ = -2.33 - (-2.33) = 0 (usual minimum)
102
102
102-4
102-5
Questions
Criterion
• The flip side of sensitivity is criterion or
response bias.
• 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.
and Pfa values?
d’ = .fg
h
Ph = .ej
Pfa= .be
• What are his P
• What is is d’?
• 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.
103
104
103
104
Link back to data
(#91)
Criterion
Isosensitivity Curves
(a.k.a. “ROC curves”)
A range of Ph and Pfa values can produce the same d’.
•
•
c = [z(Ph) + z(PFA)] / -2
P
P
z(P
Albert: Ph = .9 ∴ z = 1.28; PFA = .2 ∴ z = -0.84
∴ c = (1.28 - 0.84) / -2 = -.22 [tends to “yes”]
0.8
0.4
0.84 -0.25 1.09 -0.295
•
Ben: Ph = .8 ∴ z = 0.84; PFA = .1 ∴ z = -1.28
∴ c = (0.84 -1.28) / -2 = .22 [tends to “no”]
0.6
0.2
0.25 -0.84 1.09 0.295
•
Claire: Ph = .9 ∴ z = 1.28; PFA = .3 ∴ z = -0.52
∴ c = (1.28 - 0.52) / -2 = -.38 [tends to “yes”]
z(P
d’
c
0.35 0.07 -0.39 -1.48 1.09 0.935
This occurs when sensitivity remains the same, but
criterion shifts
105
106
105
106
Isosensitivity Curves
Isosensitivity Curves
Plotting results for different criterion levels at the same
sensitivity yields an isosensitivity curve (aka, ROC curve)
Plotting results for different criterion levels at the same
sensitivity yields an isosensitivity curve (aka, ROC curve)
1
1
ROC
Curve
d'
=
1.09
0.8
0.8
0.6
0.6
ROC
Curve
d'
=
1.09
Hit
Rate
Hit
Rate
d’ = 1.09, criterion = -0.30
0.4
0.4
0.2
0.2
0
0
0
0.2
0.4
0.6
False
Alarm
Rate
0.8
1
0
0.2
0.4
0.6
False
Alarm
Rate
107
107
107-1
107-2
0.8
1
Isosensitivity Curves
Isosensitivity Curves
Plotting results for different criterion levels at the same
sensitivity yields an isosensitivity curve (aka, ROC curve)
Plotting results for different criterion levels at the same
sensitivity yields an isosensitivity curve (aka, ROC curve)
1
1
ROC
Curve
d'
=
1.09
0.8
ROC
Curve
d'
=
1.09
0.8
d’ = 1.09, criterion = -0.30
d’ = 1.09, criterion = -0.30
Hit
Rate
0.6
Hit
Rate
0.6
0.4
d’ = 1.09, criterion = 0.30
0.4
d’ = 1.09, criterion = 0.94
d’ = 1.09, criterion = 0.94
0.2
0.2
0
0
0
0.2
0.4
0.6
0.8
1
0
False
Alarm
Rate
107
107
107-3
107-4
0
.5
0
0.5
0.6
0.8
1
Why Does
Criterion Shift?
0.0
1.0
1.0
Miss Rate (Pm)
Hit Rate (Ph)
0.5
.5
0
0.4
False
Alarm
Rate
Correct Rejection Rate (Pcr)
1.0
1.0
0.2
• 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”)
False Alarm Rate (Pfa)
108
109
108
109
Example of a Pay-off Matrix
Leading to a Lax Criterion
Example of a Pay-off Matrix
Leading to a Strict Criterion
Cancer is...
Radiologist
Says...
Accused person’s guilt 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
Judge Says...
Participant says...
Yes, I see it
+10$
-$10
No, I don’t
-$10
+10$
+100$
-$10
No, I don’t
-$10
+10$
No, I don’t
Guilty man
Released
Innocent Man
Released
Strict
Present
(n =100)
Absent
(n=100)
Yes, I see it
+10$
-$10
No, I don’t
-$10
+100$
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.
The stimulus is really...
Participant says...
Participant says...
Yes, I see it
Innocent
Man
Convicted
111
Absent
(n=100)
Absent
(n=100)
Guilty Man
Convicted
110
Present (n =100)
Present
(n =100)
Yes, I see it
111
The stimulus is really...
Lax
Absent
(n=100)
110
The stimulus is really...
Neutral
Present
(n =100)
112
113
112
113
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?
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”
114
115
114
115
Signal Detection Theory
SDT
•
•
•
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)
•
•
•
Example:You’re in the shower and expecting a call.
•
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.
Signal: Phone ringing
Noise: Sound of shower (plus all other sources of
sound), as well as your own internal neuron chatter.
