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Research Design & Analysis 2: Class 23
Announcement re. Extra class: • April 10th 10-12 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 : www.courseeval.com
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.Detection2.Identification3.Discrimination4.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
0
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11 12
Stimulus Strength
Pe
rce
nt
Pe
rce
ive
d (
% "
Ye
s")
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
intensity1413121110987654321
---
-- -
-------
+
+++++
+
--+++++
--++
-
-+++++
-
Trial number & type
1 2 4 63 5
Mean descendingthreshold =
(8.5+6.5+9.5)/3=8.2
Mean ascendingthreshold =
(6.5+8.5+7.5)/3=7.5
Mean absolutethreshold =
(8.2+7.5)/2=7.8
psyc 2023 class #23 (c) Peter McLeod
8
Staircase Method
0 1 2 3 4 5 6 7 8 9 10 11 12
Trial Number
Sti
mu
lus
Str
en
gth
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 oneConstant background stimulation for any
signalEndogenous 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
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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% thresholdis 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
Response
SignalYes No
Present Hit MissAbsent False Alarm Correct Negative
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
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Outcome Matrix: Signal Present 50% of Trials
Response
SignalYes No
Present .75 .25Absent .25 .75
psyc 2023 class #23 (c) Peter McLeod
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Outcome Matrix: Signal Present 90% of Trials
Response
SignalYes No
Present .95 .05Absent .63 .37
psyc 2023 class #23 (c) Peter McLeod
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Outcome Matrix: Signal Present 10% of Trials
Response
SignalYes No
Present .35 .65Absent .04 .96
psyc 2023 class #23 (c) Peter McLeod
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Response (10% Present)
SignalYes No
Present .35 .65Absent .04 .96
Response (90% Present)
SignalYes No
Present .95 .05Absent .63 .37
Response (50% Present)
SignalYes No
Present .75 .25Absent .25 .75
psyc 2023 class #23 (c) Peter McLeod
23
Response (10% Present)
SignalYes No
Present .35 .65Absent .04 .96
Response (90% Present)
SignalYes No
Present .95 .05Absent .63 .37
Response (50% Present)
SignalYes No
Present .75 .25Absent .25 .75
Note that for all of these, the signal strength and receiver’s sensitivity are constant!
psyc 2023 class #23 (c) Peter McLeod
24
0
1
0 1P(FA)
P(H
it)
Isosensitivity(ROC)Curve
If guessingBias 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
0
1
0 1P(FA)
P(H
it)
IsosensitivityCurve
If guessing
d’d’
Two participants with different sensitivities
or one receiver and two signals of different strengths
Zero sensitivityWeak sensitivityGood 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 Assumptions1) 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
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Sensory Activity Level
Lik
elih
oo
d o
f O
ccu
ran
ceSignal present
trials
Signal absenttrials
Mean of noise alonedistribution
Mean of signal plusnoise distribution
d’
psyc 2023 class #23 (c) Peter McLeod
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Sensory Activity Level
Lik
elih
oo
d o
f O
cc
ura
nc
e
Signal presenttrials
Signal absenttrials
Stronger Signal (or More Sensitive Receiver)
d’
psyc 2023 class #23 (c) Peter McLeod
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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
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Signal presenttrials
Signal absenttrials
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 presenttrials
Signal absenttrials
Lax or Liberal Criterion
Say “YES”Say “NO”
psyc 2023 class #23 (c) Peter McLeod
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Signal presenttrials
Signal absenttrials
Strict or Conservative Criterion
Say “YES”Say “NO”
psyc 2023 class #23 (c) Peter McLeod
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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
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Signal presenttrials
Signal absenttrials
Criterion
Say “YES”Say “NO”
Hits
psyc 2023 class #23 (c) Peter McLeod
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Signal presenttrials
Signal absenttrials
Criterion
Say “YES”Say “NO”
Misses
psyc 2023 class #23 (c) Peter McLeod
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Signal presenttrials
Signal absenttrials
Criterion
Say “YES”Say “NO”
FalseAlarms
psyc 2023 class #23 (c) Peter McLeod
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Signal presenttrials
Signal absenttrials
Criterion
Say “YES”Say “NO”
CorrectNegatives
psyc 2023 class #23 (c) Peter McLeod
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Signal Detection Theory
d’ can then be measured in z-sore units by:
d' = ZFA - ZHit
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, ZFA can be found by looking up the z-score associated with (50 - False Alarm %).