Course C - Week 5 PSYCHOPHYSICAL METHODS Z. SHI

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

1

T X

L X LX

L X

L +X LX

L LX X LX

3

2

L X

L L X X

L X L L +X X

L L LX X X

4

3

L X

L L X X

L X L L +X X

L L LX X X

5

4

L X

L L X X

L X L T +X X

L L LX X X

6

5

X L

LX LX

X L

+LX LX

LX TX LX

7

6

L X

L L X X

L X L L +X X

L L LX X X

8 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

Conditions Presentation time P(‘Yes’) (sec) 1 0.2 1/16 2 0.4 14/16 3 0.6 16/16

9 Stimuli and sensation

• Non-linear relation between and

Undetectable region Saturated region

Sensation – psychology

Stimulus intensity – physical property

• have an operating range

10 Point of subjective equality (PSE)

• Is the vertical?

100%

50% Point of Subjective Equality - PSE % Vertical response 0%

11 Just noticeable difference (JND)

• Difference in stimulation that will be noticed in 50%

75% = Upper threshold

25% = Lower threshold % Vertical response

– = Uncertainty interval = JND 2

12 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 detect Just Noticeable Difference (JND)

14 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

100%

75% 75% 67% 2AFC 50% 50% 3AFC 25% Yes/No 0%

16 MEASURING THRESHOLDS

17 Measuring psychometric function

The method of constant stimuli

Classical The method of adjustment methods

The method of limits Psychophysical methods Staircase methods

Adaptive Parameter estimation by methods sequential testing (PEST)

Maximum-likelihood adaptive procedures (QUEST, MLP)

18 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

19 Example

20 Method of Constant Stimuli & Psychometric Function

• Multiple Intensity levels, Proportion of “yes” responses

multiple repetition 100% • Prop. of responses • Represented roughly 50% shape of psychometric curve • Estimation of Intensity

Psychometric curve: JND, - - - - - + + + PSE - - + - - - + + - - - + + + + + + - - + + + + + ------+ + + + + + + ------+ + + +

21 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 stops 3. Averaging the stopping values across several trials yields thresholds

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

104 y y y

103 y y y

102 y y y

101 y y y y

100 y n y y y

99 y n n y y n (Brightness) 98 n n n y n Stimulus Intensity

97 n n n n

96 n n n

95 n n n (99+98)/2 Transition point = 98.5 100.5 99.5 98.5 97.5 99.5 = 99

24 Example of the method of limits • Sound

25 Method of limits and psychometric function

• Psychometric function

• Not required • Multiple ascending Internal criterion and descending method of limits Prop. Of ‘Yes’ measure Threshold Stimuli • PSE ascending

descending ascending

descending

26 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.

27 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

ascending

descending ascending

descending

Stimuli Intensity

28 3. The method of adjustment

• Subject controls (adjust) the stimulus intensity • – 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

29 Example

Trial 1 Trial 2

• Threshold is the mean of all trials

30 Method of adjustment and Psy. function • Psychometric function • Not required • Threshold • Internal criterion of Internal criterion responses

• Continuous Prop. Of ‘Yes’ adjustment of stimuli intensity Threshold • Fine tuning at the end Stimuli of trial • PSE Trial 1.

Time Trial 2.

31 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

32 Methods of adjustments in clinics

33 Measuring psychometric function

The method of constant stimuli

Classical The method of adjustment methods

The method of limits Psychophysical methods Staircase methods

Adaptive Parameter estimation by methods sequential testing (PEST)

Maximum-likelihood adaptive procedures (QUEST, MLP)

34 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

35 From the method of limit to staircase

104 y y y

y y y 103

102 y y y

101 y y y y

100 y n y y y

99 y n n y y n

98 n n n y n (Brightness) 97 n n n n Stimulus Intensity 96 n n n

95 n n n

Zhuanghua Shi 36 Run 1 Run 2 Run 3 Run 4 Run 5 Run 6

104 y

103 y

102 y

101 y y

100 y n y y y y

99 y n n n y n (Brightness) 98 n y n Stimulus Intensity

97 n

96

95

Transition point 98.5 100.5 99.5 98.5 97.5 99.5 = 99

37 One-up – one-down staircase

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

38 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%

39 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

40 Staircase method - evaluation

• Hysteresis effect – the starting point makes a difference • Higher thresholds for ascending staircase then for descending • Expectation effect • Many trials necessary

41 Controlling for hysteresis and expectation

• Interleaved staircases

42 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

43 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

44 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

45 Adaptive staircase methods (QUEST and MLP)

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

Unseen Seen 50%

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

46 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 • to learn and understand

47 QUEST

• A Bayesian adaptive psychometric method • Watson & Pelli, & 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

50 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 Summary

The method of constant stimuli

Trial Classical methods The method of adjustment

Tim e 1. Trial 2.

ascendin The medhod of limits descendin g g ascendin Psychophysical descendin g methods g Staircase methods

Adaptive methods Parameter estimation by sequential testing (PEST)

Maximum-likelihood adaptive procedures (QUEST, MLP)

52 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

53