Psychophysical Methods

Question 1

What is measured with the stimuli (e.g. sinewave gratings & optotypes) in psychophysics? Describe threshold?

Answer 1

In many visual psychophysical tests, threshold of a certain aspect of vision such as contrast or size is most frequently measured quantity
Threshold: absolute minimum so weakest stimulus strength or intensity that results in change or perception. OR strength of signal required to attain a specific level of task performance e.g. 75% correct performance level or 90% and so on

Question 2

What is a psychophysical task?

Answer 2

What observer needs to do in experiment that is designed to measure threshold underlying perceptual process of interest

Question 3

Describe subjective refraction as a psychophysical experiment - stimulus, measuring, task, procedure, method & analysis?

Answer 3

• Stimulus: optotype
• Measuring: recognition or identification threshold
  o Measuring absolute threshold: smallest letter size px can correctly identify
• Task: px must correctly identify or recognise letter presented
  o Aspect of vision being tested is size of letter – size of visual stimulus & this is changing throughout process
• Procedure: forced choice  px presented with number of alternatives in visual stimulus  2 alternative forced choice procedure
  o Objective as px’s response can be verified with correct answer
  o Target stimulus is always presented so choice between alternative responses are supposedly on “equal footing”
   Good thing  reduces criteria fluctuation due to the uncertainty by forcing px to use their best guesses
• Px will make lucky guesses sometimes but unlucky guesses as well so they will cancel each other out assuming alternatives are presented at random and in no predictable pattern
• Method: method of limits (featuring threshold estimation)
• Analysis: concerns how threshold is calculated at end of each method
  o Adopting specific method will determine how collected date will be converted into threshold measurements

Question 4

What are psychophysical methods?

Answer 4

• Classical (aka Fechnerian):
  o Method of limits
  o Method of adjustment
  o Method of constant stimuli – not frequently used
• Modified Fechnerian:
  o Staircase method (2-up-1-down, 3-up-1-down, interleaved)
  o Computer-intensive method (QUEST, ψ Method)
• A trial: single presentation of stimulus
• A session: a series or block of trials

Question 5

Describe measuring absolute threshold?

Answer 5

• Absolute threshold: minimum intensity of any aspect of stimulus that observer can barely detect or identify
• Stimulus intensity (e.g. letter size) < absolute threshold of px: unrecognisable or undetectable
• Stimulus intensity (e.g. letter size) > absolute threshold of px: identified or detected
• Subj refraction e.g.: stimulus intensity of interest is size of letter

Question 6

Describe the generalised steps of Methods of Limits?

Answer 6

1. On the 1st trial, a stimulus with intensity well above (for descending series) or below (for ascending series) the expected threshold will be presented
   o Descending: experiment begins w/ presenting stimulus with high enough intensity so that most people can detect or identify it
   o Ascending: 1st trial starts with stimulus intensity so low that it’s expected to be unrecognisable/undetectable by most people
2. The observer reports if they could see the stimulus or not
3. In each consecutive trial, decrease/increase intensity until observer changes direction of response from yes to no or vice versa – session is over
4. Threshold estimate: average intensity between last & second last intensity – threshold located between two intensities in which observer’s response switches

Question 7

Describe absolute threshold of Methods of Limits?

Answer 7

• VA measurement is e.g. of descending series method of limits -> measurement starts with large enough optotype assumed to be recognised by most people (6/60)
• Going down chart where size of letter progressively decreases until px cannot read it
• Final threshold (i.e. best uncorrected VA) is considered to be smallest read line

Question 8

Describe subjective refraction as a psychophysical experiment - measure & task, Procedure, method & analyis?

Answer 8

• Measure and Task:
  o In process of subj refraction, what measuring is difference threshold – ask px if they see difference in clarity with or w/o added power of lens you present
  o Difference threshold: minimum intensity difference between a pair of stimuli that is noticeable to observer  AKA just noticeable difference (JND) or difference limen
  o One of pair called standard or reference stimulus
  o Other of pair called comparison or test stimulus
  o If intensity difference between pair of stimuli is below difference threshold of subject, then difference is undetectable
  o If intensity difference between pair of stimuli is above difference threshold, then difference is detectable
• Procedure:
  o Px faced w/ 2 choices: whether letter looks clearer or not
  o Even though px forced to choose 1 or 2 alternative, this procedure is different from 2-alternatives, forced choice procedure as cannot verify if px’s response if systematic or random  hence name subj redraction
  o Yes-no Procedure
• Method & Analysis:
  o Method of limits where zone in on optimal refractive power needed for px
  o Method of Limits (feat. Threshold estimation)

Question 9

Describe methods of adjustment?

