Transcript Signal Detection Theory

The Method of
Constant Stimuli &
Signal Detection Theory
VISN2211
Sieu Khuu
David Lewis
Three Psychophysical
Methods
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
The Method of Limits
The Method of Adjustment
The Method of Constant Stimuli
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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.


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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.
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.
QuickTime™ and a
decompressor
are needed to see this picture.
Decision outcomes &
consequences
SIGNAL: Are the spots on the screen enemies?
yes
DECISION:
Should you
scramble the jets?
no
yes
no
Hit
False
alarm
Miss
Correct
reject
Another Example

Children tend to be afraid of
the dark and this can lead to
a response bias.

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
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.
QuickTime™ and a
decompressor
are needed to see this picture.
Decision outcomes &
consequences
SIGNAL: Are the noises coming from monsters?
yes
yes
DECISION:
Should you cry for
mommy?
no
no
Saved Scolded
Eaten
Sleep
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
probability
SDT: Discrimination
Noise
Signal
(monster)
stimulus intensity
SDT: Medium Discriminability
-
 Criterion  +
Cry for
mommy
probability
Go back
to bed
Noise
Signal
(monster)
stimulus intensity
SDT: High Discriminability
probability
-
 Criterion  +
Go back
to bed
Cry for
mommy
Noise
Signal
(monster)
stimulus intensity
SDT: Low Discriminability
-
 Criterion  +
Cry for
mommy
probability
Go back
to bed
Noise
Signal
(monster)
stimulus intensity
Discriminabilty is independent
of Criterion
Discriminabilty (d’)
Cry for
mommy
probability
Go back
to bed
Noise
Signal
(monster)
stimulus intensity
Estimation of d’

d’ is the difference between the means of the noise (mN) and
the signal+noise (mSN) distributions, divided by the standard
deviation of the noise (sN).
d’ = [mSN - mN] / sN

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.

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The noise and stimulus are
highly overlapping.
d’ = 0: pure chance
Noise
stimulus intensity
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)
Signal
(monster)
high d’
probability

probability
Low d’
Noise
Signal
(monster)
stimulus intensity
SDT Review
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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)
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.
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
or
RIGHT
Center 0°
Surround
0°
Center 0°
Surround
15°
Center 0°
Surround
75°
Center 0°
Surround
90°