Signal Detection Theory
description
Transcript of Signal Detection Theory
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Signal Detection Theory
I. Challenges in Measuring Perception
II. Introduction to Signal Detection Theory
III. Applications of Signal Detection Theory
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Part 1
Challenges in Measuring Perception
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Psychophysics
Psychophysics is the science of establishing quantitative relations between physical stimulation and perceptual events.
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The Method of Limits
Experimenter adjusts intensityuntil the stimulus is detected.
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The Method of Limits
Advantage: Measurements are madequickly.
Disadvantage: It is not clear exactlywhat’s being measured(no control for bias).
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“Catch Trials”
The subject is asked to make a responsewhen no stimulus has been presented(also called “noise only” trials).
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Not All Errors Are Equal
1. Reporting stimulus is present when it’s absent (“false alarm”).
Versus
2. Reporting stimulus is absentwhen it’s present (“miss”).
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Correct Responses Differ, Too
1. Reporting stimulus is present when it’s present (“hit”).
Versus
2. Reporting stimulus is absentwhen it’s absent (“correct rejection”).
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Stimulus-Response Matrix
Response
Sti
mu
lus
“No” “Yes”
Pre
sen
tA
bse
nt
Miss
CorrectRejection
Hit
FalseAlarm
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Part II
Introduction to Signal Detection Theory
S.D.T. In Words
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Signal Detection Theory
S.D.T. is a procedure for measuringsensitivity to stimulation, independent of the subject’s response bias.
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Signal Detection Theory
S.D.T. reduces the stimulus-responsematrix to two meaningful quantities.
1. Detectability (d’) - a subject’s sensitivity to stimulation.
2. Criterion () - a subject’s inclination to favor a particular response; bias.
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Part II
Introduction to Signal Detection Theory
S.D.T. In Pictures
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Distributions of Sensory ResponsesP
roba
bili
ty
Level Of Neural Activity (Arbitrary Units)
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Distributions of Sensory ResponsesP
roba
bili
ty
Level Of Neural Activity (Arbitrary Units)
Spontaneous Activity is Constant
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Distributions of Sensory ResponsesP
roba
bili
ty
Level of Neural Activity (Arbitrary Units)
Spontaneous Activity is Normally Distributed
The “Noise”Distribution
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Distributions of Sensory Responses
The “Noise”Distribution
The “Signal + Noise” Distribution
A Mild Stimulus is Presented (d’=1)
Pro
babi
lity
Level of Neural Activity (Arbitrary Units)
d'
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Distributions of Sensory Responses
The “Noise”Distribution
The “Signal + Noise” Distribution
A Moderate Stimulus is Presented (d’=2)
Pro
babi
lity
Level of Neural Activity (Arbitrary Units)
d'
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Distributions of Sensory ResponsesP
roba
bili
ty
Level of Neural Activity (Arbitrary Units)
d'
The “Noise”Distribution
The “Signal + Noise” Distribution
An Intense Stimulus is Presented (d’=3)
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Distributions of Sensory Responses
Sub-Threshold Stimulus is Presented (d’=0)
Pro
babi
lity
Level of Neural Activity (Arbitrary Units)
The “Noise”Distribution
The “Signal + Noise” Distribution
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Pro
babi
lity
Level of Neural Activity (Arbitrary Units)
"No, I don'tsee it"
"Yes,I see it"
Criterion
The “Noise”Distribution
The “Signal + Noise” Distribution
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Neutral Criterion
The “Noise”Distribution
The “Signal + Noise” Distribution
Pr
Pr
of S
+N
Neural Activity"No" "Yes"
Hits Misses
Pr
of N False
Alarms
CorrectRejections
.5
.5
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Liberal (low) CriterionP
rP
r of
S+
N
Neural Activity"No" "Yes"
Hits Misses
Pr
of N False
Alarms
CorrectRejections
The “Noise”Distribution
The “Signal + Noise” Distribution .2
.6
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Conservative (high) Criterion
The “Noise”Distribution
The “Signal + Noise” Distribution
Pr
of S
+N
Neural Activity
Hits Misses
"No" "Yes"
Pr
Pr
of N False
Alarms
CorrectRejections
.6
.2
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Receiver Operating Space
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
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Receiver Operating Characteristics
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
d’=0
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R.O.C. Curves
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
d’=1
d’=0
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R.O.C. Curves
d’=1
d’=0
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
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R.O.C. Curves
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
d’=1
d’=2
d’=0
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R.O.C. Curves
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
d’=1
d’=2d’=
3
d’=0
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R.O.C. Curves
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
?
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R.O.C. Curves
0
1
Pro
por
tion
of
Hit
s
0 1Proportion of False Alarms
d’ = -1
d’ = -2
d’ = -3
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Part II
Introduction to Signal Detection Theory
S.D.T. In Numbers
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Normal Distributions
S.D.T. is based on normal distributions.
Each normal distribution is described bya mean and a standard deviation.
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Normal Distributions
A given point on a normal distributioncan be described be described 3 ways.
1. Percentile (also proportion)
2. Z-score (# of standard deviations)
3. Probability Density (likelihood)
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Computing Detectability
d’ = zHits - zFalse Alarms
In excel, the “normsinv” function is used: Input = proportion Output = z-Score
Conceptually, detectability (d’) increaseswith the area under the R.O.C. curve.
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Computing Criterion
= Hit Density / False Alarm Density
In excel, the “normsdist” function is used: Input = z-Score Output = density
Conceptually, is equal to the slopeof the R.O.C. curve at single point.
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Part III
Applications of Signal Detection Theory
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S.D.T. Applications
S.D.T. can be used in perceptualdiscrimination experiments.
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S.D.T. And DiscriminationP
roba
bili
ty
Perceived Speed
"No, 2nd Stimuluswas not faster"
"Yes,2nd stimuluswas faster"
The “slow”distribution
The “fast”distribution
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S.D.T. Applications
S.D.T. can be used in non-perceptualresearch, including memory experiments.
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S.D.T. And Memory
The “new items”distribution
The “old items” distributionP
roba
bili
ty
Subjective Memory Strength (Arbitrary Units)
"No,I don'trecognizeit"
"Yes,I recognizeit"