Research Design & Analysis 2: Class 23 Announcement re. Extra class: April 10th BAC 237 Discrete Trials Designs: Psychophysics & Signal Detection Theory – tutorial run: y:percept at menu pick “E. Theory and Methodology” at menu pick “B. Signal Detection Theory” The introduction works, part B usually doesn’t Course evaluations (volunteer?) –also :

psyc 2023 class #23 (c) Peter McLeod 2 Number Numbness … With the US court antitrust ruling against Microsoft, Bill Gates lost $13,000,000,000 yesterday Approximately the GDP of Lebanon Enough to send 6 space stations into orbit Build 20 confederation bridges Sympathy? –He is still worth $72,000,000,000

psyc 2023 class #23 (c) Peter McLeod 3 Characteristics of Discrete Trials Designs 1) individual subjects receive each treatment condition dozens (perhaps hundreds) of times. Each exposure to the treatment, or trial, produces one data point for each DV measured. 2) Extraneous variables are tightly controlled. 3) If feasible, the order of presenting the treatments is randomized or counterbalanced. 4) The behaviour of individual subjects undergoing the same treatment may be compared to provide intersubject replication.

psyc 2023 class #23 (c) Peter McLeod 4 Psychophysics Concerned with the four perceptual problems of: 1.Detection 2.Identification 3.Discrimination 4.Scaling

psyc 2023 class #23 (c) Peter McLeod 5 Psychophysics Absolute thresholds are often used as the index of an individuals sensitivity to a specific stimuli, or differences between stimuli. Gustav Theodor Fechner (1860) defined the absolute threshold as the stimulus that "lifted the sensation or sensory difference over the threshold of consciousness"

psyc 2023 class #23 (c) Peter McLeod 6 The Absolute Threshold The threshold is 6.5

psyc 2023 class #23 (c) Peter McLeod 7 Method of Limits Participant’s Response + “yes” - “no” Signal intensity Trial number & type 11 22 44 66 33 55 Mean descending threshold = ( )/3=8.2 Mean ascending threshold = ( )/3=7.5 Mean absolute threshold = ( )/2=7.8

psyc 2023 class #23 (c) Peter McLeod 8 Staircase Method Participant’s Response  “yes”  “no”         

psyc 2023 class #23 (c) Peter McLeod 9 Why do Thresholds Seem to Vary? Stimuli being presented is not the only one Constant background stimulation for any signal Endogenous noise Noise - any background stimulus other than the one to be detected. Can be visual, chemical, mechanical, thermal, or auditory. Can also be lapses of attention, fatigue, and other psychological changes.

psyc 2023 class #23 (c) Peter McLeod 10 Determining the “Absolute” Threshold: Method of Constant Stimuli Ogive

psyc 2023 class #23 (c) Peter McLeod 11 Psychophysics Basic assumption in doing psychophysics is that any type of behaviour has some strength. In Psychophysics the measure of strength most often used is response probability. p(yes) = #yes responses /(#yes+ #no responses)

psyc 2023 class #23 (c) Peter McLeod 12 Determining the “Absolute” Threshold: Method of Constant Stimuli The 50% threshold is 4 Somewhat arbitrary where we define the “absolute”threshold

psyc 2023 class #23 (c) Peter McLeod 13 Approximate Thresholds Vision: Candle flame from 48km on a dark clear night Audition: Wristwatch from 6m in a quiet room Taste: 1 tsp sugar in 7.5 litres water Olfaction: 1 drop of purfume in a 3 room apartment Touch: a bee’s wing falling on your cheek from 1cm

psyc 2023 class #23 (c) Peter McLeod 14 Signal Detection Theory A mathematical, theoretical system that recognises that individuals are not merely passive receivers of stimuli. Participants are also engaged in the process of deciding whether they are confident enough to say "Yes, I detect that stimuli" when engaged in psychophysics experiments.

psyc 2023 class #23 (c) Peter McLeod 15 Signal Detection Theory Problem: subjects may wish to appear sensitive (or insensitive). Subject bias. To account for decision making component, can introduce “catch trials”

psyc 2023 class #23 (c) Peter McLeod 16 Signal Detection Theory With two possible experimental trials (signal present or absent) and two possible participant responses ("yes" it is present or "no" it isn't there) there are four possible outcomes to each of many trials. Participants' responses on each trial are going to be consequences of both their perceptual sensitivity to the stimuli presented and their decision strategy or bias toward saying some thing is there or not when they are in doubt.

