Term 2: Lecture 9PS3012: Advanced Research Methods1 / 43 PS3012: Advanced Research Methods Lecture 9: Psychophysics, psychophysical methods, and signal

Term 2: Lecture 9 PS3012: Advanced Research Methods

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PS3012: Advanced Research MethodsLecture 9:

Psychophysics, psychophysical methods,

and signal detection theory

Jonas LarssonDepartment of Psychology

RHUL


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Today’s lecture

• Introduction to psychophysics• Thresholds and psychometric functions• Psychophysical methods • Signal detection theory


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What is psychophysics?

• The study of the relationship between physical stimuli and their subjective correlates, or percepts [Wikipedia]

• The scientific study of the relation between stimulus and sensation [Gescheider, 1976]

• Central idea: measurements of behavioural parameters (accuracy, reaction time, sensory thresholds) can be used to infer mental state (percept) of subjects


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What can psychophysics be used for?

• Sensory system neurophysiology/neuropsychology– Sensory limits of vision, hearing, touch…– Interspecies comparison (e.g., monkeys vs humans)– Inferring neuronal mechanisms (e.g. illusions, after-

effects)• Experimental psychology

– Visuomotor interactions– Perception of speed, motion– Attention

• Quantitative measurement of perceptual states– Diagnostic tool (e.g., vision tests)– Assessment tool (e.g., therapeutic effectiveness)


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Example: treatment of anorexia

• Distorted self-image in anorexia: subjects perceive themselves as disproportionally overweight

• Suppose you want to test effectiveness of therapy to improve self-image (reduce distortion). How can its effectiveness be quantified?

• Use psychophysical methods to identify “ideal body proportions” (using manipulated photos of subjects with different shape/weight) as a threshold: perceptual boundary between too fat / too thin)

• Measure ideal proportions before & after therapy• Test difference (if any) statistically for

effectiveness of therapy


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Example: treatment of anorexia

• Show photos of subjects manipulated (Photoshop) to show different body size (BMI)

• Subjects have to rate photos as “too thin” or “too fat”; measure % judged “too fat”

• Fit psychometric function to data– Note shape (logistic)

• Perceptual boundary (threshold): BMI where 50% of photos judged “too fat” Body mass index (BMI)

Perc

eiv

ed

sh

ap

e(%

im

ag

es ju

dg

ed

too f

at)100

0

Before therapy

After therapy

50 50 % threshold


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The power of psychophysics

• Quantitative - objective scale of measurement• Does not suffer from subjectivity of introspection• Can be used to study “pure” mental phenomena -

e.g. attention• Valid inter-subject, inter-species, and inter-method

comparisons – E.g. colour perception in humans and bees– Sensitivity of neurons vs sensitivity of brains (humans)

• Can be used to study subliminal percepts (e.g. above-chance recognition without awareness)

• Can identify (possibly subconscious) response bias


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The concept of thresholds

• Detection threshold (classical definition): smallest detectable stimulus intensity (energy) (that yields a sensory percept)– Threshold for sight (weakest detectable light): about 10

photons!– Threshold for sound (weakest detectable air vibration): about

the diameter of an atom!• Discrimination threshold : smallest detectable

difference between two stimuli (that yields a perceptual difference)– Smallest detectable difference in orientation of two lines– Smallest difference in colour corresponding to a colour

category change • Thresholds correspond to a perceptual boundary• Thresholds can be measured quantitatively


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Thresholds & psychometric functions

• Psychometric function: plot of proportion of stimuli detected or discriminated vs stimulus intensity

• Ideal psychometric function: always 100% above threshold, always 0% below threshold - a step function

• Why is the real psychometric function not a step function?

• Because of NOISE Stimulus intensityPro

port

ion

sti

mu

li d

ete

cte

d (

%)

50% threshold

100

0

50

Ideal psychometric function:Step function (fixed threshold)

Real psychometric function:S-shaped (sigmoid or logistic) function


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Psychophysical methods

• Method of limits• Method of adjustment• Method of constant stimuli• Adaptive methods

– Staircases– Adaptive versions of constant stimuli


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Method of limits

• Stimulus intensity (for discrimination tasks, the difference between two stimuli) is changed from trial to trial by a fixed amount either upwards from very weak intensity (ascending series) or downwards (descending series)

• Subjects report the stimulus intensity when they can no longer detect or discriminate the stimuli (descending series) or when they begin to be able to detect/discriminate stimuli (ascending series)

• These stimulus intensities are averaged to give a threshold estimate

• Ascending & descending series are done in alternation


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Method of limits

descending series ascending series

Sti

mu

lus in

ten

sit

y

Stimulus no longer

detected

Stimulus detected

Threshold:

average stimulus intensity


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Method of adjustment

• Subjects adjust stimulus intensity (or difference between two stimuli) until they can just about detect or discriminate the stimulus

