1. Jonas Larsson Department of Psychology RHUL
PS3012: Advanced Research Methods Lecture 9: Psychophysics, psychophysical methods, and signal detection theory
Jonas Larsson
Department of Psychology
RHUL
Term 2: Lecture 9
PS3012: Advanced Research Methods

2. PS3012: Advanced Research Methods
Today’s lecture
Introduction to psychophysics
Thresholds and psychometric functions
Psychophysical methods
Signal detection theory
Term 2: Lecture 9
PS3012: Advanced Research Methods

3. PS3012: Advanced Research Methods
What is psychophysics?
The study of the relationship between physical stimuli and their subjective correlates, or percepts [Wikipedia]
The scientific study of the relation between stimulus and sensation [Gescheider, 1976]
Central idea: measurements of behavioural parameters (accuracy, reaction time, sensory thresholds) can be used to infer mental state (percept) of subjects
Term 2: Lecture 9
PS3012: Advanced Research Methods

4. What can psychophysics be used for?
Sensory system neurophysiology/neuropsychology
Sensory limits of vision, hearing, touch…
Interspecies comparison (e.g., monkeys vs humans)
Inferring neuronal mechanisms (e.g. illusions, after-effects)
Experimental psychology
Visuomotor interactions
Perception of speed, motion
Attention
Quantitative measurement of perceptual states
Diagnostic tool (e.g., vision tests)
Assessment tool (e.g., therapeutic effectiveness)
Term 2: Lecture 9
PS3012: Advanced Research Methods

5. Example: treatment of anorexia
Distorted self-image in anorexia: subjects perceive themselves as disproportionally overweight
Suppose you want to test effectiveness of therapy to improve self-image (reduce distortion). How can its effectiveness be quantified?
Use psychophysical methods to identify “ideal body proportions” (using manipulated photos of subjects with different shape/weight) as a threshold: perceptual boundary between too fat / too thin)
Measure ideal proportions before & after therapy
Test difference (if any) statistically for effectiveness of therapy
Term 2: Lecture 9
PS3012: Advanced Research Methods

6. Example: treatment of anorexia
Show photos of subjects manipulated (Photoshop) to show different body size (BMI)
Subjects have to rate photos as “too thin” or “too fat”; measure % judged “too fat”
Fit psychometric function to data
Note shape (logistic)
Perceptual boundary (threshold): BMI where 50% of photos judged “too fat”
100
Before therapy
After therapy
(% images judged too fat)
Perceived shape
50 %
threshold 50
Body mass index (BMI)
Term 2: Lecture 9
PS3012: Advanced Research Methods

7. The power of psychophysics
Quantitative - objective scale of measurement
Does not suffer from subjectivity of introspection
Can be used to study “pure” mental phenomena - e.g. attention
Valid inter-subject, inter-species, and inter-method comparisons
E.g. colour perception in humans and bees
Sensitivity of neurons vs sensitivity of brains (humans)
Can be used to study subliminal percepts (e.g. above-chance recognition without awareness)
Can identify (possibly subconscious) response bias
Term 2: Lecture 9
PS3012: Advanced Research Methods

8. The concept of thresholds
Detection threshold (classical definition): smallest detectable stimulus intensity (energy) (that yields a sensory percept)
Threshold for sight (weakest detectable light): about 10 photons!
Threshold for sound (weakest detectable air vibration): about the diameter of an atom!
Discrimination threshold : smallest detectable difference between two stimuli (that yields a perceptual difference)
Smallest detectable difference in orientation of two lines
Smallest difference in colour corresponding to a colour category change
Thresholds correspond to a perceptual boundary
Thresholds can be measured quantitatively
Term 2: Lecture 9
PS3012: Advanced Research Methods

9. Thresholds & psychometric functions
Ideal psychometric function:
Step function (fixed threshold)
Psychometric function: plot of proportion of stimuli detected or discriminated vs stimulus intensity
Ideal psychometric function: always 100% above threshold, always 0% below threshold - a step function
Why is the real psychometric function not a step function?
Because of NOISE
100
Real psychometric function:
S-shaped (sigmoid or logistic) function
Proportion stimuli detected (%) 50
50%
threshold
Stimulus intensity
Term 2: Lecture 9
PS3012: Advanced Research Methods

10. Psychophysical methods
Method of limits
Method of adjustment
Method of constant stimuli
Adaptive methods
Staircases
Adaptive versions of constant stimuli
Term 2: Lecture 9
PS3012: Advanced Research Methods

