The Method of Constant Stimuli &

Signal Detection Theory

VISN2211

Sieu Khuu

David Lewis

Three Psychophysical Methods

The Method of Limits The Method of Adjustment The Method of Constant Stimuli

Signal Detection Theory

Used to determine perceptual sensitivity by measuring the point at which a stimulus is reported as being present (detection), or has changed in some manner (discrimination). NOTE: This presentation will only describe these methods

in terms of detection.

The Method of Limits

Stimulus intensity is either increased by a fixed amount from trial to trial, or decreased by a fixed amount.

Participants report when the start to be able to perceive the stimulus (increasing intensity), or when they can no-longer perceive the stimulus (decreasing intensity).

The Method of Adjustment

Stimulus intensity is adjusted by the participants until they can just barely perceive it’s presence.

Method of Constant Stimuli

Stimulus intensity is randomly altered from one trial to the next (within a fixed intensity range).

For each trial participants report the presence or absence of the stimulus. The participants’ responses for each trial are

plotted against the stimulus intensity to give a psychometric function.

For example…

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Trial 6

Trial 7

Trial 8

Response Bias

Participants in psychophysical experiments can be biased towards a certain response. I.e. “For every correct response you get a dollar.”

This would cause the participant to respond more often, resulting in more correct responses, but also more false alarms.

I.e. “For every correct response you lose a dollar.” This would cause the participant to respond less often,

resulting in less correct responses, but also less false alarms.

Signal Detection Theory (SDT)

Used to explain how stimuli are detected when there is background noise. The more noise there is the harder it is to detect a

stimulus. The less noise there is the easier it is to detect a

stimulus. Response bias can have a strong affect on a

participant’s responses. SDT allows measurement of sensitivity

regardless of response bias.

Signal Detection Theory History

In World War II radar waves were used to detect enemy aircraft.

The soldiers had to determine if the little spots of light are enemies, or simple noise (I.e. birds). There was no clearly defined criteria for making these

kinds of decisions.

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Consequences: If a enemy went undetected, people

could be killed. If noise was interpreted as an enemy,

time and money would be lost and people would be put in harm’s way.

Decision outcomes & consequences

HitFalse alarm

MissCorrect reject

yes

no

SIGNAL: Are the spots on the screen enemies?

DECISION:Should you scramble the

jets?

yes no

Another Example

Children tend to be afraid of the dark and this can lead to a response bias. In the dark strange noises seem

to come from a monster under the bed or in the closet.

In the light most strange noises are completely ignored because no apparently threats are present.

Consequences: Monsters could eat me. (worse) Mommy could yell at me.

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Decision outcomes & consequences

Saved Scolded

Eaten Sleep

yes

no

SIGNAL: Are the noises coming from monsters?

DECISION:Should you cry for mommy?

yes no

Response Bias & Outcome

Response bias is based on a participant’s preference for a particular outcome. Preferences are based on costs & rewards

For example, If a monster will eat me because I failed to detect

him, that is a very high cost. If mommy yells at me for waking her up for no

reason, that is not a very high cost.

Criterion Level

Criterion level is set based on outcome preferences.

Criterion level: The intensity at which a signal will be reported as being present (Not the intensity at which it is perceived). High Criterion: less hits but also less false alarms Low criterion: more hits but also more false

alarms

stimulus intensity

probability

SDT: Discrimination

Noise Signal(monster)

SDT: Medium Discriminability

stimulus intensity

probability

Cry for mommy

Go back to bed

Noise Signal(monster)

- Criterion +

SDT: High Discriminability

stimulus intensity

probability Cry for

mommyGo back to bed

NoiseSignal

(monster)

- Criterion +

SDT: Low Discriminability

stimulus intensity

probability

Cry for mommy

Go back to bed

Noise Signal(monster)

- Criterion +

Discriminabilty is independent of Criterion

stimulus intensity

probability

Cry for mommy

Go back to bed

Noise Signal(monster)

Discriminabilty (d’)

Estimation of d’

d’ is the difference between the means of the noise (N) and the signal+noise (SN) distributions, divided by the standard deviation of the noise (N).

d’ = [SN - N] / N

d’ is more easily computed from the hit rate and the false alarm rate. Convert hit & false alarm rates (which are probabilities) to z scores

from tables of z distribution: Hit rate = P(yes|SN) => z( yes|SN ) False alarm rate = P( yes|N ) => z( yes|N )

d’ = z( yes|SN ) - z( yes|N ) Note: Decision criterion cannot change for the participant

during the experiment or this equation will not work.

Interpreting d’

If d’ is low, then this means there is low discriminability. The noise and stimulus are

highly overlapping. d’ = 0: pure chance

If d’ is high, then this means there is high discriminability. d’ = 1: moderate performance d’ = 4.65: “optimal”

(corresponds to hit rate=0.99, false alarm rate=0.01)

stimulus intensity

probability

Noise Signal(monster)

stimulus intensity

probability

Noise Signal(monster)

Low d’

high d’

SDT Review Perceptual decisions are made in the real world, which is full

of noise. Perceptual responses are biased with respect to a criterion. A criterion level can change based on the preference for

particular outcomes. There is a trade-off between hit rate and false alarm rate. Sensitivity/discriminability - the ability to discriminate a

stimulus from noise - it is independent of the criterion. d’ is a measure of discriminability that is insensitive to the

criterion level. d’ can be computed from the hit rate (proportion of stimuli

detected when present) and the false alarm rate (proportion of stimuli reported when not present)

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QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Experiment: Psychophysical Methods

• Use the method of constant stimuli to study the tilt illusion.

• Determine if center circle is tilted to the

LEFT RIGHTor

Center 0°

Surround 0°

Center 0°

Surround 15°

Center 0°

Surround 75°

Center 0°

Surround 90°