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Page 1: Signal Detection Theory

Signal Detection Theory

I. Challenges in Measuring Perception

II. Introduction to Signal Detection Theory

III. Applications of Signal Detection Theory

Page 2: Signal Detection Theory

Part 1

Challenges in Measuring Perception

Page 3: Signal Detection Theory

Psychophysics

Psychophysics is the science of establishing quantitative relations between physical stimulation and perceptual events.

Page 4: Signal Detection Theory

The Method of Limits

Experimenter adjusts intensityuntil the stimulus is detected.

Page 5: Signal Detection Theory

The Method of Limits

Advantage: Measurements are madequickly.

Disadvantage: It is not clear exactlywhat’s being measured(no control for bias).

Page 6: Signal Detection Theory

“Catch Trials”

The subject is asked to make a responsewhen no stimulus has been presented(also called “noise only” trials).

Page 7: Signal Detection Theory

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”).

Page 8: Signal Detection Theory

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”).

Page 9: Signal Detection Theory

Stimulus-Response Matrix

Response

Sti

mu

lus

“No” “Yes”

Pre

sen

tA

bse

nt

Miss

CorrectRejection

Hit

FalseAlarm

Page 10: Signal Detection Theory

Part II

Introduction to Signal Detection Theory

S.D.T. In Words

Page 11: Signal Detection Theory

Signal Detection Theory

S.D.T. is a procedure for measuringsensitivity to stimulation, independent of the subject’s response bias.

Page 12: Signal Detection Theory

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.

Page 13: Signal Detection Theory

Part II

Introduction to Signal Detection Theory

S.D.T. In Pictures

Page 14: Signal Detection Theory

Distributions of Sensory ResponsesP

roba

bili

ty

Level Of Neural Activity (Arbitrary Units)

Page 15: Signal Detection Theory

Distributions of Sensory ResponsesP

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Level Of Neural Activity (Arbitrary Units)

Spontaneous Activity is Constant

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Distributions of Sensory ResponsesP

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Level of Neural Activity (Arbitrary Units)

Spontaneous Activity is Normally Distributed

The “Noise”Distribution

Page 17: Signal Detection Theory

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'

Page 18: Signal Detection Theory

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'

Page 19: Signal Detection Theory

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)

Page 20: Signal Detection Theory

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

Page 21: Signal Detection Theory

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

Page 22: Signal Detection Theory

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

Page 23: Signal Detection Theory

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

Page 24: Signal Detection Theory

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

Page 25: Signal Detection Theory

Receiver Operating Space

0

1

Pro

por

tion

of

Hit

s

0 1Proportion of False Alarms

Page 26: Signal Detection Theory

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

Page 30: Signal Detection Theory

R.O.C. Curves

0

1

Pro

por

tion

of

Hit

s

0 1Proportion of False Alarms

d’=1

d’=2d’=

3

d’=0

Page 31: Signal Detection Theory

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

Page 33: Signal Detection Theory

Part II

Introduction to Signal Detection Theory

S.D.T. In Numbers

Page 34: Signal Detection Theory

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)

Page 36: Signal Detection Theory

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.

Page 37: Signal Detection Theory

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.

Page 38: Signal Detection Theory

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

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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

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Subjective Memory Strength (Arbitrary Units)

"No,I don'trecognizeit"

"Yes,I recognizeit"


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