Independent and parallel visual processing of ensemble statistics: Evidence from dual tasks

Independent and parallel visual processing of ensemble
statistics: Evidence from dual tasks
Vladislav Khvostov
and Igor Utochkin
spoiler
Part #1

An example

Greater or smaller than average?

Ensemble summary statistics
The visual system can compute mean (Alvarez & Oliva, 2009), numerosity (Halberda, Sires, & Feigenson, 2006), variance/range (Dakin & Watt, 1997)
Ensemble statistics can be calculated for low-level features:
color (Gardelle & Summerfield, 2011),
orientation (Parkes, Lund, Angelucci, Solomon, & Morgan, 2001),
size (Ariely, 2001),
and for high-level features:
- emotions, gender, etc. (Sweeny & Whitney, 2014, Haberman & Whitney, 2007, 2009).

Independence

Correlational approach
Prediction
Independence

Parallelism
Non-parallel access
(interference)

Parallelism test
Single task
“Calculate MEAN”
MEAN report
Dual task
Observers should compute only one statistics
“Calculate MEAN and RANGE”
MEAN report
RANGE report
Observers should compute both statistics

Parallelism test
Prediction
Access

Experiment 1
Whether mean and numerosity can be calculated independently and in parallel?
N=23

Procedure
Baseline condition
2 blocks (MEAN or NUMEROSITY)
Both condition
1 block (MEAN+ NUMEROSITY)

Design
MEAN baseline
3 blocks
MEAN
NIMEROSITY
BOTH
6 “variables”
NIMEROSITY baseline
MEAN reported first
NIMEROSITY reported first
NIMEROSITY reported second
MEAN reported second

Data analysis
(1) Correlation between mean errors of 6 variables (across observers)
(2) Trial-by-trial correlation between an error in the mean judgment and an error in the numerosity judgment (separately for each participants)
(3) Comparison of mean errors in baseline and both conditions
Independence
Parallelism

Positive correlation between errors in reporting MEAN in different conditions
Reliable measure of MEAN calculation across conditions

Positive correlation between errors in reporting NUMEROSITY in different conditions
Reliable measure of NUMEROSITY calculation across conditions

No correlation between errors in reporting different statistics
Independence between MEAN and NUMEROSITY calculations

Individual correlations
Only one participant showed significant correlation between raw errors in both condition
Independence between MEAN and NUMEROSITY calculations

Average errors
No difference between mean errors in baseline condition and the first response in both condition
(both for NIMEROSITY and MEAN).

Conclusion
Mean and numerosity are calculated
independently and in parallel

Experiment 2
Whether mean and range can be calculated independently and in parallel?
N=20

Procedure
Baseline condition
2 blocks (MEAN or RANGE)
Both condition
1 block (MEAN+ RANGE)

Design
MEAN baseline
3 blocks
MEAN
RANGE
BOTH
6 “variables”
RANGE baseline
MEAN reported first
RANGE reported first
RANGE reported second
MEAN reported second

Positive correlation between errors in reporting MEAN in different conditions
Reliable measure of MEAN calculation across conditions

Positive correlation between errors in reporting RANGE in different conditions
Reliable measure of RANGE calculation across conditions

No correlation between errors in reporting different statistics
Independence between MEAN and RANGE calculations

Individual correlations
No one showed significant correlation between raw errors in both condition
Independence between MEAN and RANGE calculations

Average errors
No difference between mean errors in baseline condition and the first response in both condition
(both for RANGE and MEAN).

Conclusions
Ensemble summary statistics (mean and numerosity, mean and range) are calculated
independently and in parallel

Conclusions (2)
Independent calculation of ensemble summary statistics means:
(1) Different summaries are calculated by different (partly non-overlapping) brain regions.
(2) The result of one calculation does not influence the result of the other calculation (unlike in mathematical statistics)

For details and even one more experiment please read:
Khvostov V.A., Utochkin I. S. Independent and parallel visual processing of ensemble statistics: Evidence from dual tasks // Journal of Vision. 2019. Vol. 19. No. 9. P. 1-18. doi:10.1167/19.9.3

Thank you for being with me till the end of the first part

Confidence intervals in within-subject designs
*Based on Cousineau, 2005
Part #2

It is all from this 4-pages paper

The problem
Different subjects can perform very differently which increases a size of error bars
Inconsistency between the results of ANOVA and the graph:
ANOVA shows the effect, but the graph do not

ANOVA results
an experiment with two factors, the first with two levels and the second with 5 levels

Results of the experiment
Error bars show the mean ± 1 standard error.

The individual results of the 16 participants
The first level of the first factor.
The second level of the first factor.

The solution of the problem
the
participant
mean
Y =
_
+
the
group
mean
results of the participant in a particular condition

Example of calculations
550–580+635=605
580–580+635=635
610–580+635=665
605 – 635 +635
635 – 635 +635
655 – 635 +635
660 – 690 +635
690 – 690 +635
710 – 690 +635

The individual results of the 16 participants after the individual differences were removed
The first level of the first factor.
The second level of the first factor.
Participants mean
Overall mean

The graph after the individual differences were removed
Error bars show the mean ± 1 standard error.

NOTE: Y is only useful for graphing
purposes; for the analyses, continue to use the original data.
the
participant
mean
Y =
_
+
the
group
mean
results of the participant in particular condition

Example from real life
Error bars show SEM.

Example from real life
Error bars show SEM.