Lecture 8 Detection and Discrimination Experiments

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Lecture 8Detection and Discrimination
Experiments

• Martin Giese

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What you should learn today

• Perceptual threshold
• Detection and discrimination experiments
• Psychometric function (PMF)
• Classical methods of psychophysics
• Models for thresholds
• Signal Detection Theory and ROC
• Scaling methods

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A Detection Experiment
Indicate when you see the stimulus on the gray
background !
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Detection Experiment Results

• Stimulus seen only beyond certain contrast level
• Different people started to see the stimulus at
  different times
• The same subjects see the same stimulus sometimes
  and sometimes not
• The number of people who see the stimulus
  increases with contrast.

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Detection Experiment Interpretation

• non-trivial relationship physical
  stimulus percept
• Probabilistic relationship
• P(stimulus seen) f(contrast)
• Threshold contrast P0 if contrast
  smaller

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Detection and Discrimination Experiments
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Psychophysics
Gustav Fechner (1860) Elemente der
Psychophysik (Elements of Psychophysics)
Aim New science that investigates relationship
physical stimulus sensation
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Psychophysics

• Psychophysical function
• P(stimulus seen) f(contrast)
• Determined form measurements!

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Possible Measurements

• Detection experimentAbsolute threshold When do
  subjects start to perceive the stimulus ?
• Limits of the perceptual system
• Discrimination experimentDifference threshold
  (just noticeable difference, JND) how sensitive
  are subjects for changes in the stimulus
• Sensitivity to changes

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Psychometric Function (for Detection)
Theshold
Sekuler Blake (1994)
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Psychometric Function Quantification

• 50 threshold S50 S for which P 0.5
• Steepness Steepness of the function at S50
• Curve fitting P(S) F(S, a)

• Free parameters a
• fit a gt a
• solve for S50 and steepness using F(S50, a)
  0.5

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Psychometric Function Quantification
Example functions P(S) F(S, a)
Logistic function Normal
function (Gaussian error function)
Weibull function
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Difference Thresholds (for Discrimination)

• 2 stimuli
• Reference
• Test

• Presentation
• At the same time
• Sequential
• Reference can be omitted(mean as reference)

Reference
Test
Did stimulus change ?
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Difference Thresholds Quantification
Just noticeable difference (JND) minimal
physical change of the stimulus such that change
in sensation is reported (e.g. P75 P25) Point
of subjective equivalence (PSE) physical
strength of the stimulus that is perceived as
equally strong as reference
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Difference Thresholds Quantification
Difference thresholds depend on the reference
value !
Stimulus strength
Snodgrass et al. (1985)
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Webers Law
E.H. Weber (1850) Experiments on lifting
weights
Reference Test
Webers law
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Fechners Law
Fechner (1860) Aim finding psychophysical
function that maps stimulus strength S onto
sensation strength S Assumption
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Fechners Law
Fechners law
S
S
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Psychophysical Functions

• Variation of threshold with parameter
• (family of thresholds)
• Examples
• Contrast threshold dependent on spatial frequency
• Audibility function depends on temporal frequency
  (next lecture)
• ..

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Psychophysical Functions
Sekuler Blake (1994)
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Classical Methods of Psychophysics
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Fechners Classical Methods

• Method of constant stimuli
• fixed stimulus intensities
• presentation in random order
• Ask subject if it perceives the stimulus
• plotting of P(S) for several discrete levels
• Subject does not know order of presentation
• Many trials

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Fechners Classical Methods

• Method of limits
• stimulus intensity increased (or decreased) until
  subjects starts (or ceases) to see the stimulus
• threshold intensity recorded
• Few trials sufficient
• Subject knows direction of intensity change gt
  systematic errors

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Fechners Classical Methods

Error of expectancy tendency to change
response expecting a stimulus change Error of
habituationtendency to persist with previous
response
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Fechners Classical Methods

• Method of Adjustmentsubject adjusts the
  stimulus intensity so that the stimulus is barely
  perceived
• Very fast
• No information about steepness of PMF

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Staircase Method
(Cornsweet, 1962)

Sekuler Blake (1994)