psyc 2023 class #23 (c) Peter McLeod 17 Signal Detection Theory These are called outcome or confusion matrices Relations among these four outcomes depends upon the strength of the stimulus, as well as both the receiver’s sensitivity, and their decision process (or bias)

psyc 2023 class #23 (c) Peter McLeod 18 Manipulating Bias By varying the conditions of the experiment bias can be altered. alter expectations or alter the relative importance of the two types of error. (Payoff matrix)

psyc 2023 class #23 (c) Peter McLeod 19 Outcome Matrix: Signal Present 50% of Trials

psyc 2023 class #23 (c) Peter McLeod 20 Outcome Matrix: Signal Present 90% of Trials

psyc 2023 class #23 (c) Peter McLeod 21 Outcome Matrix: Signal Present 10% of Trials

psyc 2023 class #23 (c) Peter McLeod 22

psyc 2023 class #23 (c) Peter McLeod 23 Note that for all of these, the signal strength and receiver’s sensitivity are constant!

psyc 2023 class #23 (c) Peter McLeod 24 Isosensitivity (ROC)Curve If guessing Bias to say “no” conservative Bias to say “yes” liberal d’ The curve is generated by the subject’s changing response pattern (bias) not changing sensitivity to the stimulus.

psyc 2023 class #23 (c) Peter McLeod 25 Isosensitivity Curve If guessing d’ Two participants with different sensitivities or one receiver and two signals of different strengths Zero sensitivity Weak sensitivity Good sensitivity

psyc 2023 class #23 (c) Peter McLeod 26 Calculating d' From a Single Outcome matrix Data required for each point on an isosensitivity (ROC) curve requires hundreds of trials (to get accurate probabilities for Hits and False Alarms). With a few assumptions, d' can be calculated from a single outcome matrix using Signal Detection Theory.

psyc 2023 class #23 (c) Peter McLeod 27 Signal Detection Theory Assumptions 1) Noise is normally distributed. Presenting a signal on top of that noise, will therefore shift the amount of sensory activity to the right (higher), by an amount equal to that sensory systems sensitivity to that signal. The difference between the mean amount of sensory activity generated by the noise alone trials and the signal+noise trials will equal sensitivity (d') measured in z-score (standard deviation) units.

psyc 2023 class #23 (c) Peter McLeod 28 Signal present trials Signal absent trials Mean of noise alone distribution Mean of signal plus noise distribution d’

psyc 2023 class #23 (c) Peter McLeod 29 Signal present trials Signal absent trials Stronger Signal (or More Sensitive Receiver) d’

psyc 2023 class #23 (c) Peter McLeod 30 Signal Detection Theory Assumptions 2) Participants adopt a criterion () for dealing with those values of sensory activity that could result from either noise alone or signal plus noise (the area where the noise and signal+noise distributions overlap). If the amount of sensory activity exceeds that amount, the participant will say the detected the signal, any amount less than that and they will say they did not detect the signal.

psyc 2023 class #23 (c) Peter McLeod 31 Signal present trials Signal absent trials Criterion  Say “YES” Say “NO” Range of sensory activity that could arise from either noise or the signal

psyc 2023 class #23 (c) Peter McLeod 32 Manipulation of Bias We can now interpret the manipulation of a receiver’s motivation to say “yes” when in doubt (due to either changing expectations of payoffs) as effecting the placement of the criteria

psyc 2023 class #23 (c) Peter McLeod 33 Signal present trials Signal absent trials Lax or Liberal Criterion  Say “YES” Say “NO”

psyc 2023 class #23 (c) Peter McLeod 34 Signal present trials Signal absent trials Strict or Conservative Criterion  Say “YES” Say “NO”

psyc 2023 class #23 (c) Peter McLeod 35 Sensitivity Criterion location has no effect on sensitivity Sensitivity refers to the average amount of sensory activity generated by a signal compared with the average amount of noise generated sensory activity

psyc 2023 class #23 (c) Peter McLeod 36 Signal Detection Theory With two assumptions: 1) Noise is normally distributed, 2) Participants adopt a criterion () for dealing with those values of sensory activity that could result from either noise alone or signal plus noise, The four cells of an outcome matrix (Hits, Misses, False Alarms & Correct Negatives) can be represented as areas under the two normal distributions.

psyc 2023 class #23 (c) Peter McLeod 37 Signal present trials Signal absent trials Criterion  Say “YES” Say “NO” Hits

psyc 2023 class #23 (c) Peter McLeod 38 Signal present trials Signal absent trials Criterion  Say “YES” Say “NO” Misses

psyc 2023 class #23 (c) Peter McLeod 39 Signal present trials Signal absent trials Criterion  Say “YES” Say “NO” False Alarms

psyc 2023 class #23 (c) Peter McLeod 40 Signal present trials Signal absent trials Criterion  Say “YES” Say “NO” Correct Negatives

psyc 2023 class #23 (c) Peter McLeod 41 Signal Detection Theory d’ can then be measured in z-sore units by: d' = Z FA - Z Hit Tables for the z-score distribution or percent area under the normal curve typically present the z-score distances between the mean and the Criterion value (). If you are using such a table, Z FA can be found by looking up the z-score associated with (50 - False Alarm %).