Signal Detection Theory

transcript

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

“No” “Yes”

CorrectRejection

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

Level Of Neural Activity (Arbitrary Units)

Spontaneous Activity is Constant

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)

A Moderate Stimulus is Presented (d’=2)

An Intense Stimulus is Presented (d’=3)

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

"No, I don'tsee it"

"Yes,I see it"

Criterion

Neutral Criterion

Neural Activity"No" "Yes"

Hits Misses

of N False

Alarms

CorrectRejections

Liberal (low) CriterionP

Neural Activity"No" "Yes"

Hits Misses

of N False

Alarms

CorrectRejections

The “Signal + Noise” Distribution .2

Conservative (high) Criterion

Neural Activity

Hits Misses

"No" "Yes"

of N False

Alarms

CorrectRejections

Receiver Operating Space

0 1Proportion of False Alarms

Receiver Operating Characteristics

d’=0

R.O.C. Curves

d’=1

d’=0

R.O.C. Curves

d’=1

d’=0

R.O.C. Curves

d’=1

d’=2

d’=0

R.O.C. Curves

d’=1

d’=2d’=

d’=0

R.O.C. Curves

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

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

Subjective Memory Strength (Arbitrary Units)

"No,I don'trecognizeit"

"Yes,I recognizeit"

Signal Detection Theory

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