• This stimulus intensity (or difference) is the threshold

• Usually done in ascending and descending series like method of limits (but under subjects’ control)


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Method of constant stimuli

• Stimuli with a fixed range of intensity levels (or fixed range of differences for discrimination tasks) are presented in random order

• Subjects report stimulus absent/present (or for discrimination tasks, same/different or weaker/stronger than reference stimulus)

• Subjects’ reports are plotted against stimulus intensity / difference magnitude to give a psychometric function

• Usually a psychometric function is then fit (by nonlinear function fitting or logistic regression) to psychometric data

• Threshold is midway between chance level performance (bottom of psychometric function, e.g. 50% for a 2AFC task) and 100% detection / discrimination


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Method of constant stimuliS

tim

ulu

s in

ten

sit

y

Stimulus detected

Stimulus not

detected


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Pro

port

ion

sti

mu

li d

ete

cte

d (

%)

50% threshold

100

0

50

Stimulus intensity

Method of constant stimuli

• For each level of stimulus intensity, calculate and plot proportion of stimuli detected/discriminated

• Fit psychometric (sigmoid) function to data

• Threshold is stimulus intensity at inflection point (middle of curve)

• Corresponds to halfway between 100% performance and chance level performance (guessing)


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Adaptive methods: staircases

• Similar to method of limits, but series reverse direction whenever decision changes (e.g. for a descending series, when subject can no longer detect stimulus, series ascends instead)

• More effective at “homing in” on threshold• Threshold is average of reversal stimulus intensity• More complex reversal rules are often used (“1-up,

2-down”) with different methods for computing thresholds

• To avoid subject prediction, often uses several interleaved staircases (series) randomly interspersed


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Adaptive methods: adjusting constant stimuli

• Similar to constant stimuli, but range of stimulus intensity levels to use are changed over course of experiment (not fixed)

• Allows more time to be spent measuring responses near threshold (like staircases)

• Unlike staircase methods, good for fitting psychometric functions (samples responses over entire psychometric function curve)

• Various methods exist (Best PEST, QUEST etc)


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The effect of noise on psychometric functions

• Detection or discrimination of stimulus is always subject to noise:– Neural – Stimulus (physical)– Attention– (Response)

• On any trial, noise will randomly increase or decrease perceived signal intensity

• Subject perceives signal+ noise (cannot tell the difference)

• Changes step function to sigmoid (logistic) function Stimulus intensityPro

port

ion

sti

mu

li d

ete

cte

d (

%)

100

0

50

Above threshold: random noise will weaken signal for some trials, making detection <100%

Below threshold: random noise will strengthen signal for some trials, making detection > 0%


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Detecting stimuli in noise: Signal Detection Theory (SDT)

• How stimuli are detected/discriminated against background noise

• How to make decisions in the presence of uncertainty• How to make optimal decisions from ambiguous data• How to make good decisions from bad information• SDT explains why shape of psychometric function

varies with noise• SDT explains how a subject’s criterion (response bias)

affects decisions and how to measure it• SDT allows measurement of sensitivity (ability to

make correct responses/decisions) regardless of criterion/bias


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Origin of SDT: WW2 radar operator

• Task: warn of incoming aircraft

• Are the blobs enemy aircraft? Or just noise (e.g. clouds)?

• Decision depends on subjective criterion: how big must the blobs be to be aircraft

• Decision has consequences:– If you miss an aircraft, people

might get killed– If you mistake noise for

aircraft, fuel, manpower & resources are wasted

Radar screen


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Decision outcomes & consequences

HitFalse alarm

MissCorrect reject

yes

no

SIGNAL: are the blobs real enemy aircraft?

DECISION:should you alert

the air force?

yes no


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Decision depends on criterion

• Low criterion: alert for every blob: make sure you never miss - but many false alarms

• High criterion: only alert for really big blobs: no false alarms - but many misses

• Which criterion is “best” (optimal)?• Depends on the costs of making errors...• which errors are acceptable...• but also on how good your information is

(uncertainty)


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Example 2: mugger or friend?

• You’re walking alone on an empty street• Somebody behind you calls out to you: “hey!”• You don’t recognize the voice, and can’t see the

person’s face clearly• Is it a friend or a mugger? (how familiar is the

person’s appearance?)• Do you run or stay?


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run

stay

SIGNAL: is the person a friend or a mugger?

DECISION:should you run or stay?

mugger friend

Lucky escape!

Friend gets

upset

You got mugged!

Head to the pub


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HitFalse alarm

MissCorrect reject

run

stay

SIGNAL: is the person a mugger or friend?

DECISION:should you run or stay?

mugger friend


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Decision criterion depends on penalties and uncertainty

• How would your decision to run or stay change if:– it’s in the middle of the night on campus? (high

uncertainty, high penalty for false alarms)– it’s the middle of the day on campus? (low

uncertainty, high penalty for false alarms)– it’s in the middle of the night in the South Bronx?

