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Psychophysical Methods Z 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 LX LX LX T X LX + LX 3 LX LX LX 2 LX LX LX X L L X + LX 4 LX LX LX 3 LX LX LX X L L X + LX 5 LX LX LX 4 LX LX TX L X L X + LX 6 LX LX LX 5 LX LX LX X L LX + LX 7 LX TX LX 6 LX LX LX X L L X + LX 8 LX LX LX 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 physics and psychology Undetectable region Saturated region Sensation – psychology Stimulus intensity – physical property • Senses have an operating range 10 Point of subjective equality (PSE) • Is the stimulus 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 • 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 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 • Complex to learn and understand 47 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.
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