PS3012: Advanced Research Methods Lecture 9: Psychophysics, psychophysical methods, and signal detection theory

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

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

3. What is psychophysics? • The study of the relationship between physical stimuli and their subjective correlates, orpercepts [Wikipedia] • The scientific study of therelation 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 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) 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 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 Perceived shape (% images judged too fat) 50 % threshold 50 0 Body mass index (BMI) 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 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 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 50 Proportion stimuli detected (%) 50% threshold 0 Stimulus intensity 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 PS3012: Advanced Research Methods

11. 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 PS3012: Advanced Research Methods

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

13. 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) 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 PS3012: Advanced Research Methods

15. Method of constant stimuli Stimulus detected Stimulus intensity Stimulus not detected 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 50 Proportion stimuli detected (%) 50% threshold 0 Stimulus intensity 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 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) 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% 50 Proportion stimuli detected (%) Below threshold: random noise will strengthen signal for some trials, making detection > 0% 0 Stimulus intensity 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 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 PS3012: Advanced Research Methods

22. Decision outcomes & consequences SIGNAL: are the blobs real enemy aircraft? yes no yes DECISION: should you alert the air force? no 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) 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? PS3012: Advanced Research Methods

25. Decision outcomes & consequences SIGNAL: is the person a friend or a mugger? mugger friend run DECISION: should you run or stay? stay PS3012: Advanced Research Methods

26. Decision outcomes & consequences SIGNAL: is the person a mugger or friend? mugger friend run DECISION: should you run or stay? stay 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)? PS3012: Advanced Research Methods

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

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

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

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

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

35. Decision criterion Response: No Response: Yes SDT & psychophysics 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 PS3012: Advanced Research Methods

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

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

38. 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! PS3012: Advanced Research Methods

39. 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) PS3012: Advanced Research Methods

40. 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) PS3012: Advanced Research Methods

41. Controlling decision criterion • Criterion influenced by stimulus probability and decisionconsequences (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 PS3012: Advanced Research Methods

42. 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) PS3012: Advanced Research Methods

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