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Advanced Research Methods PSYC325 Signal Detection Theory with special thanks to Dr. Murray White. Dr. Jan Lauwereyns EA619, ext. 5042 Jan.Lauwereyns@vuw.ac.nz. Lecture notes, available on website http://pavlov.psyc.vuw.ac.nz/325 Brief concepts - PowerPoint PPT Presentation
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Advanced Research MethodsPSYC325
Signal Detection Theory
with special thanks to Dr. Murray White
Dr. Jan Lauwereyns
EA619, ext. 5042
Jan.Lauwereyns@vuw.ac.nz
• Lecture notes, available on website
http://pavlov.psyc.vuw.ac.nz/325
• Brief concepts
Green, D. M., & Swets, J. A. (1966). Signal Detection Theory and Psychophysics. New York: John Wiley.
HitMiss
Correct Rejection
False Alarm
Response
No Yes
Present
Absent
The 2 X 2 Stimulus-Response MatrixStimulus – Response Matrix
Response
Sti
mu
lus
928
42 58
You said
No Yes
Present
Absent
100
100
1st session
4258
92 8
You said
No Yes
Present
Absent
100
100
2nd session
Stim
ulu
sS
timu
lus
Response
Response
Stimulus Detection: The Dice Game Analogy
6
3?0?
6 3?
0?
Special die:three or naught
Certainty
+ + =
Certainty
+ + =
3
14
Uncertainty
+ + = 8
+ + = 8
?
?
If the total is 3…
If the total is 14…
If the total is 8…
The specialdie has to be0
The specialdie has to be3
The specialdie can beeither 0 or 3
+ + = 6
+ + = 6
+ + = 6
+ + = 6
+ + = 6
+ + = 6
+ + = 6
Sp
ecia
l die
= 0
Sp
ecia
l die
= 3
If the total is 6…
Total score from the three dice
3 4 5 6 7 8 9 10 11 12 13 14 152
2 3 4 5 6 5 4 3 2 1 0 0 01
0 0 1 2 3 4 5 6 5 4 3 2 10
0
3
3 4 5 6 7 8 9 10 11 12 13 14 152
Total score from the three dice
1/36
2/36
3/36
4/36
5/36
6/36
Possible outcomes of each throw
HitMiss
Correct Rejection
False Alarm
you say
0 3
3
0
Possible outcomes of each throw
You say…
Th
e sp
ecia
l die
is…
3 97
28 72
100
100 6
8 92
42 58 7
17 83
58 42
28 72
72 28
42 58
83 17
58 42
92 8
8
9
10
11
Say “3” when the total is
Outcome from 200 throws
>
>
>
>
>
>
.028
3 4 5 6 7 8 9 10 11 12 13 14 152
Total score from the three dice
8 92
42 58
100
100
You said
0 3
0
3
False Alarms
Hits
.056
.083
.111
.139
.167
Criterion
(Note: .028 = 1/36, etc.)
.028
3 4 5 6 7 8 9 10 11 12 13 14 152
Total score from the three dice
42 58
83 17
100
100
You said
0 3
0
3
False Alarms Hits
.056
.083
.111
.139
.167
Criterion
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1
Probability of a False Alarm
710
> 7
> 10
What rule might you adopt if you were asked not to miss too many “3s”?
Suppose you adopted the rule to say 3 when the total was 10
Suppose you adopted the rule to say 3 when the total was 7
You said
0 3
0
3 42 58
83 17
You said
0 3
0
3 8 92
42 58
6 4
> 10 > 7
-$580
+$460
-$170
+$290
-$10
What rule might you adopt if you were given $5 for each Hit and penalised $10 for each False Alarm? The payoff matrix would look like this:
You said
0 3
0
3 +$5
Suppose you adopted the rule to say 3 when the total was 10
Suppose you adopted the rule to say 3 when the total was 7
64
> 10 > 7
+$120 -$120
Now let’s use a different die:
A special die withthree faces ‘6’and three faces ‘0’
instead ofthree faces ‘3’and three faces ‘0’
.028
.056
.083
.111
.139
.167
Total score from the three dice
3 4 5 6 7 8 9 10 11 12 13 14 152
2 3 4 5 6 5 4 3 2 1 0 0 01
0 0 1 2 3 4 5 6 5 4 3 2 10
0
6
Total score from the three dice
16 17 18
0 0 0
0 0 0
3 4 5 6 7 8 9 10 11 12 13 14 152 16 17 18
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1
Probability of a False Alarm
When the special die has 6 on three faces and 0 on three.
compared with when special die had 3 on three faces
Level of activation
low highmoderate
Signal absent
Signal present
d´= 1.0
Compare with when dice values are 3 and 0
There is a 3
There is no 3
Total of the three dice
Special die with 3’s and O’s
Level of activation
low highmoderate
d´= 2.0
Compare with when dice values are 6 and 0
There is a 6There is no 6
Total of the three dice
Special die with 6’s and O’s
Criterion
risky
ß
False Alarms
Criterion
No Yes
Left liberal
Criterion
risky cautious
ß
False Alarms
CriterionNo Yes
Right conservative
beta versus d’
• Effects of – signal-to-noise ratio (d’) – decision criteria (beta)
• Effects of – perceptual sensitivity – response bias
Effects of Scene Context
on Object Perception
Biederman& co.
Context facilitatesthe perception of congruent objects
De Graef,Henderson,
Hollingworth
There is only a response bias
Effects of Reward Expectation
on Neural Mechanisms of Visual Discrimination
Lauwereyns et al. (2002, Neuron): “wishful seeing”
Reward leads to general increase of neural activity = bias effect; no change in d’
Summary
• Signal detection theory allows you to…
– Consider choice situations systematically– Tease apart underlying processes
• Sensitivity– d’ (“d prime”)– Signal to noise ratio– Information characteristics
• Bias– beta (criterion)– Likelihood of response– Demand characteristics
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