Diapositiva 1

1
Confidence grows with uncertainty in visual
search
by Stefano Baldassi, David Burr Nicola
Megna Dept. of Psychology University of Florence
2
Visual search and the Signed-Max rule
If this is true, then the observers performance
can be predicted by the distribution of maxima
over trials produced at different set sizes.
3
Distributions of maxima over trials
d1
Errors Correct Answers
Here we propose a novel technique to test this
effect
4
Stimuli
The search display contains 1 target, in a random
position, and n-1 distractors (0 to 15).
Elements are shown for 100 msec at 5º
eccentricity For all set sizes, we used 6 angles
for each direction of tilt, ranging from 0.5º to
16º. The direction of tilt was randomly set
trial-to-trial. Then a response page appeared
5
Task the Response page
The Response Page contained the whole set of 12
possible targets. The mouse cursor appeared at
the center and subjects were asked to report the
stimulus that best matched the target One single
click allowed recording of both the direction of
tilt (CW vs CCW) and the perceived magnitude
(-16º to 16º). NB every subject measured 1000
trials per set size
6
Predictions

• Analyzing the direction of tilt data should
  confirm previous work showing set size function
  with log-log slopes around 0.5 and psychometric
  functions steeper with set size.
• Analyzing the perceived magnitude responses
  should allow to sketch high-resolution plots of
  the response distributions for different set
  sizes more specifically,
• the function relating proportion of responses to
  the perceived magnitude should follow the
  distributions of maxima for any given set size

7
Direction of tilt data
Thresholds vs Set Size functions
10
Threshold
Slope 0.6
1
NM
1
10
Set size
8
Perceived magnitude data ranges
1.00
Above threshold (high d)
0.90
0.80
Around threshold (mid d)
Pc
Threshold (d1)
0.70
Below threshold(low d)
0.60
0.50
Angle
9
Perceived magnitude Set Size 1 - mid d
0.50
CB
NF
0.40
0.30
0.20
0.10
0.00
P(responses)
-10
-5
0
5
10
-10
-5
0
5
10
0.50
NM
SB
0.40
0.30
0.20
0.10
0.00
Errors Correct Answers
-10
-5
0
5
10
-10
-5
0
5
10
Perceived Magnitude
10
Perceived magnitude Set Size 16 - mid d
0.50
CB
NF
0.40
0.30
0.20
0.10
0.00
P(responses)
0.50
NM
SB
0.40
0.30
0.20
0.10
0.00
-20
-15
-10
-5
0
5
10
15
20
-20
-15
-10
-5
0
5
10
15
20
Perceived Magnitude
11
Perceived magnitude all set sizes mid d
Set size 1
CB
0.40
0.30
Set size 2
P(Responses)
0.20
0.10
Set size 4
0.00
Set size 8
-20
-15
-10
-5
0
5
10
15
20
Perceived Magnitude
Set size 16
-20
-15
-10
-5
0
5
10
15
20
Perceived Magnitude
-20
-15
-10
-5
0
5
10
15
20
Perceived Magnitude
-20
-15
-10
-5
0
5
10
15
20
Perceived Magnitude
20
-20
-15
-10
-5
0
5
10
15
Perceived Magnitude
12
Response distributions 2D maps
Noiseless (perfect) performance
-16
Confidence
Perceived magnitude
0
Correct responses
Errors
16
0
16
-16
Physical Angle
13
Response distributions 2D maps
Set Size 1
Set Size 2
Set Size 4
Set Size 8
Set Size 16
NF
CB
Perceived magnitude
NM
Physical angles
14
Response distributions error maps
Set Size 1
Set Size 2
Set Size 4
Set Size 8
Set Size 16
NF
CB
Perceived magnitude
NM
Physical angles
15
Response distributions data vs model
Set Size 1
Set Size 2
Set Size 4
Set Size 8
Set Size 16
NM
Physical angles
Perceived magnitude
MonteCarlo simulation On each trial is chosen
the probe that best matches the max output
16
Summary and conclusions
By using a novel technique that expands the basic
signed 2afc task, we have measured the response
distributions of an orientation search
task. This allowed us to verify a simple
prediction of the Signed-Max model of visual
search that high-confidence responses are more
likely under conditions of high uncertainty.
17
Summary and conclusions

• In particular we have found that
• the task does not affect the standard
  psychometric measures, as thresholds and
  psychometric functions confirmed previous
  results
• the response distributions at set size 1 are
  gaussian-like and unimodal
• the response distributions at set sizes gt 1
  become bimodal, with two lobes that are
  progressively more sharp and distant with set
  size, implying increased confidence
• So

18
Summary and conclusions
the novel technique we devised allowed us to
show data in favor of the apparent paradox that
uncertainty increases confidence, at least in
visual search.