Signal Detection Theory

Signal Detection Theory

I. Challenges in Measuring Perception

II. Introduction to Signal Detection Theory

III. Applications of Signal Detection Theory

Part 1

Challenges in Measuring Perception

Psychophysics

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

The Method of Limits

Experimenter adjusts intensityuntil the stimulus is detected.

The Method of Limits

Advantage: Measurements are madequickly.

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

“Catch Trials”

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

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”).

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”).

Stimulus-Response Matrix

Response

Sti

mu

lus

“No” “Yes”

Pre

sen

tA

bse

nt

Miss

CorrectRejection

Hit

FalseAlarm

Part II

Introduction to Signal Detection Theory

S.D.T. In Words


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


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.

Part II


S.D.T. In Pictures

Distributions of Sensory ResponsesP

roba

bili

ty

Level Of Neural Activity (Arbitrary Units)


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Level Of Neural Activity (Arbitrary Units)

Spontaneous Activity is Constant


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Level of Neural Activity (Arbitrary Units)

Spontaneous Activity is Normally Distributed

The “Noise”Distribution

Distributions of Sensory Responses


The “Signal + Noise” Distribution

A Mild Stimulus is Presented (d’=1)

Pro

babi

lity


d'




A Moderate Stimulus is Presented (d’=2)

Pro

babi

lity


d'


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d'



An Intense Stimulus is Presented (d’=3)


Sub-Threshold Stimulus is Presented (d’=0)

Pro

babi

lity




Pro

babi

lity


"No, I don'tsee it"

"Yes,I see it"

Criterion



Neutral Criterion



Pr

Pr

of S

+N

Neural Activity"No" "Yes"

Hits Misses

Pr

of N False

Alarms

CorrectRejections

.5

.5

Liberal (low) CriterionP

rP

r of

S+

N

Neural Activity"No" "Yes"

Hits Misses

Pr

of N False

Alarms

CorrectRejections


The “Signal + Noise” Distribution .2

.6

Conservative (high) Criterion



Pr

of S

+N

Neural Activity

Hits Misses

"No" "Yes"

Pr

Pr

of N False

Alarms

CorrectRejections

.6

.2

Receiver Operating Space

0

1

Pro

por

tion

of

Hit

s

0 1Proportion of False Alarms

Receiver Operating Characteristics

0

1

Pro

por

tion

of

Hit

s


d’=0

R.O.C. Curves

0

1

Pro

por

tion

of

Hit

s


d’=1

d’=0

R.O.C. Curves

d’=1

d’=0

0

1

Pro

por

tion

of

Hit

s


R.O.C. Curves

0

1

Pro

por

tion

of

Hit

s


d’=1

d’=2

d’=0

R.O.C. Curves

0

1

Pro

por

tion

of

Hit

s


d’=1

d’=2d’=

3

d’=0

R.O.C. Curves

0

1

Pro

por

tion

of

Hit

s


?

R.O.C. Curves

0

1

Pro

por

tion

of

Hit

s


d’ = -1

d’ = -2

d’ = -3

Part II


S.D.T. In Numbers

Normal Distributions

S.D.T. is based on normal distributions.

Each normal distribution is described bya mean and a standard deviation.

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)

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.

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.

Part III

Applications of Signal Detection Theory

S.D.T. Applications

S.D.T. can be used in perceptualdiscrimination experiments.

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

S.D.T. Applications

S.D.T. can be used in non-perceptualresearch, including memory experiments.

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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Signal Detection Theory