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[1] Rensink, R.A., & Baldridge, G. (2010). The perc eption of correlation in

scatterplots. Computer Graphics Forum, 29(3), 1203–1210.

[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 =

0.937

●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

stimuli?

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].

Background

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.

Methods

Results

Stimuli Future Directions

References

Conclusions

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 ' "

6-

Webe r’s Law

best: measure of

offset in correlation

estimation

bdisc: measure of offset in

correlation discrimination

k: measure of variability

(instance of Weber’s

fraction)

rA:" 7 89: ; ./0 (avg. of

base and var iant

correlations)

systematically

related by:

bias paramete r,

b (best and bdisc)

Correlation (rA)Objective Correl ation ( r)