(high uncertainty, high penalty for misses)– it’s in the middle of the day in the South Bronx? (low

uncertainty, high penalty for misses)• So how do you decide which decision criterion is

best (optimal)?


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Use Signal Detection Theory

unfamiliar appearance (stimulus intensity)

pro

babili

ty

criterionrun (mugger)stay (friend)

friend mugger


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SDT & effect of criterion: radar operator example

Blob size (stimulus intensity)

pro

babili

ty

criterionyes (aircraft)no (noise)

noise aircraft


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SDT & effect of criterion: radar operator example

pro

babili

ty


noise aircrafthits

misses

correct

rejects

false alarms


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Low criterion: few misses, many false alarms

pro

babili

ty

aircraft

false alarms

noise


hitscorrec

t rejects


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High criterion: many misses, few false alarms

pro

babili

ty

aircraftnoise

misses


hitscorrec

t rejects


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Low noise: high discriminability & sensitivity (few misses & false

alarms)


pro

babili

ty

noise aircraft

Small overlap between distributions of noise and stimulus+noise (aircraft)

discriminability d’(distance between means)


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High noise: low discriminability & sensitivity (many misses &

false alarms)


pro

babili

ty

noise aircraft

Large overlap between distributions of noise and stimulus+noise (aircraft)

discriminability d’


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SDT & psychophysics

Stimulus intensity

pro

babili

ty

Decision criterionResponse: YesResponse: No

Discriminability (sensitivity): d-prime (d’) - the distance between the means of (N) and (SN) in units of S.D.

d’

Noise (N)Stimulus+Noise

(SN)


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Discriminability (d’) is independent of criterion

Stimulus intensity

pro

babili

ty


d’ d’ depends only on the distance between the means of (N) and (SN)


(SN)


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Discriminability (d’) is independent of criterion

Stimulus intensity

pro

babili

ty



(SN)

d’ d’ depends only on the distance between the means of (N) and (SN)


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Estimation of d’

• d’ is the difference between the means of the noise (N) and stimulus+noise (SN) distributions, in units of standard deviations of the noise (N) distribution:

d’ = [SN - N] / N

• But these distributions are not usually known!• d’ is more easily computed from the hit rate

(proportion of stimuli reported when present, [yes|SN] ) and the false alarm rate (proportion of stimuli reported when not present, [yes|N] ):– 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 )• Decision criterion must be fixed!


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Interpreting d’

• Low d’ means stimulus (signal) + noise (SN) distribution is highly overlapping with noise (N) distribution– d’ = 0: chance level performance (N and SN overlap

exactly)• High d’ means SN and N distributions are far

apart– d’ = 1: moderate performance– d’ = 4.65: “optimal” (corresponds to hit rate=0.99,

false alarm rate=0.01)


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Example

• Performance on visual detection task before drinking alcohol:– Hit rate 0.7, false alarm rate 0.2

• Performance of task after drinking alcohol:– Hit rate 0.8, false alarm rate 0.3

• Did performance or sensitivity (discriminability) improve?• Before drinking alcohol:

d’ = z(hit rate) - z(false alarm rate) = 0.542 - (-0.842) = 1.366• After drinking alcohol:

d’ = z(hit rate) - z(false alarm rate) = 0.842 - (-0.542) = 1.366• Alcohol did not improve performance (d’)• Alcohol did change criterion (by lowering it)


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Controlling decision criterion

• Criterion influenced by stimulus probability and decision consequences (payoffs - rewards & penalties)

• Need to know chance level performance (performance when no stimulus present)

• Present noise stimuli on some constant proportion of trials - this proportion is then equal to chance level performance

• Use fixed payoff (e.g. reward for hits, penalties for false alarms)

• Best: use forced choice methods:– Most common: use two-alternative forced choice (2AFC);

present two stimuli on each trial (one with stimulus, one with just noise) and force subject to decide which one contained the stimulus - chance level performance is then 50%

– Performance often above chance even when subject is guessing


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Summary of SDT

• Decisions (perceptual judgments) are always made in the presence of noise (internal/neural and external/physical)

• Decisions are made with respect to a criterion (response bias)• Criterion is variable & reflects probability of stimulus and

payoffs/ consequences of decision• Performance (hit rate) is a biased measure - depends on

criterion• There is a trade-off between hit rate and false alarm rate• Sensitivity/discriminability - the ability to discriminate a

stimulus from noise - is independent of the criterion• d’ is a measure of discriminability that is insensitive to criterion• 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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And finally…

• Reading: see course web page– Ehrenstein & Ehrenstein: Psychophysical Methods

• Next week: last lecture (DW)

Documents

Term 2: Lecture 9PS3012: Advanced Research Methods1 / 43 PS3012: Advanced Research Methods Lecture 9: Psychophysics, psychophysical methods, and signal