Answer 9

• Observer has control over stimulus intensity to measure their own threshold except for initial intensity
• E.g. turning down volume until comfortable
• Initial intensity is set to be far from expected threshold value
• Can be ascending or descending as method of limits
• Instructed to adjust intensity by a physical or software device (e.g. knob or slider) until it is just detectable or just undetectable
  o Intensity of stimulus can be ascending or descending, and threshold can be determined v quickly but not v precisely with this method
  o Rarely used in PP experiments
• “quick & dirty” way to measure thresholds

Question 10

What are the issues with Method of Limits & Adjustment?

Answer 10

• Advantages:
  o Simple, quick, efficient
  o Clinical advantage (e.g. audiometry, VA testing)
• Disadvantages:
  o Habituation: tendency to repeat same answer even after sensation has changed - ↑ threshold in ascending series & ↓ threshold in descending series
  o Expectation: premature change in response prior to actual change in sensation due to anticipation – opposite effect to habituation - ↑ threshold in descending series & ↓ threshold in ascending series
  o Choice of initial value & step size between trials can sometimes be tricky
   If initial value is too far from threshold, will take longer to get to threshold  more chance of habituation
   If initial value too low – observer may get confused & fluctuate in answe
• Recommendation to avoid these issues:
  o Repeat both series multiple times & take average for final threshold estimate because:
   Each series may yield different results
   Results can be variable even using same series
• Both rarely used in serious PP experiments

Question 11

Describe the general considerations of Psycophysical methods?

Answer 11

• PP method concerns way in which final threshold is estimated effectively
  o Stimulus placement: how to present stimuli to maximise info about parameter of interest
   Determine initial stimulus intensity for the 1st trial
   Stimulus intensity for following trials
   Step size – if too jumpy, method will quickly approach threshold zone, but threshold estimation will be coarse
  o Threshold estimation: how to calculate final threshold?
   Ultimate goal of PP testing – obtaining unbiased & precise threshold estimate at end of testing is v important
  o Termination: when to stop the experiment? – want to make sure threshold obtained after certain no. of trials is accurate & precise
   Generally, estimation will get better with more data in terms of precision & accurate but have to end experiment at some point before observer gets too tired

Question 12

Describe the staircase method: measuring absolute light detection threshold?

Answer 12

• x-axis: trial number from 1 to n
• y-axis: brightness of dot presented in each trial
• Trial-by-trial progression of stimulus intensity changes according to subject’s response
• In staircase: both ascending & descending series are combined together & changes according to subject’s response
• Session ends  total number of trials used in this session was n=17
• Over the 17 trials, 4 reversals occurred in session  final analysis to estimate threshold is to take average light intensities where reversal occurred (red extrapolated lines from reversals)
  o Threshold estimate = mean of last m reversals (1st few reversals are quite variable so are discounted)
• Stimulus: a dot
  o In each trial, brightness of dot will change according to rules of staircase  brightness will go down when user says can see dot & go up when user says no
• Measure: threshold
• Task: detection  minimum brightness of dot subject can see
• Procedure: yes-no  subjective procedure as cannot verify subject’s answers, can only trust subject is giving genuine responses to brightness of dot
  o Subject’s response can be criterion-dependent & prone to bias  if subject more concerned about missing target, then they will be prone to say “yes” more than necessary
  o Wherever possible, it is always best to use forced choice procedure where subjects response can be verified
• Method: 1-down, 1-up staircase  stimulus intensity decreased after positive response or increased after negative response  1:1 staircase
• Analysis: average of reversals

Question 13

Describe the staircase (psychophysics)?

Answer 13

• Stimulus placement
  o Initial stimulus intensity for 1st trial: well below or above threshold depending on initial direction of change in intensity (same as classical method of limits or adjustment)  pretty much guesswork & no set rule to determine this
  o Stimulus intensity for subsequent trials: changes upon preceding response of observer  1:1 rule
  o Step size: % difference from last intensity or an octave scale (=log2(i1/i2)) is used
   Octave – name for log scale w/ base of 2 – often used in auditory perception
   % Difference is less frequently used – e.g. initial brightness was 100% and response to this was +ve then next brightness will be ↓ to 90% so step size used here is 10%
• Common practice to use multiple step sizes to ↑ precision of final threshold estimation  start large & get smaller
• Termination: when to stop experiment?  after (1) n number of reversals or (2) n number of trials or (3) whichever comes first
  o 1:1 staircase (simplest) takes ~couple of mins but if change rules of staircase to 2:1, 3:1, 4:1 then amount of time to finish a staircase gets longer
• Threshold estimation: how to calculate final threshold?  average of stimulus intensities at last m (<n) reversals (stimulus intensity at which direction od stimulus intensity presentation changes):
  o Typically take average of last 7 or 8 reversals when staircase is set to terminate after 10 reversals  first few reversals are highly variable and may be far from final threshold

Question 14

Describe the simple up-down staircase?