116
117
116
117
Probability Distributions of Noise and Signal+Noise
Probability Distributions of Noise and Signal+Noise
not at all
phone +
noise
Probability
noise
only
Probability
noise
only
a bit
kinda
a lot
unmistakably
not at all
How much it sounds subjectively like a phone
a bit
kinda
a lot
unmistakably
How much it sounds subjectively like a phone
Link back to
matrix
Link back to
matrix
118
118
118-1
118-2
Probability That a Given Perceptual
Effect is Due to N or S+N
Probability That a Given Perceptual
Effect is Due to N or S+N
noise
only
not at all
phone +
noise
Probability
phone +
noise
Probability
noise
only
a bit
kinda
a lot
completely
How much it sounds subjectively like a phone
not at all
a bit
kinda
a lot
completely
How much it sounds subjectively like a phone
119
119
119-1
119-2
Probability That a Given Perceptual
Effect is Due to N or S+N
noise
only
not at all
a bit
kinda
a lot
completely
not at all
How much it sounds subjectively like a phone
kinda
119-3
119-4
Probability
phone +
noise
kinda
a lot
completely
How much it sounds subjectively like a phone
completely
Different Criteria One Can Adopt
noise
only
Lax
Result:
Pfa = .50
Ph = .95
d' = 1.64
phone +
noise
Probability
Result:
Pfa = .50
Ph = .95
d' = 1.64
a lot
How much it sounds subjectively like a phone
119
noise
only
a bit
a bit
119
Different Criteria One Can Adopt
not at all
phone +
noise
Probability
phone +
noise
Probability
noise
only
Probability That a Given Perceptual
Effect is Due to N or S+N
not at all
a bit
kinda
a lot
completely
How much it sounds subjectively like a phone
120
120
120-1
120-2
phone +
noise
Probability
noise
only
Lax
Result:
Pfa = .50
Ph = .95
d' = 1.64
not at all
a bit
kinda
a lot
completely
Different Criteria One Can Adopt
noise
only
Lax
not at all
How much it sounds subjectively like a phone
kinda
120-4
phone +
noise
kinda
a lot
completely
How much it sounds subjectively like a phone
completely
Different Criteria One Can Adopt
noise
only
Lax
Result:
Pfa = .50
Ph = .95
d' = 1.64
phone +
noise
Probability
Result:
Pfa = .50
Ph = .95
d' = 1.64
a lot
How much it sounds subjectively like a phone
120-3
Probability
a bit
a bit
120
noise
only
Lax
not at all
phone +
noise
120
Different Criteria One Can Adopt
Result:
Pfa = .50
Ph = .95
d' = 1.64
Probability
Different Criteria One Can Adopt
not at all
a bit
kinda
a lot
completely
How much it sounds subjectively like a phone
120
120
120-5
120-6
phone +
noise
Probability
noise
only
Lax
Result:
Pfa = .50
Ph = .95
d' = 1.64
not at all
a bit
kinda
a lot
completely
Different Criteria One Can Adopt
noise
only
not at all
How much it sounds subjectively like a phone
kinda
121-1
kinda
a lot
completely
How much it sounds subjectively like a phone
completely
Different Criteria One Can Adopt
noise
only
phone +
noise
Strict
Probability
phone +
noise
Strict
Result:
Pfa = .05
Ph = .50
d' = 1.64
a lot
How much it sounds subjectively like a phone
120-7
Probability
a bit
a bit
121
noise
only
not at all
phone +
noise
120
Different Criteria One Can Adopt
Result:
Pfa = .05
Ph = .50
d' = 1.64
Probability
Different Criteria One Can Adopt
not at all
a bit
kinda
a lot
Result:
Pfa = .05
Ph = .50
d' = 1.64
completely
How much it sounds subjectively like a phone
121
121
121-2
121-3
phone +
noise
Strict
Probability
noise
only
not at all
a bit
kinda
a lot
Result:
Pfa = .05
Ph = .50
d' = 1.64
completely
Different Criteria One Can Adopt
noise
only
not at all
How much it sounds subjectively like a phone
kinda
121-4
121-5
kinda
a lot
completely
How much it sounds subjectively like a phone
completely
Different Criteria One Can Adopt
noise
only
phone +
noise
Strict
Probability
Probability
phone +
noise
Strict
Result:
Pfa = .05
Ph = .50
d' = 1.64
a lot
Result:
Pfa = .05
Ph = .50
d' = 1.64
How much it sounds subjectively like a phone
121
noise
only
a bit
a bit
121
Different Criteria One Can Adopt
not at all
phone +
noise
Strict
Probability
Different Criteria One Can Adopt
not at all
a bit
kinda
a lot
Result:
Pfa = .05
Ph = .50
d' = 1.64
completely
How much it sounds subjectively like a phone
121
121
121-6
121-7
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.
Different Criteria One Can Adopt
not at all
a bit
kinda
completely
a lot
noise
only
phone +
noise
d’ (large)
Probability
phone +
noise
Strict
Probability
noise
only
Result:
Pfa = .05
Ph = .50
d' = 1.64
How much it sounds subjectively like a phone
not at all
a bit
kinda
a lot
completely
How much it sounds subjectively like a phone
121
122
121-8
122-1
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.
phone +
noise
d’ (small)
Probability
d’ (large)
Probability
noise
only
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.
not at all
a bit
kinda
a lot
completely
How much it sounds subjectively like a phone
noise
only
not at all
a bit
phone +
noise
kinda
a lot
completely
How much it sounds subjectively like a phone
122
123
122-2
123-1
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.
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?
Probability
d’ (small)
noise
only
not at all
a bit
phone +
noise
kinda
a lot
• A guard is watching the woods for visible
completely
signs of intruders. What are some likely
sources of “noise” in his situation?
How much it sounds subjectively like a phone
123
124
123-2
124
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.
125
125