psychophysical methods

PSYCHOPHYSICAL METHODSZ. SHI

Course C - Week 5

1

Let’s do a detection task

Please identify if the following display contain a letter T. If Yes, please raise your hand!

T among Ls

2

+

3

L

LL

LL

L

T

L L

X

XX

XX

X

X

X X

1

+

4

L

LL

LL

L

L

L L

X

XX

XX

X

X

X X

2

+

5

L

LL

LL

L

L

L L

X

XX

XX

X

X

X X

3

+

6

L

LL

TL

L

L

L L

X

XX

XX

X

X

X X

4

+

7

L

LL

LL

T

L

L L

X

XX

XX

X

X

X X

5

+

8

L

LL

LL

L

L

L L

X

XX

XX

X

X

X X

6

Results

Trial No Yes No

1 (Present) 1 15

2 (Absent) 0 16

3 (Absent) 0 16

4 (Present) 14 2

5 (Present) 16 0

6 (Absent) 0 16

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Conditions Presentation time (sec)

P(‘Yes’)

1 0.2 1/16

2 0.4 14/16

3 0.6 16/16

• Non-linear relation between physics and psychology

• Senses have an operating range

Stimuli and sensation

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Stimulus intensity – physical property

Sen

sati

on

– p

sych

olo

gy

Undetectable region

Saturated region

Point of subjective equality (PSE)

• Is the stimulus vertical?

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% V

erti

cal r

esp

on

se

0%

100%

50% Point of Subjective Equality - PSE

Just noticeable difference (JND)

• Difference in stimulation that will be noticed in 50%

12

% V

erti

cal r

esp

on

se

25%

75%

–

2= JND

= Upper threshold

= Lower threshold

= Uncertainty interval

JND and sensitivity

• Which psychometric function, full or dashed line, exhibits a greater sensitivity?

• Dashed - the smaller the JND the greater (steeper) the slope, and greater the sensitivity is

13

Psychometric function

• Absolute thresholds (Absolute limen)

the level of stimulus intensity at which the subject is able to detect the stimulus. Some time it is called point of subjective equality (PSE)

• Discrimination thresholds (Difference limen)the difference between two stimuli intensities that the participant is able to detectJust Noticeable Difference (JND)

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Psychometric function and threshold percentiles

• PSE – threshold percentile is half-way between the minimum and maximum of the function

• BUT – the min and max vary depending on the task

• SO – the exact threshold percentile depends on the task

Threshold percentiles

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0%

100%

50%

25%

75%

Yes/No

2AFC

3AFC

50%

75%67%

MEASURING THRESHOLDS

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Measuring psychometric function

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Psychophysical methods

Classical methods

The method of constant stimuli

The method of adjustment

The method of limits

Adaptive methods

Staircase methods

Parameter estimation by sequential testing (PEST)

Maximum-likelihood adaptive procedures (QUEST, MLP)

1. The method of constant stimuli

• Full control of presented stimuli

• Several fixed stimuli are presented in a random order, many times

• For each stimulus participants perform the same task, e.g., whether or not they see a stimulus

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Example

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Method of Constant Stimuli & Psychometric Function

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• Multiple Intensity levels, multiple repetition

• Prop. of responses • Represented roughly

shape of psychometric curve

• Estimation of Psychometric curve: JND, PSE

100%

Intensity

50%

Proportion of “yes” responses

---+----

-----+--

-+---+--

--++-+--

--++-+-+

+-++-+-+

++++-+-+

++++-+-+

Method of constant stimuli - evaluation

• Whole psychometric function can be estimated

• Many trials are:

• Costly

• not for special groups ( e.g., kids, ADHD)

• Repeating the same stimulus many time can yield learning effects

22

2. Method of limits

1. On some trials the intensity ascends from low to high intensity• When the stimulus or a difference between stimuli is

noticed the trial stops 2. On other trials the intensity descends from high to low

intensity• When the stimulus or a difference between stimuli is not

noticed any more the trial stops3. Averaging the stopping values across several trials yields

thresholds

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24

Stim

ulu

s In

ten

sity

(B

righ

tnes

s)

n

n

n

n

y

n

n

n

n

n

y

n

n

n

n

n

n

y

95

96

97

98

99

100

101

102

103

104

Transition point

y

y

y

y

y

n

y

y

y

y

y

y

y

n

y

y

y

y

y

y

n

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6

(99+98)/2= 98.5 100.5 99.5 98.5 97.5 99.5 = 99

Example of the method of limits

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• Sound

Method of limits and psychometric function

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• Psychometric function• Not required

• Multiple ascending and descending method of limits measure• PSE

Threshold

Internal criterion

Stimuli

ascending

descending

ascending

descending

Prop

. Of ‘

Yes

’

Method of limits - evaluation

• Estimates only certain points on the psychometric curve

• Prone to habituation errors • Falsely increasing thresholds on ascending trials.• Falsely decreasing thresholds on descending trials.

• Prone to expectation errors• Anticipation of the stimulus arrival and prematurely report.• Falsely decreasing thresholds on ascending trials.• Falsely increasing thresholds on descending trials.

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How to prevent errors

• Shorten trial series – avoids habituation errors• Variable starting points in the series – avoids

expectation errors• When comparing different stimuli, i.e., standard and

test counterbalance their position and order

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ascending

descending

ascending

descending

Stimuli Intensity

3. The method of adjustment

• Subject controls (adjust) the stimulus intensity

• Absolute threshold – Adjust stimulus intensity so that the stimulus is barely perceived

• Discrimination threshold – Adjust one stimulus so that it match the standard stimulus

• Average error of all trials

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• Threshold is the mean of all trials

Example

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Trial 1 Trial 2

Method of adjustment and Psy. function

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• Psychometric function• Not required

• Threshold• Internal criterion of

responses• Continuous

adjustment of stimuli intensity

• Fine tuning at the end of trial• PSE

Threshold

Internal criterion

Stimuli

Prop

. Of ‘

Yes

’ Ti

me

Trial 1.

