Psychometric function (basic, Laure-Anne) Flashcards
What is the definition of psychophysics?
Scientific study of the (quantitative) relations between physical stimuli and sensations.
What did classical psychophysics focus on?
Threshold measurements as an indirect scaling method.
What does modern psychophysics focus on?
Signal detection theory and direct scaling methods (more broadly applicable than sensory modalities).
What does RL mean?
= Reiz Limen
Absolute threshold
Limit that indicates the transition between absence and presence of a sensation
(i.e. minimum stimulation needed to detect a stimulus).
What does DL mean?
= Difference Limen
Differential threshold
The smallest added stimulus intensity that allows perceiving a just noticeable
difference (JND).
What does Weber’s law say?
(1834)
The stimulus intensity must be increased by a constant fraction of its value in order to obtain a just noticeable difference
k = delta(I) / I
What does Fechner say about Weber’s law?
(1860)
The absolute threshold (RL) and the just noticeable difference (JND) can be used to determine the starting point and the measurement unit, respectively (both necessary to truly measure sensations)
S = k * log(R)
To increase the strength of the sensation (S) as an arithmetic sequence (summed with a constant), one has to increase the stimulus intensity (R) according to a geometric sequence (multiplied by a constant).
Weber-Fechner Law (based on indirect scaling method):
What is Stevens’ Power law?
(based on a direct scaling method, “magnitude estimation”)
S = k * R^n
What is a psychometric function?
A function that describes the relationship between stimulus intensity and probabilities of observer responses in a classification (forced-choice) task
What are the 2 main task categories that can be used to determine limits?
1) Adjustment
Subject has to adjust the stimulus
–> non-forced choice
2) Classification
Subject has to classify the simulus
–> forced choice
Classification is more standardized
What are the 3 types of classification tasks?
1) Yes/no
What is the stimulus?
2) 2AFC
In which interval was the stimulus present/stronger?
3) Identificaiton
What is the stimulus?
What is a positive and a negative point of a yes/no task?
+ Very simple, low cognitive load
- Subjects can use their own criterion to answer yes/no (response bias)
–> Threshold can only be dissociated from this internal cirterion if catch trials are included, to measure hit rate (HR) and false alarm rate (FAR)
How can we obtain a ROC graph from a yes/no task and what does a ROC show?
By influencing the criterion during the instructions (reward, punishment, …) the different criterion valeus of the HR and FAR can be plotted in a ROC (Receiver Operating Characteristics).
The area under the curve is a good measure of the sensitivity tot the signal, independent of the response bias.
What are the 2 distinctions to make in a 2AFC task?
1) Discrimination or Detection?
2) Simultaneous or Successive
What is the difference between 2AFC and 2IFC?
2AFC: the 2 stimuli are presented together on the screen
2IFC: the 2 stimuli are presented in the same display position but in temporal order
Give one positive and one negative aspect of using a 2AFC task.
+ Due to random assignment of the 2 stimuli, performance can be easily compared to chance.
–> Under certain conditions the % correct responses corresponds to the area under the ROC-curve.
- Large number of trials is needed (especially if yuo want to know the complete psychometric function)
What is the difference between a yes/no task and a 2AFC task?
Yes/no: the 2 alternatives are presented on different trials
2AFC: the 2 alternatives are presented within the same trial
Which tradeoff is made in a identification task?
Identification task: presenting a number of stimuli and asking subject to identify the stimuli
If a small number of stimuli is presented:
- identification is easier
- guess rate is higher
If a large number of stimuli is presented:
- identification is harder (higher cognitive load)
- guess rate is lower
OPTIMUM
= choosing 4 stimuli
What are the 3 main classical methods to measure thresholds?
1) Method of adjustment
Subject freely adjusts the magnitude of a stimulus in order to reach a criterion, for example a threshold.
2) Method of limits
Subjects are presented a series of stimuli with increasing or decreasing magnitude, and report when the stimulus appears to change state.
3) Method of constant stimuli
The magnitude of the stimulus presented on each trial is selected form a predefined set.
What are characteristics of the method of adjustment.
It’s a classical method
1) It is usually measured by alternating a number of ascending and descending sequences.
- -> averaged to mean value
2) Instructions are very important because the subject controls the stimulus level himself.
–> Use Matching Instructions
Setting the test stimulus in such a way that it corresponds to a standard or reference stimulus.
What are characteristics of the method of limits?
It’s a classical method
1) The threshold will be determined by alternation of a number of ascending and descending sequences
2) The mean of the stimulus intensity of the last two trials in is used as a transition point within each sequence
3) The mean of the transition points within several sequences can be used as a measure of threshold
What are characteristics of the method of constant stimuli?
It’s a classical method
1) The experimenter chooses a number of stimulus values around the threshold (e.g., based on adaptive procedure). Each of the stimulus values (e.g., 5 or 7) is presented a fixed number of times (e.g., 50) in random order.
2) 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 the two alternative responses in 2AFC), possibly as a proportion or percentage.
–> Such a graph is called a psychometric function.
= Usually a continuous S-shaped function
–> Exact threshold determination is not trivial.
- Many trials are necessary and not all data points are useful –> adaptive procedure
What is the theoretical point of view to fit a sigmoid as a psychometric function?
Data are often fitted with a cumulative Gaussian distribution.
–> the internal representation of the stimulus is supposed to have a normal distribution.