Answer 14

• Rule of staircase is 1:1  direction of stimulus intensity changes in way that every -ve response ↑ stimulus intensity by 5db of previous intensity whereas intensity ↓by 5db after every +ve response until 14th trial or 5 reversals
• In staircase w/ 1:1  +ve & -ve response are equally weighted -> technicaly speaking, threshold measured using 1:1 staircase will converge onto the stimulus intensity at which subject is completely uncertain about their perception as response to this stimulus intensity will generate +ve & -ve responses w/ 50/50 chance

Question 15

Describe transformed staircase?

Answer 15

• To make threshold we are measuring converge onto somewhere less than certain for either +ve or -ve responses
• 3:1 staircase  subject must provide 3 +ve responses in a row for reduction of stimulus intensity  whereas only 1 -ve response will ↑ stimulus intensity w/ same step size in both directions
• Probability for staircase to change its direction is not equal between the +ve & -ve responses
• Probability that stimulus ↑ is 50% only after single -ve response whereas probability of intensity ↓ is the probability of obtaining 3 +ve responses in a row
• 3:1 staircase converges onto the threshold building ~79.4% of the times compared to the -ve responses
• Popular PP method of choice for long time to measure threshold

Question 16

Describe threshold & psychometric function (PF)?

Answer 16

• Perceptual representation of a stimulus is not constant due to small additive random errors introduced to visual system called internal noise
• Smooth probabilistic curve monotonically increasing as stimulus intensity ↑
• From continuous curve, absolute threshold is defined as stimulus intensity yielding perceptual experience 50% of the time on curve when observer’s response is binary

Question 17

Describe “modern” adaptive methods in Psychophysics?

Answer 17

• Importance of measuring PF has been emphasised
• To model a PF, need to measure lot more thresholds than just a single threshold –> increases burden of data collection from experimenter and subject
  o Gets much worse when multiple levels of variable to be measured
• However, characterising a PF can be quite labour intensive and time-consuming
• Thanks to ↑ in computing power, a PF can be estimated with a reasonable amount of effort & precision
• Psi-method (Kontsevich & Tyler, 1999)
  o Based on Bayesian principle to estimate an underlying segmented function of an observer for any perceptual task
  o In every trial, Psi method will estimate observer’s psychometric function based on their previous response to the optimally selected stimulus intensity (precomputed)
  o Trial by trial estimation of observer’s PF is based on observer’s response to optimal stimulus intensity that is computed by the Psi method algorithm to maximise info gain at next trial
  o Estimation of Psi method converges to true location parameter & true slope parameter -> estimation of PF closes in to true PF after 300 trials

Question 18

Describe Psychometric Function (PF)?

Answer 18

• Family of functions relating physical characteristic of stimulus (e.g. contrast) to corresponding sensation (e.g. proportion of correct responses, or proportion of trials perceived brighter/dimmer)
• Probability of an observer’s response as a function of stimulus strength:
  p (r|s) = ψ (s;a, β, γ, λ) = y + (1-γ-λ) F (s;a;β)

(1-γ-λ) - quantity inside this bracket will determine max value(% correct) in psychometric function considering lapse rate)
F (s;a;β) - determined by location parameter & slope -> F(function) determined by stimulus strength (s) on x-axis

o p=probability of subject’s response, represented by r, given stimulus intensity s
o Psi –> psychometric function has 4 parameters – stimulus intensity s, location parameter a, β=slope parameter (how quickly perception changes as function of stimulus strength, γ=guess rate (0.5 or 50% in case of the 2 alternative forced choice task, λ=lapse rate (accounts for some finger error)
o Intensity is outcome measure
* Typically: PFs have an s (sigmoidal) shape

Question 19

Describe absolute & general threshold and describe forced choice procedure?

Answer 19

• Absolute threshold is point where it yields 50% of response from the subject
• In general threshold is stimulus intensity yielding a specific level of performance – so can cut psychometric function anywhere want – e.g. threshold definition yielding 60% performance
• If using a forced choice procedure, can plot PF relating % correct performance as a function of stimulus intensity
• Threshold for n number of alternative forced choice procedure is usually defined as stimulus intensity yielding a midway percent correct response between guessing rate & 100%
  o Therefore, threshold for 2 alternative forced choice experiment is defined at intensity yielding 75% correct performance level