11. PS3012: Advanced Research Methods
Method of limits
Stimulus intensity (for discrimination tasks, the difference between two stimuli) is changed from trial to trial by a fixed amount either upwards from very weak intensity (ascending series) or downwards (descending series)
Subjects report the stimulus intensity when they can no longer detect or discriminate the stimuli (descending series) or when they begin to be able to detect/discriminate stimuli (ascending series)
These stimulus intensities are averaged to give a threshold estimate
Ascending & descending series are done in alternation
Term 2: Lecture 9
PS3012: Advanced Research Methods

12. Stimulus no longer detected Threshold: average stimulus intensity
Method of limits
Stimulus detected
Stimulus no longer detected
Threshold: average stimulus intensity
Stimulus intensity
descending series
ascending series
Term 2: Lecture 9
PS3012: Advanced Research Methods

13. PS3012: Advanced Research Methods
Method of adjustment
Subjects adjust stimulus intensity (or difference between two stimuli) until they can just about detect or discriminate the stimulus
This stimulus intensity (or difference) is the threshold
Usually done in ascending and descending series like method of limits (but under subjects’ control)
Term 2: Lecture 9
PS3012: Advanced Research Methods

14. Method of constant stimuli
Stimuli with a fixed range of intensity levels (or fixed range of differences for discrimination tasks) are presented in random order
Subjects report stimulus absent/present (or for discrimination tasks, same/different or weaker/stronger than reference stimulus)
Subjects’ reports are plotted against stimulus intensity / difference magnitude to give a psychometric function
Usually a psychometric function is then fit (by nonlinear function fitting or logistic regression) to psychometric data
Threshold is midway between chance level performance (bottom of psychometric function, e.g. 50% for a 2AFC task) and 100% detection / discrimination
Term 2: Lecture 9
PS3012: Advanced Research Methods

15. Method of constant stimuli
Stimulus detected
Stimulus intensity
Stimulus not detected
Term 2: Lecture 9
PS3012: Advanced Research Methods

16. Method of constant stimuli
For each level of stimulus intensity, calculate and plot proportion of stimuli detected/discriminated
Fit psychometric (sigmoid) function to data
Threshold is stimulus intensity at inflection point (middle of curve)
Corresponds to halfway between 100% performance and chance level performance (guessing)
100
Proportion stimuli detected (%) 50
50%
threshold
Stimulus intensity
Term 2: Lecture 9
PS3012: Advanced Research Methods

17. Adaptive methods: staircases
Similar to method of limits, but series reverse direction whenever decision changes (e.g. for a descending series, when subject can no longer detect stimulus, series ascends instead)
More effective at “homing in” on threshold
Threshold is average of reversal stimulus intensity
More complex reversal rules are often used (“1-up, 2-down”) with different methods for computing thresholds
To avoid subject prediction, often uses several interleaved staircases (series) randomly interspersed
Term 2: Lecture 9
PS3012: Advanced Research Methods

18. Adaptive methods: adjusting constant stimuli
Similar to constant stimuli, but range of stimulus intensity levels to use are changed over course of experiment (not fixed)
Allows more time to be spent measuring responses near threshold (like staircases)
Unlike staircase methods, good for fitting psychometric functions (samples responses over entire psychometric function curve)
Various methods exist (Best PEST, QUEST etc)
Term 2: Lecture 9
PS3012: Advanced Research Methods

19. The effect of noise on psychometric functions
Detection or discrimination of stimulus is always subject to noise:
Neural
Stimulus (physical)
Attention
(Response)
On any trial, noise will randomly increase or decrease perceived signal intensity
Subject perceives signal+ noise (cannot tell the difference)
Changes step function to sigmoid (logistic) function
100
Above threshold: random noise will weaken signal for some trials, making detection <100%
Proportion stimuli detected (%) 50
Below threshold: random noise will strengthen signal for some trials, making detection > 0%
Stimulus intensity
Term 2: Lecture 9
PS3012: Advanced Research Methods

20. Detecting stimuli in noise: Signal Detection Theory (SDT)
How stimuli are detected/discriminated against background noise
How to make decisions in the presence of uncertainty
How to make optimal decisions from ambiguous data
How to make good decisions from bad information
SDT explains why shape of psychometric function varies with noise
SDT explains how a subject’s criterion (response bias) affects decisions and how to measure it
SDT allows measurement of sensitivity (ability to make correct responses/decisions) regardless of criterion/bias
Term 2: Lecture 9
PS3012: Advanced Research Methods

