SIGNAL DETECTION THEORY

SIGNAL DETECTION THEORY

Week 7 – BCS 208 Spring 2012

Baggage screening example

Signal Detection Theory

Who has better hearing, Julie or Regina?

Problem of criterion

• Perceptual decisions are influenced by many factors:

SOLUTION: Measure sensitivity independent of criterion = Signal detection theory

- Strength of signal relative to background level of noise - Person’s sensitivity to the signal - Relative frequency of occurrence of the signal - Person’s level of motivation -! Costs associated with hits and false alarms -! Personal biases (individual differences)

Signal Detection Theory (SDT)"

- Detecting faint sounds (e.g., murmur heard through stethoscope)

- Diagnosing X-ray images (e.g., “is it a tumor?”)

- Interpreting “blips” on a radar screen (“plane vs flock of birds”

- Stock market transactions (“buy or sell?”)

- Jury decision (“innocent vs guilty”)

- Deciding whether or not two lines are identical in length

•! Set of assumptions and procedures for measuring perceptual performance (decision making) under conditions of uncertainty

•! The goal being to distinguish performance changes/differences attributable to sensitivity vs criterion.

•! Originates from World War II: aircraft detection on radar signals

•! Today: widely used in psychophysics, medicine, radiology and machine learning

- Background noise in a hearing task

- Misleading evidence in a legal trial

- Flock of birds on a radar screen

- Scar tissue on a mammogram

Signal Detection Theory (SDT)"•! Discrete observations occasioned by presence of “noise” only

or “signal plus noise”

•! “Noise” is anything that complicates detection of “signal” by introducing uncertainty about whether or not the signal is present

• Discrete observations occasioned by presence of “noise” only or “signal plus noise”

Signal Detection Theory (SDT)

signal

signal +

noise

“S” response “S” response “S” response “S” response “S” response “S” response

noise

“S” response “S” response “S” response “S” response “S” response “S” response

+

=

Four possible outcomes:""- Signal was present and person says “yes” - HIT""- Signal was present and person says “no” - MISS""- Signal was not present and person says “no” - CORRECT REJECTION""- Signal was not present and person says “yes” - FALSE ALARM"

Signal Detection Theory (SDT)"

Medical Diagnosis example:

tumor Patient#s condition no tumor

Dia

gnos

is

abnormal

normal correct

correct

incorrect

incorrect


Dia

gnos

is

abnormal

normal correct

correct

incorrect

incorrect

Hit – correct diagnosis of disease Miss – physician tells patient that no disease exists when one does False alarm – unnecessary operation or treatment Correct rejection – patient properly diagnosed with no disease


Dia

gnos

is

abnormal

normal Correct rejection

Hit

Miss

False alarm

Hit – correct diagnosis of disease Miss – physician tells patient that no disease exists when one does False alarm – unnecessary operation or treatment Correct rejection – patient properly diagnosed with no disease

Which error is more costly?!

Accused is"guilty

Accused is"innocent

innocent

Jury

dec

isio

n

guilty

correct

verdict

verdict

correct

mistake

mistake

Which error is more costly?!

P? P

R R

R

R

R

R

R

R

R

R

“noise” “signal + noise”

Magnitude of sensory response

Strong response -- signal highly likely

Weak response -- signal highly unlikely



moderate response -- signal or noise?


criterion criterion criterion


criterion




criterion

“hit” “miss”

“Signal present”

“no” “yes”




criterion

“false alarm” “correct rejection”

“Signal absent”

“no” “yes”














balanced conservative liberal

Balanced: false alarm and miss rates are equal Liberal: the observer says “yes” whenever there may be a signal Conservative: decision is yes only when it is almost certain that

there is a signal


criterion



Discriminability: how well the observer can separate the presence of signal from its absence - overlap between the two distributions - Measured by d’ (discriminability index, also called sensitivity) - computed as: d" = z(Hit) – z(FA)

Prob

abili

ty

Internal response strength (arbitrary unit)

Tumor absent Tumor present

CR FA

M H

Liberal criterion

Practical example: medical diagnosis

Prob

abili

ty

Internal response strength (arbitrary unit)

Tumor absent Tumor present

CR H

Conservative criterion

FA

M

M CR

Practical example: medical diagnosis

Receiver operating characteristic (ROC):"

false alarm rate

hit r

ate

100%

100%

The ROC curve is traced out by plotting Hits against False Alarms as the criterion moves."


criterion


criterion


criterion


criterion

Receiver Operating Characteristic: ROC


criterion



criterion



criterion



criterion


d’

ROC Curve Questions"•! Why do ROC curves start at (0,0)? Why do they go to (100,100)?"•! If d-prime is zero, what is the shape of the ROC curve?"•! If d-prime is large (e.g. 4 or larger) what is the shape of the ROC curve?"

ROC Curve"

False alarm rate (%)"

Hit

rate

(%)"

0"

20"

40"

60"

80"

100"

0" 20" 40" 60" 80" 100"

d# = 0"d# = 1"

d# = 3"

ROC Curve"

False alarm rate (%)"

Hit

rate

(%)"

0"

20"

40"

60"

80"

100"

0" 20" 40" 60" 80" 100"

D!

A!

C!B!

•! Which observer did best?"

•! Who was just there completing the subject pool requirement?"

E!

http://www-psych.stanford.edu/~lera/psych115s/notes/signal/

http://psych.hanover.edu/JavaTest/Media/Chapter02.html Interactive Model 2.x: Signal Detection Theory Interactive Model 2.x: Signal Detection Illustration Interactive Model 2.x: Decisions In SDT Interactive Model 2.x: Receiver Operating Characteristic

Signal Detection Theory (SDT)- Online demos

Signal Detection Theory (SDT)

•! Explains yes-no decisions •! Detecting signal in noise (S + N)

•! Noise (N) is what makes detection hard (internal + external noise) •! Sensitivity (discriminability) vs. criterion (bias) •! Sensitivity (d’) depends on

•! signal strength •! noise strength •! observer sensitivity

•! Criterion depends on •! Personal bias •! Cost/benefit factors (risk factors) •! Signal frequency

•! ROC curve •! used to visualize SDT concepts & results

Signal Detection Theory (SDT) - experiment 1.2

•! Sensitivity (d’) depends on •! signal strength •! noise strength •! observer sensitivity

•! Criterion depends on •! Personal bias •! Cost/benefit factors (risk factors) •! Signal frequency

Signal Detection Theory (SDT) - experiment 1.2

•! Sensitivity (d’) depends on •! signal strength •! noise strength

•! Criterion depends on •! Cost/benefit factors (risk factors) •! Signal frequency

•! Half of the class will do one of the experiments manipulating the criterion •! Version #2 - Payoffs

•! The other half will do one of the experiments manipulating sensitivity •! Version #4 – Manipulation of the intensity of noise

•! Cover general SDT issues in intro •! Compute C and d’ (detailed instruction in SG: pages 1.11 - 1.12) •! Hand plot YOUR data on the empty ROC curve

•! use empty symbols for criterion exp (2X, label each, connect by line) •! use full symbols for sensitivity exp (2X, label each, connect by line)

•! Group data will be emailed

Documents

SIGNAL DETECTION THEORY