Psychometric fucntions (Basics) Mehtods and procedures

Question 1

Classical psychophysical methods

Answer 1

Simpel: Present stim and ask subject if they perceives the stimulus
However: Biological system is subject to noise
Thus: the absolute threshold ≠ stimulus level below
which 0% perception and above which 100% perception
Threshold determination requires a statistical approach

Question 2

Fechner: Three measurement methods

Answer 2

Methods of constant stimuli
Methods of limits
Method of adjustment

Question 3

types of tasks to detirmine limits

Answer 3

Adjustment

classifications

Question 4

Adjustment task

Answer 4

Ask subject to set physical stimulus value in a certain way:
Absolute value until subject detects the stimulus
Usually by alternating a number of ascending and descending sequences
Instructions are very important in adjustment tasks as
the subject controls the stimulus level him/herself

• The easiest are matching instructions
matching tasks: setting the test stimulus in such a way that it
corresponds to a standard- or reference stimulus

Question 5

Classification task

Answer 5

To obtain more standardized measurements, it is better
not to have the subject determine the stimulus level
him/herself
In such case, the subject is asked to classify the presented stimuli in one way or another
Three possibilities:
1. Was the stimulus present? (yes/no task)
2. In which interval was the stimulus present? (two-alternative
forced-choice or 2AFC task)
3. What was the stimulus? (identification task)

Question 6

Yes/No task

Answer 6

Very simple low cognitive load
Important disadvantage: subject can use his/her own criterion to answer yes or no (response bias)
the threshold can only be dissociated from his internal criterion if catch trials are used, so that both HR and FAR can be measured
By influencing the criterion during the instruction (e.g. by
reward/punishment) the different criterion values of the
HR and FAR can be plotted in a so-called ROC-graph
(ROC = Receiver Operating Characteristics)
The area under the ROC-curve is an excellent measure
for the sensitivity to the signal, independent of the
response bias

Question 7

2AFC task

Answer 7

Two stimuli
- Detection task: one signal one blank
- Discrimination task: Two signals (strongest signal)
Other disctinction
- Succesive: 2IFC
- Simultaneous: 2AFC
Important advantage: by assigning two kinds of stimuli randomly to both intervals or positions, performance can easily be compared to chance
Under certain conditions the % correct corresponds to the area under the ROC curve without obligation to use the same cumbersome procedure
Important disadvantage: Large number of trials needed

Question 8

Identification task

Answer 8

Most efficient method: presenting a limited number of stimuli and asking the subject to identify these
Tradeoff:
Small number of possible stimuli: easier to learn but higher guess rate
Large number of possible stimuli: lower guess rate but identification is harder to learn
optimum = 4 stimuli

Question 9

Methods of limits

Answer 9

Variation of the stimulus intensity of just one stimulus (luminace or volume)
Threshhold will be determined by alternation of a number of ascending and descending sequences
Mean of the simulus intesity of the last two trials is used as a transition point within each sequence
The mean of the transition points within several
sequences can be used as threshold

Question 10

Method of constant stimuli

Answer 10

the experimenter chooses a number of stimulus values around the threshold ( based on adaptive procedure)
Each stim value presented a fixed number of times
For each of these stimulus values a frequency can be
plotted for a number of response categories (e.g., ‘yes’ answers in a yes/no task or one of both answers in 2AFC), possibly as a proportion or percentage
Such a graph is called a psychometric function
Disadvantage: many trials necessary and not all data
points are useful (solution: adaptive procedure; see
below)

Question 11

Function estimation

Answer 11

Theoretical point of view: data are often fitted with a cumulative Gaussian/normal distribution
probit analysis is a possibility
Reason: the internal representation of the
stimulus is supposed to have a normal distribution

The perceived difference between two stimuli is
inverse proportional to the overlap between both
normal distributions (z-scores)
if a discrete threshold needs to be determined an arbitrarty choice is to be made

Two frequent choices: Half
-the distance alog the abcissa betwee the 20% and 80% points on the ordinate
- Half the distance along the abscissa between the
25% and 75% points on the ordinate

Question 12

50% point of subjective equality

Answer 12

point of subjective equality or PSE

Not located on the 0 value (response bias)

Question 13

Very important for threshold determination

Answer 13

choice of the stimulus levels:
– Mostly points around the 20% and 80% answer
options; the 0% and 100% points are theoretically
redundant
– In practice, it is useful to include the easy conditions
to keep the subjects motivated

Question 14

Adaptive test procedures: Three main categories

Answer 14

Adaptive “staircase” procedures
PEST-procedures
Maximum-likelihood adaptive procedures

Question 15

Adaptive “staircase” procedures: how does it work

Answer 15

Start with an arbitrary, but large enough stimulus
value
- Correct answer: lower the stimulus value with a fixed
increment
– Wrong answer: raise the stimulus value with a fixed
increment
6-9 turning points to estimate the threshhold

Question 16

Adaptive “staircase” procedures: Advantage/Disadvantage

Answer 16

Advantage: more efficient because most of the stimulus values are centered around a threshold

Disadvantage: Subject can figure out the modification

Solution two staircased mixed= interleaved staircases

Question 17

Adaptive “staircase” procedures: Other disadvantages

Answer 17

Threshold converges to 50% correct

Question 18

Adaptive “staircase”: Levitt (1971)

Answer 18

Developed a general transformation procedure to acquire specific values on the psychometric curve through an adaptive staircase procedure

Idea: To attain higher performance level the subject needs to give several correct answers before the stimulus level is lowerd.
Two-down one up converges to 70.71 percent
Three-down one up converges to 79.4 percent

Question 19

Adaptive “staircase” procedure

Answer 19

Most frequently used adaptive test procedure because most straight forward
- choice of the next stimulus level, increment stop criterion, threshold very easy
no assumption shape of psychometric function
only assumption monotonic link between stimulus lvl and performance lvl

Question 20

Parameter estimation by

sequential testing” (PEST): How does it work

Answer 20

Essentail: More complex algorithm for the search of the threshold by:
Changing criteria for a change of the stimulus intesity
Changing the increment as the number of trials increases
Concreatly:
Statistical test used to check wheter the performance level up to a given moment is higher or lower than the target performance level
The increment halves with every subsequent direction change

Question 21

PEST: Threshold

Answer 21

stimulus intensity at the
end of the sequence = Threshold

Criterion for the efficiency of the procedure: product of the number of trials and the variance of the measurements

For PEST estimated at 40 to 50%

Question 22

“Maximum-likelihood”

adaptive procedures: how does it work

Answer 22

Essential: performance up to a given moment is used to estimate as well as possible the entire psychometric function
Assumptions with regard to the shape of the psychometric function (parametric)
E.g. “best PEST”:
– Logistic function
– The best possible estimation of 50% performance point (according to “maximum-likelihood” criterion)
– Final threshold: last stimulus value

Question 23

Maximum-likelihood”

adaptive procedures: QUESt

Answer 23

(Watson & Pelli, 1983), all information is used to determine the next stimulus level by means of Bayesian methods
For a sequence of stimuli of a definite length the
QUEST-procedure is more efficient (e.g., 84%
as opposed to 40 to 50%)
The last couple of years better (and more
efficient) procedures are developed, e.g.,
MUEST, ZEST, etc.