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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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) = 0.542 - (-0.842) = 1.366 After drinking alcohol: d’ = z(hit rate) - z(false alarm rate) = 0.842 - (-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

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

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

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