21. Origin of SDT: WW2 radar operator
Task: warn of incoming aircraft
Are the blobs enemy aircraft? Or just noise (e.g. clouds)?
Decision depends on subjective criterion: how big must the blobs be to be aircraft
Decision has consequences:
If you miss an aircraft, people might get killed
If you mistake noise for aircraft, fuel, manpower & resources are wasted
Radar screen
Term 2: Lecture 9
PS3012: Advanced Research Methods

22. Decision outcomes & consequences
SIGNAL: are the blobs real enemy aircraft?
yes no
Hit
False alarm
Miss
Correct reject
yes
DECISION:
should you alert the air force? no
Term 2: Lecture 9
PS3012: Advanced Research Methods

23. Decision depends on criterion
Low criterion: alert for every blob: make sure you never miss - but many false alarms
High criterion: only alert for really big blobs: no false alarms - but many misses
Which criterion is “best” (optimal)?
Depends on the costs of making errors...
which errors are acceptable...
but also on how good your information is (uncertainty)
Term 2: Lecture 9
PS3012: Advanced Research Methods

24. Example 2: mugger or friend?
You’re walking alone on an empty street
Somebody behind you calls out to you: “hey!”
You don’t recognize the voice, and can’t see the person’s face clearly
Is it a friend or a mugger? (how familiar is the person’s appearance?)
Do you run or stay?
Term 2: Lecture 9
PS3012: Advanced Research Methods

25. Decision outcomes & consequences
SIGNAL: is the person a friend or a mugger?
mugger
friend
Lucky escape!
Friend gets upset
You got mugged!
Head to the pub
run
DECISION:
should you
run or stay?
stay
Term 2: Lecture 9
PS3012: Advanced Research Methods

26. Decision outcomes & consequences
SIGNAL: is the person a mugger or friend?
mugger
friend
Hit
False alarm
Miss
Correct reject
run
DECISION:
should you
run or stay?
stay
Term 2: Lecture 9
PS3012: Advanced Research Methods

27. Decision criterion depends on penalties and uncertainty
How would your decision to run or stay change if:
it’s in the middle of the night on campus? (high uncertainty, high penalty for false alarms)
it’s the middle of the day on campus? (low uncertainty, high penalty for false alarms)
it’s in the middle of the night in the South Bronx? (high uncertainty, high penalty for misses)
it’s in the middle of the day in the South Bronx? (low uncertainty, high penalty for misses)
So how do you decide which decision criterion is best (optimal)?
Term 2: Lecture 9
PS3012: Advanced Research Methods

28. Use Signal Detection Theory
criterion
run (mugger)
stay (friend)
probability
mugger
friend
unfamiliar appearance (stimulus intensity)
Term 2: Lecture 9
PS3012: Advanced Research Methods

29. SDT & effect of criterion: radar operator example
yes (aircraft)
no (noise)
probability
aircraft
noise
Blob size (stimulus intensity)
Term 2: Lecture 9
PS3012: Advanced Research Methods

30. SDT & effect of criterion: radar operator example
yes (aircraft)
no (noise)
probability
correct rejects
hits
aircraft
noise
misses
false alarms
Term 2: Lecture 9
PS3012: Advanced Research Methods

31. Low criterion: few misses, many false alarms
yes (aircraft)
no (noise)
probability
correct rejects
hits
aircraft
noise
false alarms
Term 2: Lecture 9
PS3012: Advanced Research Methods

32. High criterion: many misses, few false alarms
yes (aircraft)
no (noise)
probability
correct rejects
hits
aircraft
noise
misses
Term 2: Lecture 9
PS3012: Advanced Research Methods

33. Low noise: high discriminability & sensitivity (few misses & false alarms)
discriminability d’
(distance between means)
Small overlap between distributions of noise and stimulus+noise (aircraft)
probability
noise
aircraft
Blob size (stimulus intensity)
Term 2: Lecture 9
PS3012: Advanced Research Methods

34. High noise: low discriminability & sensitivity (many misses & false alarms)
discriminability d’
Large overlap between distributions of noise and stimulus+noise (aircraft)
probability
noise
aircraft
Blob size (stimulus intensity)
Term 2: Lecture 9
PS3012: Advanced Research Methods

