research design & analysis 2: class 23 announcement re. extra class: april 10th 10-12 bac 237...

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

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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


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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.


4

Psychophysics

Concerned with the four perceptual problems of:

1.Detection2.Identification3.Discrimination4.Scaling


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"


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


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


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”


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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.


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Determining the “Absolute” Threshold:Method of Constant Stimuli

Ogive


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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)


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Determining the “Absolute” Threshold:Method of Constant Stimuli

The 50% thresholdis 4

Somewhat arbitrary where we define

the “absolute”threshold


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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


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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.


15


Problem: subjects may wish to appear sensitive (or insensitive). Subject bias.

To account for decision making component, can introduce “catch trials”


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.


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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)


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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)


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Outcome Matrix: Signal Present 50% of Trials

Response

SignalYes No

Present .75 .25Absent .25 .75


20


Response

SignalYes No



21


Response

SignalYes No



22

Response (10% Present)

SignalYes No



SignalYes No



SignalYes No



23


SignalYes No



SignalYes No



SignalYes No


Note that for all of these, the signal strength and receiver’s sensitivity are constant!


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.


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


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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.


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.


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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’


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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’


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.


31


Signal absenttrials

Criterion

Say “YES”Say “NO”

Range of sensory activity that could arise

from either noise or the

signal


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


33


Signal absenttrials

Lax or Liberal Criterion



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Signal absenttrials

Strict or Conservative Criterion



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


36


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.


37


Signal absenttrials

Criterion


Hits


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Signal absenttrials

Criterion


Misses


39


Signal absenttrials

Criterion


FalseAlarms


40


Signal absenttrials

Criterion


CorrectNegatives


41


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 %).

research design & analysis 2: class 23 announcement re. extra class: april 10th 10-12 bac 237...

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