• Much data near threshold
• Subject may infer rule of presentation

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Staircase Method

Interleaved staircases
Sekuler Blake (1994)
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Forced Choice Methods

• Subjective methods no objective criterion if
  subject was right (seen or not seen)
• Objective methods (Bregmann, 1852)
• Alternative forced choice (AFC)
• 2 trial types a) stimulus present
• b) stimulus not present
• choice objectively right or false
• Detection can be verified ! (Ask for the grating
  orientation)

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Forced Choice Methods
For equal probability of all alternatives
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Forced Choice Methods

• Possible response alternatives
• 2 AFC (two alternative forced choice)
• Stimulus present Choice
  enforced!
• Stimulus not present
• 3 RC (three response categories)
• Stimulus present No
  choice
• Stimulus not present enforced!
• No decision

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Forced Choice Methods
Thresholds for 2AFC lt Thresholds for
classical
PMF and 3RC

• Subject is forced to decide
• Often perception far below classical threshold

• Tendency to persist with dont know
• Dependence on subject-specific criterion

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Influence of the Response Criterion
Classical PMF
3RC
Respose strategy risky anxious
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FIVE
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Theories about Thresholds
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Models for Thresholds

• Classical (high threshold) theory

Never detection without stimulus!
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Models for Thresholds

• Signal (Sensory) Detection Theory (SDT)
• No fixed threshold !
• Assumption Stimulus detected in neural noise
• Internal random neural state x
• Response criterion C (adjusted dynamically)

(Green Swets, 1966)
x
Response criterion C
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Signal Detection Theory
Conditional responses and probabilities
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Signal Detection Theory
Interesting theoretical quantities

• Sensitivity
• Bias
• (likelihood ratio)

fs(x)
fn(x)
sn
ms
x
mn
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Models for Thresholds

Subject model of SDT
Judgement yes
Noise
Likelihood Ratio Test
Intrinsic neuralresponse X (random)
Stimulus (deterministic)
Judgement no
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Receiver Operating Characteristics (ROC)
detectability
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Receiver Operating Characteristics (ROC)
What we need Subject says yes for x gtc.
Hits
False alarms
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Receiver Operating Characteristics (ROC)
No dectability
Ideal detection
Area under ROC is a measure for detectability !
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Receiver Operating Characteristics (ROC)
No dectability
Ideal detection
Pfa
Area under ROC is a measure for detectability !
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Scaling Methods
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Magnitude Estimation

• Direct scaling technique (Stevens, 1960)
• Reference stimulus with strength defined as one
• Subject says how many times stronger / weaker the
  test stimulus is
• Similar methods
• Cross-modality matching
• Magnitude production (adjustment)
• Rating scales

x
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Power Laws
Sensation strength varies often with physical
stimulus strength in form of a power law
S k Sn 0 lt n
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Power Laws
n gt 1
n ? 1
n lt 1
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Power Laws
Linear relationhip log S log k n log S
Fit by linear regression (Lecture 21).
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Power Laws
Typical exponents
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Multi-dimensional Scaling
Idea Order data within and N-dimensional space
so that distances are minimally distorted.

• Distance ratings between data points
• Minimization of a measure for deviation between
  distances in N-dimensional space and original
  distances

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Multi-dimensional Scaling
1D example
2D example
Sekuler Blake (1994)
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Literature

• Suggested readings
• Snodgrass, J.G., Levy-Berger, G., Hayden, M.
  (1985). Human Experimental Psychology. Oxford
  University Press, Oxford, UK. Chapter 4.
• Elmes, D.G., Kantowitz, B.H., Roediger III, H.L.
  (1999). Research Methods in Psychology.
  Brooks/Cole Publishing, Pacific Grove. Chapter 8.
• Additional Literature
• Sekuler, R., Blake, R. (1994). Perception.
  McGraw-Hill, New York. Appendix.

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Signal Detection Theory
Example for Gaussian distributions
Random internal neural activation X
Signal present
Noise only
Subject says yes if X gt c (criterion).
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Signal Detection Theory
Signal present
Noise only
with Gaussian error function
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Signal Detection Theory

Using the inverse function F-1 follows
Elimination of c
Linear function in d

• Fit this function by linear regression !
  (Lecture 21)