outline of lecture i.intro to signal detection theory (words) ii.intro to signal detection theory...

Outline of Lecture

I. Intro to Signal Detection Theory (words)

II. Intro to Signal Detection Theory (pictures)

III. Applications of Signal Detection Theory

Part 1

Introduction to Signal Detection Theory

S.D.T. In Words

Signal Detection Theory

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

Detection Experiment• We want to measure a subject’s ability to

detect very weak stimuli.

• Signal Detection Theory requires a “Type A” experiment.

• How do we know when the subject is objectively incorrect?

“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

Stim

ulus

“No” “Yes”

Pres

ent

Abs

ent

Miss

CorrectRejection

Hit

FalseAlarm

Stimulus-Response Matrix

Response

Stim

ulus

“No” “Yes”

Pres

ent

Abs

ent

Miss

CorrectRejection

Hit

FalseAlarm

Type I error

Type II error

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.

Part 2

Introduction to Signal Detection Theory

S.D.T. In Pictures

Distributions of Sensory ResponsesPr

obab

ility

Level Of Neural Activity (Arbitrary Units)

Distributions of Sensory ResponsesPr

obab

ility

Level Of Neural Activity (Arbitrary Units)

Spontaneous Activity is Constant

Distributions of Sensory ResponsesPr

obab

ility

Level of Neural Activity (Arbitrary Units)

Spontaneous Activity is Normally Distributed

The “Noise”Distribution

Distributions of Sensory Responses

The “Noise”Distribution

The “Signal + Noise” Distribution

A Mild Stimulus is Presented (d’=1)

Prob

abili

ty

Level of Neural Activity (Arbitrary Units)

d'

Distributions of Sensory Responses

The “Noise”Distribution

The “Signal + Noise” Distribution

A Moderate Stimulus is Presented (d’=2)

Prob

abili

ty

Level of Neural Activity (Arbitrary Units)

d'

Distributions of Sensory ResponsesPr

obab

ility

Level of Neural Activity (Arbitrary Units)

d'

The “Noise”Distribution

The “Signal + Noise” Distribution

An Intense Stimulus is Presented (d’=3)

Distributions of Sensory Responses

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

Prob

abili

ty

Level of Neural Activity (Arbitrary Units)

The “Noise”Distribution

The “Signal + Noise” Distribution

About d’

So, d’ is a statistic for measuring perceptual sensitivity.

About d’

So, d’ is a statistic for measuring perceptual sensitivity.

Also, d’ often refers to “detectability”,and “discriminability” in perceptual experiments.

About d’

So, d’ is a statistic for measuring perceptual sensitivity.

Also, d’ often refers to “detectability”,and “discriminability” in perceptual experiments.

A high d’ value -----> good performance:

A low d’ value -----> poor performance.

About Bias

Now let’s consider THAT OTHERaspect of behavior… bias.

About Bias

Bias: The inclination to favor a particular response.

Example: The inclination to favor the “yes, I see it” response

over the “no, I don’t see it” response.

About Bias

Signal Detection Theory assumes that Bias can be measured according to a criterion.

Criterion: A rule for converting sensory activityinto an overt response.

Prob

abili

ty

Level of Neural Activity (Arbitrary Units)

"No, I don'tsee it"

"Yes,I see it"

Criterion

The “Noise”Distribution

The “Signal + Noise” Distribution

Neutral Criterion

The “Noise”Distribution

The “Signal + Noise” DistributionPr

Pr o

f S+N

Neural Activity"No" "Yes"

Hits Misses

Pr o

f N FalseAlarms

CorrectRejections

Stimulus-Response Matrix

Response

Stim

ulus

“No” “Yes”

Pres

ent

Abs

ent

Miss

CorrectRejection

Hit

FalseAlarm

Neutral Criterion

The “Noise”Distribution

The “Signal + Noise” DistributionPr

Pr o

f S+N

Neural Activity"No" "Yes"

Hits Misses

Pr o

f N FalseAlarms

CorrectRejections

Liberal (low) CriterionPr

Pr o

f S+N

Neural Activity"No" "Yes"

Hits Misses

Pr o

f N FalseAlarms

CorrectRejections

The “Noise”Distribution

The “Signal + Noise” Distribution

Conservative (high) Criterion

The “Noise”Distribution

The “Signal + Noise” Distribution

Pr o

f S+N

Neural Activity

Hits Misses

"No" "Yes"

PrPr

of N False

Alarms

CorrectRejections

About Bias

Just as d’ is the statistic for sensitivity,Beta () is the statistic for bias.

When… = 1, the criterion is neutral (no bias)

the criterion is low (liberal bias)

the criterion is high (conservative bias)

Part 3

Applications of Signal Detection Theory

S.D.T. Applications

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

S.D.T. And DiscriminationPr

obab

ility

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 MemoryPr

obab

ility

Subjective Memory Strength

"No, I don'trecall it"

"Yes,I recall it"

The “new items”distribution

The “old items” distribution

Learning CheckI. Draw two bell-shaped curves (Gaussian distributions) with the same mean, but different standard deviations.

II. Draw two bell-shaped curves (Gaussian distributions) with the same standard deviations, but different means.

III. Draw one signal-detection-theory plot for a subject who hasPOOR discrimination, and another signal-detection-theory plot for a a different subject is has GOOD discrimination.

IV. Finally, on the SDT plots that you just completed, draw a liberalcriterion for one subject, and a conservative criterion for the other. Labeleach of these clearly.