9/20/12

1

Psychophysics and SDT

•  Psychophysical techniques – Magnitude estimation, matching, detection/

discrimination – Forced-choice procedure

•  Weber’s Law, Fechner’s interpretation •  Signal detection theory

–  Information, criterion, internal response and noise, ROC curve, d-prime

1. Magnitude estimation 2. Matching 3. Detection/discrimination

Three methods for measuring perception

Magnitude estimation Have subject rate (e.g., 1-10) some aspect of a stimulus (e.g., how bright it appears or how loud it sounds)..

Steven’s power law

P = k Sn

P : perceived magnitude

S : stimulus intensity

k : constant

Relationship between intensity of stimulus and perception of magnitude follows the same general equation in all senses

Matching

Demo: brightness matching

In a matching experiment, the subject's task is to adjust one of two stimuli so that they look/sound the same in some respect.

Detection / discrimination

In a detection experiment, the subject's task is to detect small differences in the stimuli.

Psychophysical procedures for detection experiments

•  Method of adjustment.

•  Yes-No/method of constant stimuli.

•  Forced choice.

9/20/12

2

Concerns of the Psychophysicist

•  Bias •  Criterion •  Attentiveness •  Strategy •  Artifactual cues •  History of stimulation •  Who controls stimulation

The method of adjustment

Ask observer to adjust the intensity of the light until they judge it to be just barely detectable

Example: you get fitted for a new prescription for eye glasses. Typically the doctor drops in different lenses and asks you if this lens is better than that one.

Do these data indicate that Laurie’s threshold is lower than Chris’s threshold?

Yes/no method of constant stimuli

Per

cent

“ye

s” re

spon

ses

Tone intensity

Forced choice – Yes/no or signal-detection task

²  Present signal on some trials, no signal on other trials (catch trials).

² Subject is forced to respond on every trial either “Yes” the thing was presented” or “No it wasn’t”. If they're not sure then they must guess.

² Advantage: With the forced-choice method, we have both types of trials so we can count both the number of hits and the number of false alarms to get an estimate of discriminability independent on the criterion.

² SDT EXPERIMENT DEMO

2-interval forced-choice task ²  Two intervals (spatial side-by-side or temporal)

² Observer can’t be biased to say “yes”, because there is always a stimulus.

² Observer can have an interval bias, although that might be ameliorated with trial-by-trial feedback.

9/20/12

3

Tumor present

Tumor absent

Doctor responds “yes”

Doctor responds “no”

Hit Miss

False alarm

Correct reject

Forced choice: four possible outcomes

Tumor present

Tumor absent

Doctor responds “yes”

Doctor responds “no”

Hit Miss

False alarm

Correct reject

Information acquisition

Tumor present

Tumor absent

Doctor responds “yes”

Doctor responds “no”

Hit Miss

False alarm

Correct reject

Criterion shift Information and criterion Two components to the decision-making: information and criterion.

²  Information: Acquiring more information is good. The effect of information is to increase the likelihood of getting either a hit or a correct rejection, while reducing the likelihood of an outcome in the two error boxes.

²  Criterion: Different people may have different bias/criterion. Some may may choose to err toward “yes” decisions. Others may choose to be more conservative and say “no” more often.

Internal response: probability of occurrence curves

N S+N

The criterion

Criterion

Internal response

Prob

abili

ty d

ensi

ty

Say “yes” Say “no”

9/20/12

4

N S+N

Hits (response “yes” on signal trial)

Criterion

Internal response

Prob

abili

ty d

ensi

ty

Say “yes” Say “no”

N S+N

Correct rejects (response “no” on no-signal trial)

Criterion

Internal response

Prob

abili

ty d

ensi

ty

Say “yes” Say “no”

N S+N

Misses (response “no” on signal trial)

Criterion

Internal response

Prob

abili

ty d

ensi

ty

Say “yes” Say “no”

N S+N

False Alarms (response “yes” on no-signal

trial) Criterion

Internal response

Prob

abili

ty d

ensi

ty

Say “yes” Say “no”

Criterion shift

N S+N

Internal response

Prob

abili

ty d

ensi

ty

Discriminability (d-prime, d’)

d-prime is the distance between the N and S+N curves

d’!

9/20/12

5

Discriminability (d’) Discriminability (d’) and overlap

d’ = separation

spread

SDT review ²  Your ability to perform a detection/discrimination task is limited by internal noise.

²  Information (e.g., signal strength) and criterion (bias) are the 2 components that affect your decisions, and they each have a different kind of effect.

²  Because there are 2 components (information & criterion), we need to make 2 measurements to characterize the difficulty of the task. By measuring both hits & false alarms we get a measure of discriminability (d’) that is independent of criterion.

1

2

3

d’

Signal intensity

Low intensity High intensity

Measuring thresholds

Absolute and relative thresholds

Background intensity

Diff

eren

ce in

inte

nsity

Weber’s law

Abs

olut

e th

resh

old

Relative thresholds

9/20/12

6

Ernst Weber, c1850 Gustav Fechner, c1850

Background intensity

Inte

rnal

resp

onse

In

crea

se in

inte

nsity

Weber’s law

Fechner’s analysis

Weber’s law: To perceive a difference between a background level x and the background plus some stimulation x+Δx the size of the difference must be proportional to the background, that is, Δx = k x where k is a constant. Fechner’s interpretation: The relationship between the stimulation level x and the perceived sensation s(x) is logarithmic, s(x) = log(x). Main difference: Fechner’s is an interpretation of Weber’s law, a hypothesis.