The perceived difference between two stimuli is inversely proportional to the overlap between both normal distributions (z-scores):
- Good stimulus representation (small variance )
- -> Steep slope
- Less good stimulus representation (larger variance )
- -> Shallower slope
In the psychometric function estimation, if a discrete threshold needs to be determined an arbitrary choice is to be made (JND = IU/2), what are 2 frequently used possiblities?
1) Half the distance along the abscissa between the 20% and the 80% points on the ordinate
- -> + The chosen threshold value is in accordance with one SD of the underlying Gaussian distribution.
2) Half the distance along the abscissa between the 25% and the 75% points on the ordinate
- -> + The criterion is situated halway between chance (50%) and perfect performance (0% or 100%).
What is the definition of ‘point of subjective equality’ (PSE) in function estimation?
PSE: The physical magnitude of a stimulus at which it appears perceptually equal to that of another stimulus.
–> 50% point (usually not located on the 0 value, response bias)
What are 2 alternative functions for the psychometric function estimation?
1) Logistic function (small difference but faster)
2) Weibull (larger difference)
What are the most important points for threshold determination?
The points around 20% and 80%
The points below 20% or above 80% are not that useful (redundant) but they are often used to give the participant some easy trials.
–> choice of the stimulus levels is very important
What is essential in all the adaptive test procedures?
The stimulus level is chosen based on the performance of the subject on previous trials.
What are the 3 main categories of adaptive procedures?
1) Adaptive staircase
2) PEST
3) Maximum likelihood
What are the characteristics of an adaptive staircase method?
= An adaptive variant of the “staircase”, as described above (method of the limits).
Start with an arbitrary (but large enough) stimulus value, then:
Correct answer: lower the stimulus value with a fixed increment
Wrong answer: raise the stimulus value with a fixed ,increment
+ More efficient because most of the stimulus values are centered around a threshold.
- Subjects can figure out the modifications (and the structure of the task).
What is the solution for the problem with the adaptive staircase method where subjects can figure out the modifcations,
Interleaved staircase
= 2 staircases mixed, one starting with high stimulus (detected) intensity, the other with low (not detected).
The 2 staircases alternate over trials.
Problem: Threshold converges to 50% correct (probability of a correct answer = probability of a wrong answer); i.e., too low for some purposes.
What is a solution for the fact that the adaptive staircase method leads to a 50% correct threshold?
Other rules to increase and decrease stimulus intensity.
Levitt (1971) has developed a general transformation procedure to acquire specific values on the psychometric curve through an adaptive “staircase” procedure.
Example:
- ‘2 down - 1 up’ –> intensity goes down after 2 correct responses and intensity goes up after 1 wrong response –> converges to 70% correct
What are 2 arguments why the adaptive staircase method is the most straightforward method to use?
1) It is easy to choose the next stimulus level, increment, stop criterion and threshold (adaptive staircase PEST).
2) No assumptions with respect to the shape of the psychometric function (non-parametric maximum-likelihood).
⇨ Only assumption: monotonic link between the stimulus level and the performance level
How does PEST work and what does it stand for? (give an example)
PEST = Parameter Estimation by Sequential Testing
Designed to address the problem of step size and starting intensity.
Idea: A property of some signal (the independent variable) is adjusted to find the magnitude that results in a performance of specified accuracy (the dependent variable).
Essential: more complex algorithm for the search of the threshold by:
– Changing the criterion for a change of stimulus intensity
– Changing the increment as the number of trials increases
Concretely:
A statistical test is used to check whether the performance level up to a given moment is higher or lower than the target performance level.
–> Increment halves with every subsequent direction change.
For example (arbitrary): Target performance = >75% and <25% 4 good trials (4/4 = 100%) --> intensity is halved 3 good trials, 2 bad, 1 good (4/6 = 66%) --> intensity stays the same 2 good trials, 7 bad (2/9 = 22%) --> intensity is increased by half
What are the characteristics of the maximum likelihood method?
The stimulus intensity presented at each trial is determined by statistical estimation of the subject threshold based on all responses from the beginning of the session.
At each trial, a psychophysics function is updated and then serves to select a stimulus intensity for the upcoming trial.
There are assumptions with regard to the shape of the psychometric function (parametric).
Likelihood: The probability with which a hypothetical observer characterized by assumed model parameters would reproduce exactly the responses of a human observer. The likelihood is a function of parameter values
What are similarities and differences between the maximum likelihood method and the Best PEST method?
Similarities:
- Both use all the previous responses to calculate a likelihood function
- The stimulus to be used on next trial corresponds to the threshold estimate determined from all previous trials.
Differences:
- Maximum likelihood assumes a parametric form and estimates the entire psychometric function while Best PEST assumes a logistic function and estimates only the threshold parameter of the psychometric function.
Which trial is always the highest/lowest in a Best PEST method, and why?
The second trial, due to the fact that the experimenter has to set the range for the simulus levels.
(so it goes to the extreme on the second trial)
What is QUEST?
How does it work?
And what is an advantage of QUEST compared to PEST?
The bayesian version of the PEST.
Using QUEST, all information is used to determine the next stimulus level by means of Bayesian methods (i.e. new data serve to adjust our pre-existing knowledge or beliefs regarding the value of the threshold parameter).
Before a Quest run: the researcher postulates a prior probability distribution (mean and precision) which reflects his/her belief about the threshold.
The prior has the effect of curbing the excessive stepsizes that were observed in the best PEST run.
Prior: guide to the selection of stimulus intensities, and plays a smaller and smaller role relative to the contribution of the data collected over the trials.
For a sequence of stimuli of a definite length, the QUEST-procedure is more efficient (e.g., 84% as opposed to 40 to 50% for PEST).
