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Correlation perception in scatterplots is invariant to dot size



To determine the extent to which the perception of Pearson correlation r in a scatterplot depends on its appearance, we examined the effect of dot size on discrimination and magnitude estimation. Scatterplots were formed of 48 solid black dots on a white background, with axes 6.5 cm by 6.5 cm, and distribution standard deviations 1.3 cm. Observers (N=18) were tested via a within-observer design involving five conditions: dot diameters of 1 mm, 3 mm, 5 mm, 8 mm, and a mix of these sizes. Viewing distance was 67 cm. The methodology was that of Rensink and Baldridge (2010). In the discrimination task, observers were asked to select the plot with the higher perceived correlation; the just noticeable difference (JND) was measured at three base correlations (0.3, 0.6, 0.9). In the magnitude estimation task, observers adjusted a test plot until its perceived correlation was midway between those of two reference plots. The discrimination task was sandwiched between two sets of estimation tasks. All conditions were counterbalanced by base correlations and dot size, using a Latin square. The resulting JNDs were slightly higher than those reported by Rensink and Baldridge (2010) and Rensink (2017), but were still strongly linear functions of correlation (R^2=0.97); the Fechner assumption of equal perceived difference for each JND was also supported. Importantly, neither discrimination nor estimation were significantly affected by dot size. This further supports the proposal (Rensink, 2017) that perceived correlation in scatterplots is based not on the physical appearance of the scatterplot, but on a more abstract quantity, such as the shape of the probability density function derived from the locations of the dots in the image.
[1] Rensink, R.A., & Baldridge, G. (2010). The perc eption of correlation in
scatterplots. Computer Graphics Forum, 29(3), 12031210.
[2] Rensink, R.A. (2017). The natu re of correlation perception in sc atterplots.
Psychonomic Bulletin & Review, 24(3), 776-797.
[3] Kim, Y., & Heer, J. (2018). Assess ing effec ts of ta sk and d ata dis tribution on
the effectiveness of visua l encodings. Computer Graphics Forum, 37(3), 157-167.
[4] Elliott, M.A., & Rensink, R.A. (2019). Attentional co lor selection depends o n
task structure. Vision Sciences Society, St. Peters burg, FL, U SA, May 2019.
Within subjects-design (N= 18; 15F, 3M; AgeAve= 22.1). Computer tasks with keyboard presses.
1. Initial magnitude estimation (bisection) task: Adjust the
middle scatterplot until the correlation ris halfway of the two
reference plots.
3. Final magnitude estimation (bisection) task: Final estimation
results are the average of the initial and final bisection tasks.
2. Discrimination task: Select the scatterplot with the higher
correlation, continue until 75% accurate. Base correlations: 0.3,
0.6, 0.9.
Strong linear fits across conditions: r21mm =0.984,
r23mm = 0.998, r25mm = 0.995, r28mm = 0.947, r2mix =
k’s do not vary across conditions: F(4, 68) = 1.68,
p = 0.17. Average k = 0.16.
Correlation perception in scatterplots is invariant to dot size
Jessica Ip, Nicholas Chin, and Ronald Rensink | University of British Columbia
Perception of correlation rin scatterplots can be
reliably modeled using logarithmic and linear
functions from Fechner’s and Weber’s laws [1,2].
Scatterplots of 48 solid black dots against a white
background, with axes 6.5 cm x 6.5 cm and dot
cloud 6 cm x 6 cm.
Is correlation perception in scatterplots also
invariant to color, luminance, or shape of visual
1 mm Mix
Aim: Wh at i s the effect of dot si ze on the
perception of correlation rin scatterplots?
1. Mor e gene rally , th e perc eptio n of correl ation
in scatterplots is not inferred from the pixels in
the image. Instead, it appears to be based on
more abstract r epresentat ions of correl ation,
such as the distribution of the centroids of the
dots [1,2].
There is no significant eff ect of dot size on
correlation perception.
Figure 3. Bias estimates across dot condi tions. Error
bars represent 95% CI.
Figure 1. JND as a functi on of correl ation (rA). Error bars
represent 95% CI.
Figure 2. Subjective cor relation (g ) as a functi on of
objective correlation (r ). Error bars represent 95 % CI.
Five dot diameter conditions: 1 mm, 3 mm, 5 mm,
8 mm, and a mix of the previous four.
Stimuli Future Directions
Crucially, by the Fechner assumption: bdisc = best.
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$%,& ' ()*+-
Scatterplot designs of different distributions (e.g.,
gaussian, uniform) and quantity of dots yielded
similar performance in correlation perception [1,2].
Fechner’s L aw
Insights from the perceptual processing of visual
features in scatterplots could inform future
approaches to visualization designs.
2. Irrelevant size variations in dots noticeably
affect estimates of average value in scatterplots
[3]. In contrast, the indifference to dot size
variation found here supports the possibility that
correlation estimation relies on a different
ensemble process than that for average value. It
may al so be relate d to the finding that dots ca n
be selected based on color for perception of
average value but not for correlation [4].
bdisc vs. best not significantly different across
conditions: F(4, 170) = 2.30, p = 0.06. No
significant interaction effects (p = 0.34). Average
bdisc = 0.80. Average bes t = 0.78.
Fechner assump tion is satisfied (bdisc = best).
Subjective Correlation (g)
Just Noticea ble Differenc e (JND)
Bias Estimates
Dot Conditi ons
./0,"- # 1,&2(34*5 ' "
Webe r’s Law
best: measure of
offset in correlation
bdisc: measure of offset in
correlation discrimination
k: measure of variability
(instance of Weber’s
rA:" 7 89: ; ./0 (avg. of
base and var iant
related by:
bias paramete r,
b (best and bdisc)
Correlation (rA)Objective Correl ation ( r)
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