Trial 2.

Method of adjustments - evaluation

• Estimates only certain points on the psychometric curve

• Faster than the method of limits – a few trials suffice

• Habituation errors still present

• Expectation errors still present

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Methods of adjustments in clinics

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Measuring psychometric function

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Classical methods



The method of limits

Adaptive methods

Staircase methods



Staircase method

• Addresses the problem of choosing “the right” stimulus values• Psychometric function is only sensitive to the middle range

of stimulus values

• Presenting stimuli beyond this range is not informative

• Up – Down rule: after a transition point, present a stimulus that goes in the opposite direction:• 20 dB – yes, 15 dB – no, 20 dB

• 15 dB – no, 20 dB – yes, 15 dB

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Zhuanghua Shi 36

From the method of limit to staircase

Stim

ulus

Int

ensi

ty

(Bri

ghtn

ess)

n n n 95

n n n 96

n n n 97 n y n n 98

n y y n y 99 y y y n y 100

y y y y 101 y y y 102 y y y 103 y y y 104

n

n

n

Stim

ulu

s In

ten

sity

(B

righ

tnes

s)

n

y

n

n

y

n

n

y

95

96

97

98

99

100

101

102

103

104

Transition point

y

n

y

y

y

n

y

y

y

y

y

y

n

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6

98.5 100.5 99.5 98.5 97.5 99.5

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= 99

One-up – one-down staircase

• Procedure:• Start from above (below) threshold• Stop after a given number of transition points• Average final several transition points

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How to estimate other points on the curve

• One-up – one-down represents the 50th percentile

• Varying the number of up/down steps converges at different percentiles

• One-up – three-down, 79%

• One-up – two-down, 71%,

• One-up – one-down, 50%

• Two-up – one-down 29%

• Three-up – one-down, 21%

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How to estimate other points on the curve?

• Weighted up/down methods

•where

• For 75th percentile, p = .75, up step size should be 3 times of down step size

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Staircase method - evaluation

• Hysteresis effect – the starting point makes a difference• Higher thresholds for ascending staircase then for

descending

• Expectation effect• Many trials necessary

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Controlling for hysteresis and expectation

• Interleaved staircases

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Parameter Estimation by Sequential Testing (PEST)

• Variant of weighted step-size method

• Large steps at the beginning

• Changing the step size as the run proceeds, in a particular way

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Parameter Estimation by Sequential Testing (PEST)

1. With each response reversal, the step size is halved

2. When the minimum is reached, the step size is constant

3. When there is no reversal, the first two steps keep the same size

4. From the 3rd onward steps are doubled

5. If a reversal follows a doubling of step size, the 3rd step stays the same

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Adaptive staircase methods (QUEST and MLP)

• Uses prior knowledge about psychometric function:

• What is the function? cumulative normal, logistic, …

• Successive trials are evaluated as evidence that they belong to one or another psychometric function

• By computing maximum-likelihood that the trial belonged to a function

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Adaptive staircase methods (QUEST and MLP)

• For response on each trial one can compute its probability on the basis of different functions

• The function that produces the best fits for most trials is the winner

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50%

Seen

Unseen

Adaptive staircases - evaluation

• Random stimulus presentation – little risk of expectation or habituation errors

• Efficient – uses all responses so only few trials suffice

• Accurate – up to the extent to which the assumptions are satisfied

• Risky – if the assumptions are invalid it will not produce reliable results

• Complex to learn and understand

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QUEST

• A Bayesian adaptive psychometric method

• Watson & Pelli, Perception & Psychophysics, 1983

• available in Psychtoolbox (psychtoolbox.org).

• Method• User all prior knowledge to guide the placement of the

trials by maximum likelihood estimation of Bayesian prob.

• Psychometric function and shape must be assumed

Zhuanghua Shi 48

Quest provided by Psychtoolbox

• q=QuestCreate()• Create parameters of a weibull psychometric function

based on previous knowledge and guess• q=QuestCreate(tGuess,tGuessSd,pThreshold,beta,delta,ga

mma)• Beta: steepness of the PF• Delta: lapse rate, e.g. 0.01• Gamma: guess rate

• QuestQuantile(q);• set the stimulus level

• QuestUpdate(..);• after response, update probability density function (PDF)

Zhuanghua Shi 49

MLP: Adaptive maximum likelihood

• David Green (1990, 1993)

• Implemented by Grassi & Soranzo, 2009

• MLP: Matlab toolbox for rapid and reliable auditory threshold

• Similar to QUEST, but• Use logistic function as general psychometric function

• Downloadable:

• http://www.psy.unipd.it/~grassi/mlp.html

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http://www.psy.unipd.it/~grassi/mlp.html

Bayesian methods - evaluation

• Pros

• Efficiency and accurate

• Using all information (responses)

• Cons

• Complex procedure

• Psychometric function must be determined

• Variability of the threshold depends on particular p-target.

Adapted from Grassi, 2009 51

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Classical methods



The medhod of limits

Adaptive methods

Staircase methods



Summary

ascendingdescendin

g ascendingdescendin

g

Tim

e

Trial 1.Trial 2.

Summary

• Stimulus-to-sensation mapping is non-linear

• Sigmoidal, logarithmic, exponential

• Describing the mapping function:

• Absolute and discrimination thresholds

• Classical methods – time consuming, but little assumptions

• Adaptive methods – more efficient, but only if assumptions hold

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psychophysical methods

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