35. PS3012: Advanced Research Methods
SDT & psychophysics
Decision criterion
Response: Yes
Response: No
Discriminability (sensitivity): d-prime (d’) - the distance between the means of (N) and (SN) in units of S.D.
probability d’
Stimulus+Noise
(SN)
Noise (N)
Stimulus intensity
Term 2: Lecture 9
PS3012: Advanced Research Methods

36. Discriminability (d’) is independent of criterion
Decision criterion
Response: Yes
Response: No d’
d’ depends only on the distance between the means of (N) and (SN)
probability
Stimulus+Noise
(SN)
Noise (N)
Stimulus intensity
Term 2: Lecture 9
PS3012: Advanced Research Methods

37. Discriminability (d’) is independent of criterion
Decision criterion
Response: Yes
Response: No d’
d’ depends only on the distance between the means of (N) and (SN)
probability
Stimulus+Noise
(SN)
Noise (N)
Stimulus intensity
Term 2: Lecture 9
PS3012: Advanced Research Methods

38. PS3012: Advanced Research Methods
Estimation of d’
d’ is the difference between the means of the noise (N) and stimulus+noise (SN) distributions, in units of standard deviations of the noise (N) distribution:
d’ = [mSN - mN] / sN
But these distributions are not usually known!
d’ is more easily computed from the hit rate (proportion of stimuli reported when present, [yes|SN] ) and the false alarm rate (proportion of stimuli reported when not present, [yes|N] ):
Convert hit & false alarm rates (which are probabilities) to z scores from tables of z distribution:
Hit rate = P(yes|SN) => z( yes|SN )
False alarm rate = P( yes|N ) => z( yes|N )
d’ = z( yes|SN ) - z( yes|N )
Decision criterion must be fixed!
Term 2: Lecture 9
PS3012: Advanced Research Methods

39. PS3012: Advanced Research Methods
Interpreting d’
Low d’ means stimulus (signal) + noise (SN) distribution is highly overlapping with noise (N) distribution
d’ = 0: chance level performance (N and SN overlap exactly)
High d’ means SN and N distributions are far apart
d’ = 1: moderate performance
d’ = 4.65: “optimal” (corresponds to hit rate=0.99, false alarm rate=0.01)
Term 2: Lecture 9
PS3012: Advanced Research Methods

40. PS3012: Advanced Research Methods
Example
Performance on visual detection task before drinking alcohol:
Hit rate 0.7, false alarm rate 0.2
Performance of task after drinking alcohol:
Hit rate 0.8, false alarm rate 0.3
Did performance or sensitivity (discriminability) improve?
Before drinking alcohol:
d’ = z(hit rate) - z(false alarm rate) = (-0.842) = 1.366
After drinking alcohol:
d’ = z(hit rate) - z(false alarm rate) = (-0.542) = 1.366
Alcohol did not improve performance (d’)
Alcohol did change criterion (by lowering it)
Term 2: Lecture 9
PS3012: Advanced Research Methods

41. Controlling decision criterion
Criterion influenced by stimulus probability and decision consequences (payoffs - rewards & penalties)
Need to know chance level performance (performance when no stimulus present)
Present noise stimuli on some constant proportion of trials - this proportion is then equal to chance level performance
Use fixed payoff (e.g. reward for hits, penalties for false alarms)
Best: use forced choice methods:
Most common: use two-alternative forced choice (2AFC); present two stimuli on each trial (one with stimulus, one with just noise) and force subject to decide which one contained the stimulus - chance level performance is then 50%
Performance often above chance even when subject is guessing
Term 2: Lecture 9
PS3012: Advanced Research Methods

42. PS3012: Advanced Research Methods
Summary of SDT
Decisions (perceptual judgments) are always made in the presence of noise (internal/neural and external/physical)
Decisions are made with respect to a criterion (response bias)
Criterion is variable & reflects probability of stimulus and payoffs/ consequences of decision
Performance (hit rate) is a biased measure - depends on criterion
There is a trade-off between hit rate and false alarm rate
Sensitivity/discriminability - the ability to discriminate a stimulus from noise - is independent of the criterion
d’ is a measure of discriminability that is insensitive to criterion
d’ can be computed from the hit rate (proportion of stimuli detected when present) and the false alarm rate (proportion of stimuli reported when not present)
Term 2: Lecture 9
PS3012: Advanced Research Methods

43. PS3012: Advanced Research Methods
And finally…
Reading: see course web page
Ehrenstein & Ehrenstein: Psychophysical Methods
Next week: last lecture (DW)
Term 2: Lecture 9
PS3012: Advanced Research Methods