a psychophysical investigation of size as a physical variable
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A Psychophysical Investigation of Size as a Physical Variable
Yvonne Jansen Kasper Hornbæk
Data PhysicalizationsData Communication"a physical artifact whose geometry
or material properties encode data."Atelier Brückner, German Age Pyramid, 2013
Data Communication"a physical artifact whose geometry or material properties encode data."
Data source: dataphys.org
Data Physicalization
Data Communication Presentations Exhibitions
Joyce Hsiang & Bimal Mendis, The City of 7 Billion, 2011-2013
Atelier Brückner, German Age Pyramid, 2013
Loren Madsen, Chicago crime rates, District 5 police station, 2014
Presentations Exhibitions Public Installation
Data Physicalizations
Physical VariablesVisual Variables
Data Visualizations
How should we encode data?
Data Visualization
Tableau's Show Me feature [Source: onlinehelp.tableau.com]
1980s ranking of visual variables!! ! (Cleveland & McGill 1982-1987, Mackinlay 1986, Spence 1990)
1926 circle vs bars debate (e.g., Eels 1926, Croxton & Stryker 1927, Croxton & Stein 1932)
bibliography under yvonnejansen.me/size
Data Physicalization
Image source: Kahrimanovic et al, 2010
Psychology & Psychophysics experiments
1970 Baird, Psychophysical Analysis of Visual Space
2010 Kahrimanovic et al., haptic volume perception
1969 Stanek, volume and surface judgments
e.g.,
sequential presentation
size 10 size ? size ?
…
Sour
ce:
bala
ncea
ndm
obilit
y.com
Sour
ce: m
v.cvc
.uab
.es
Chin rests (see Baird 1970) Free head movements
Instructions matter
how large is the smaller shape (compared to the larger)?
how large appears the smaller shape?
[Teeghtsoonian, The Judgment of Size, 1965]
ratio between heights
How should we describe size?
11 cm 3 cm
ratio between ?
How should we describe size?
ratio between
(in the store) diameters
6 cm 2 cm
33 %
How should we describe size?
(in the store) diameters
113 cm3 4.2 cm3
33 %
3.7 %
How should we describe size?
ratio between
("commonly") volumes
(in the store) diameters
("commonly") volumes
(also possible) surface areas113 cm2 12.6 cm2
33 %
3.7 %
11.1 %
How should we describe size?
ratio between
How should we encode data physically?
Joyce Hsiang & Bimal Mendis, The City of 7 Billion, 2011-2013
Research Questions
1. How accurately are elementary shapes estimated?
3. Are estimates systematically biased?
2. How similar are estimates between individuals?
Experiment
Bars Spheres
28 pairs
7 sizes diameters 1.2-7cmheights 1-15cm
10 participants
Estimation Methods
Ratio estimation
e.g., Cleveland & McGill (1984)
Constant sume.g., Spence (1990)
2 methods
Constant sume.g., Spence (1990)
represents larger shape shorter shape
Ratio estimation
e.g., Cleveland & McGill (1984)
Task
"Indicate the percentage of the quantity represented by the smaller shape relative to the larger shape."
"Divide the line such that the left part represents the quantity represented by the left shape and the right part represents the quantity of the right shape.”
Task
quantity represented by larger shape
…shorter shape
Results
bar sphere
0
25
50
75
100
0
25
50
75
100constant sum
ratio estimation
0 25 50 75 100 0 25 50 75 100
true ratio
estim
ated
ratio
method
shape
estim
ated
ratio
true ratio
bar sphere
0
25
50
75
100
0
25
50
75
100constant sum
ratio estimation
0 25 50 75 100 0 25 50 75 100
true ratio
estim
ated
ratio
method
shape
estim
ated
ratio
true ratio
y = xa
(Stevens’ law)
bar sphere
0
25
50
75
100
0
25
50
75
100constant sum
ratio estimation
0 25 50 75 100 0 25 50 75 100
true ratio
estim
ated
ratio
method
shape
estim
ated
ratio
true ratio
y = xa
(logistic curve)
(Stevens’ law)
y =1
!
10
"
b+a·log"
1x−1##
+ 1
$
bar sphere
0
25
50
75
100
0
25
50
75
100constant sum
ratio estimation
0 25 50 75 100 0 25 50 75 100
true ratio
estim
ated
ratio
method
shape
estim
ated
ratio
true ratio
y = xa
y =1
!
10
"
b+a·log"
1x−1##
+ 1
$
(logistic curve)
(Stevens’ law)
Accuracy
Accuracy
bars: ratio between heights
spheres: ratio between volumes, diameters, and surface areas
absolute discrepancy (in percent)
Accuracy
2D bars (Spence)
3D bars (height)
diameter1.6
surface
diameter
volume
0 5 10 15 20
(error bars indicate 95% bootstrapped confidence intervals)
Bias in Estimates
Residuals
resi
dual
s
Bias in Estimates
−50
−25
0
25
50
0 25 50 75 100
ratio between volumes (in %)
resi
dual
s
−50
−25
0
25
50
0 25 50 75 100
ratio between diameters (in %)
resi
dual
s
volume-based encoding
Spheres
Bias in Estimates
−50
−25
0
25
50
0 25 50 75 100
ratio between volumes (in %)
resi
dual
s
−50
−25
0
25
50
0 25 50 75 100
ratio between diameters (in %)
resi
dual
s
volume-based encoding
diameter-based encoding
−50
−25
0
25
50
0 25 50 75 100
ratio between surfaces areas (in %)
resi
dual
s
Bias in Estimates
−50
−25
0
25
50
0 25 50 75 100
ratio between volumes (in %)
resi
dual
s
−50
−25
0
25
50
0 25 50 75 100
fitted values
resi
dual
s
volume-based encoding
surface-based encoding
regression-based encoding
estimates ~ linear
Take Aways – Bars
response curves similar across people
Take Aways – Bars
●
●
●
●
●
●
line (H) length
line (V) length
bar height
box height
cylinder height
bar (RE) height
0 2 4 6
Spen
ce (1
990)
lower accuracy than 2D bars
but still < 5%
Take away - Spheres
Encoding in volumes misleading representations✘diameter only marginally better
surface area
✘much better (but still more overestimations)
Take away - Spheres
Encoding in volumes misleading representations✘diameter only marginally better
surface area
✘much better (but still more overestimations)
supported by haptic perception studies (Kahrimanovic et al, 2010)
see bibliography under yvonnejansen.me/size
Open Questions / Future Work
Other physical shapes
Interactions between vision and touch
Large range of absolute sizes
Raw data, R scripts, and additional charts at
yvonnejansen.me/size(work in progress)
yvja@di.ku.dkComments, questions, requests
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