Introduction to psychophysics Steven Dakin UCL Institute of Ophthalmology [email protected]• To understand the brain, one must understand not only its components (e.g. physiology) and their purpose (e.g. via models) but also behaviour (e.g. psychophysics) • Psychophysics characterises the relationship between physical (e.g. visual) stimuli & behaviour (e.g. of humans). Reveals mechanism (e.g. trichromacy), links to other disciplines (e.g. via stats), clinical applications (e.g. diagnosis), etc. • Psychophysical experiments involve • A stimulus/phenomenon (e.g. illusions) • A task (e.g. matching) • A method (e.g. adjustment) • A performance-measure (e.g. threshold,PSE) Psychophysics/ methodology Hard Introduction Tasks, sampling methods and measures • Tasks (what does the subject do?) • Magnitude estimation (“how bright is it?”) • Detection (“is it there?”); yes/no requires criterion • Discrimination (“which is brighter”); forced choice is criterion-free Steven’s Power Law Weber-Fechner Law Tasks, sampling methods and measures • Sampling methods (how to select stimulus magnitude?) • Adjustment (under observer-control) • Method of constant stimuli (predefined set of stimulus magnitudes) • Method of limits (staircase; select stimulus based on previous responses)
• To understand the brain, one must understand not only its components (e.g. physiology) and their purpose (e.g. via models)
but also behaviour (e.g. psychophysics)
• Psychophysics characterises the relationship between physical (e.g. visual) stimuli & behaviour (e.g. of humans). Reveals mechanism (e.g. trichromacy), links to other disciplines (e.g. via
stats), clinical applications (e.g. diagnosis), etc.
• Psychophysical experiments involve• A stimulus/phenomenon (e.g. illusions)• A task (e.g. matching) • A method (e.g. adjustment)• A performance-measure (e.g. threshold,PSE)
Psychophysics/ methodology
Hard
Introduction
Tasks, sampling methods and measures
• Tasks (what does the subject do?)
• Magnitude estimation (“how bright is it?”)
• Detection (“is it there?”); yes/no requires criterion
• Discrimination (“which is brighter”); forced choice is criterion-free
Steven’s Power Law
Weber-Fechner Law
Tasks, sampling methods and measures
• Sampling methods (how to select stimulus magnitude?)
• Adjustment (under observer-control)
• Method of constant stimuli (predefined set of stimulus magnitudes)
• Method of limits (staircase; select stimulus based on previous responses)
Tasks, sampling methods and measures
• Measures: (how to characterise behaviour?)
• Reaction times (how long to judge?). Atheoretical, but popular (e.g. IAT)
• Percent correct (what level of performance at a fixed stimulus magnitude?): e.g. observers memorise 10 objects & are presented with a new set containing 5 they saw and 5 they hadn’t. Observer #1 recognises them all, observer #2 none; both score 50% correct...
• Point of subjective equality (stimulus mag. producing a perceptual match?)
• Thresholds (minimum stimulus mag. producing some level of performance?). Absolute and relative...
• Two key psychophysical measures• Point of Subjective Equality (PSE) or bias measures appearance (accuracy)• Threshold (here, increment threshold) measures limits* of performance (precision)(*generally interested in best possible performance)
(Accuracy versus precision: an accurate but imprecise clock, on average yields the right time, but individual readings vary wildly. An inaccurate but precise clock is e.g. reliably an hour slow)
0.83
Prop
ortio
n “2
is h
ighe
r”
threshold
#1
#2
BetterWorse
Psychometric functions for detection and discrimination
Slope∝1/threshold
Shift=bias orappearance
• Experiment in which two or more alternatives are present (e.g. “which side is patch on?”, “which is bigger?”)• Some difference in convention as to whether both alternatives must be present e.g. tilt. i.e. is it the stimulus or the response?• If it’s response; detection is forced choice (actually 2AFC)
“Forced-choice” vs “Non-forced choice”
“Criterion-free” vs “Criterion-dependent”• Yes/no means observer judges how strong stimulus must be to respond (“trigger happy”), forced choice does not• Different criteria bias subjects in detection. (Bias still arises in discrimination but is less problematic since less meaningful “trade-off ”...)
• Type 1 tasks have a correct answer, Type II tasks do not. i.e. can we provide feedback?
Type 1 and Type II tasks
0.0
1.0
0.5
Prop
. “1
brig
hter
”
Point of subjectiveequality (PSE)
• Subtle: this experiment is about appearance (e.g. PSE, no feedback)• Appearance: “apparent magnitude”, performance: can be “better”• Above experiment measures both (slope/threshold & PSE/offset)...
• How do we assess performance?• Decisions limited by: information & criterion
Signal detection theory (SDT; Green & Swets, 1966)
• ↑information ⇒ high H, low FA (↑sensitivity)
ResponseResponse
“Yes” “No” Total
Present
Absent
Hit, H (0.84) Miss (0.16) 1.0
False alarm, FA (0.50)
Correctreject (0.50)
1.0Stim
ulus
ResponseResponse
“Yes” “No” Total
Present
Absent
Hit, H (0.5) Miss (0.5) 1.0
False alarm, FA (0.16)
Correctreject (0.84)
1.0Stim
ulus
• Doctors weigh errors differently• e.g. One considers missed diagnoses fatal, another minimises unnecessary procedures• Not information but bias/criterion that sets performance
• Uncertainty on such tasks arises from two types of noise
Noise
Increasing external noise →
• External noise: measurements, variation in lung tissue• Assume doctor uses neural responses to detect tumour, those responses are variable. This internal noise contributes to an internal response
Internal-response probability of occurrence curves for noise alone & signal+noise trials
Could be firing rate →noise
• Base response on some minimum/criterion response
Criterion
• Effects of criterion shift
Internal-response probability of occurrence curves for noise alone & signal+noise trials
d’=1.0d’=1.0 d’=1.0
H=98%, FA=84% H=84%, FA=50% H=50%, FA=16%
• Doctors cannot set their criterion to achieve only hits and no false alarms; noise ⇒ overlap in prob. of occurrence curves ⇒ internal response
on noise-alone must sometimes exceed signal+noise response
Hit
rate
(H)
False alarm rate (F)
0.00.0
d’=0.5d’=1
d’=2
0.5 1.0
0.5
1.0
d’=z(H)-z(F)
Bias
“No”
Betterdiscrim.
d’=0random
“Yes”
• Receiver operating curves (ROCs) plot a series of H/FA measurements; show choices made by doctor
Receiver operating curves & d’
• ↑ information (e.g. ↑signal) ⇒ better separation
• Reducing noise improves performance too• Good measure of information content of internal representation is: d’=separation/spread • ROC curves: practical & theoretical use
False alarm rate (FA)
Low med. high
criteria
d’=1.0,lots of overlap
d’=2.0less overlap
Note upward bowing curves (typically H>FA)
Psychometric functions & SDT
• d’=z(H)-z(FA) where z() is the inverse of the cumulative Gaussian distribution• Consider 2AFC orientation discrimination
• Means that essentially thresholds measure σ, your uncertainty about a stimulus • Weber’s law (thresholds rise as a proportion of magnitude); SDT tells us variability rises• Neurons exhibit multiplicative noise; the more active, the more variable
0.0
0.5
Cumulative Gaussianfunction
1.0
0.0 3.0-3.0
σProb“CW”
Prob“CW”
Prob“CW”
• Psychophysics maps physical world to behaviour (and perceptual representation)• Tasks, methods & measures...• Psychometric functions, thresholds & PSE• Type of experiment (Type 1/2, criterion, forced-choice?)
• Signal detection theory (d’) and notion of response variability
