Evaluating Perceptual Bias During Geometric Scaling of ScatterplotsYating Wei1, Honghui Mei1, Ying Zhao2, Shuyue Zhou1, Bingru Lin1, Haojing Jiang2, Wei Chen1

1: State Key Lab of CAD&CG, Zhejiang University2: Central South University

Introduction

• Scatterplots are a common type of visualization.• Various display devices• Collaborative data analysis

Introduction

Motivation

• Geometric scaling• Enlarge or shrink the entire plot

together with the objects inside it synchronously and proportionally.

Geometric scaling may cause a perceptual bias.

The deviation between the perceived and physical values of visual features.

• Design decisions of scatterplot

Introduction

[Wang et al. 2019]

[Tory et al. 2009]

[Heer et al. 2006]

…

Related Work

• Usage issues of scatterplots in multiple devices

Introduction

[Butscher et al. 2018]

[Blascheck et al. 2019]

[Ni et al. 2006]

Related Work

Introduction

1Conduct evaluation experiments to verify the existence of the bias.

2Obtain instructive findings to guide visual design.

Goal

Hypotheses

• H3: Changing the radius of points can reduce the bias.

• H1: Geometric scaling causes a bias in the perceived visual features of scatterplots.

• H2: The bias caused by geometric scaling can be affected by data distribution.

Numerosity Correlation Cluster separation

Normal

Uniform

radii

Hypotheses

• H3: Changing the radius of points can reduce the bias.

• H1: Geometric scaling causes a bias in the perceived visual features of scatterplots.

• H2: The bias caused by geometric scaling can be affected by data distribution.

Numerosity Correlation Cluster separation

Normal

Uniform

radii

Hypotheses

• H3: Changing the radius of points can reduce the bias.

• H1: Geometric scaling causes a bias in the perceived visual features of scatterplots.

• H2: The bias caused by geometric scaling can be affected by data distribution.

Numerosity Correlation Cluster separation

Normal

Uniform

radii

Experimental Design

2D scatterplot- Aspect ratio = 1- 𝑥𝑥,𝑦𝑦 ∈ [0,1]- Gray background & black thin borders- Black circles with the same radii

Experimental Design

StimuliCommon displays

25% 40% 63% 100% 159% 252% 400%

originshrink enlarge

Seven Scale Ratios

• The value range of the testing visual feature

−6 level −5 level −4 level +6 level+5 level+4 level

Experimental Design

Variable and Data

Numerosity𝑛𝑛 ∈ [11,730]

Correlation𝑟𝑟 ∈ [0.15,0.9]

Cluster Separation𝑠𝑠 ∈ [0.11,0.65]

• Simulate scatterplot scaling scenarios.• Measure people’s subjective experience.

Experimental Design

2IFC & 2WS Method

• 2IFC (two-interval forced choice)• Measure the subjective experience of a person through his/her choice pattern.• 2IFC sequence: measure the bias from the choice pattern.

• 2WS (two-way staircase)• Decide the order of appearance of feature levels

Make the right choiceMake the right choice

Make the wrong choice

Experimental Design

2IFC & 2WS Method

Experimental Design

Experimental settings

E1(H1) E2(H2) E3(H3)

VariableScale ratio, feature, feature level

Scale ratio, feature, feature level

Point radius, feature, feature level

ConstantPoint radius Point radius Two scale ratios

Data distributionNormal distribution Uniform

distributionNormal distribution

63% 252%

1. The overall difficulty level (DL) of making 2IFC judgments

Do the changes of scatterplot size make your judgments on the perception of normal-distributed numerosity difficult? If so, then how difficult is it?

2. The difficulty tendency (DT) of making 2IFC judgments with different scale ratios or point radii.

How does the difficulty of making judgments change on the perception of normal-distributed numerosity with the changes in scatterplot size from small to large?

Experimental Design

Subjective Questionnaire• Two types of questions

Pilot study Preparation Introduction & tutorial Pre-experiment Formal experiment

10 2 3 4

• Participants • Apparatus• 20 participants • an independent, quiet laboratory

• a Dell 25 in U2515H monitor

Experimental Design

Procedure

EXPERIMENTAL RESULTS

• Abnormal choice patterns identification.• Fiercely fluctuating• Early fluctuating

Experimental Results

Analysis ApproachFe

atur

e Le

vels

Trials

Feat

ure

Leve

ls

Trials

• Bias measurement• PSE (point of subjective equality) − POE (point of objective equality)

• Significance analysis• Shapiro−Wilk test• Non-parametric Friedman• ANOVA test

Experimental Results

Analysis Approach

Feature value of test scatterplotPr

ob. T

est<

Refe

renc

e

H1: Geometric scaling causes a bias in perceiving the three visual features. The bias has a significant linear relationship with the scale ratio.

FULLY CONFIRMED!

Experimental Results

Objective Result Analysis —— H1

Scale Ratio (%)

Bias

Numerosity

65 → 89

Prob

. Tes

t<Re

fere

nce

Feature value of test scatterplot

Experimental Results

Objective Result Analysis —— H1Numerosity

Bias

Scale Ratio

Perceived Numerosity

Experimental Results

Objective Result Analysis —— H1

Scale Ratio Perceived Correlation Perceived Cluster Separation

Correlation Cluster Separation

Bias

Bias

Scale Ratio (%) Scale Ratio (%)

Experimental Results

Objective Result Analysis —— H2

Scale Ratio (%) Scale Ratio (%) Scale Ratio (%)

Bias Bias

Bias

Correlation Cluster SeparationNumerosity

H2: The bias can be affected by data distribution. FULLY NEGATED!

H3: Changing the point radius can reduce the bias. PARTIALLY CONFIRMED!

Experimental Results

Objective Result Analysis —— H3

Numerosity

Bias

Point Radius

E3 (6

3%)

Numerosity

Point Radius

Bias

E3 (2

52%

)

Experimental Results

Objective Result Analysis —— H3Correlation Cluster SeparationNumerosity

E3 (6

3%)

E3 (2

52%

)

Experimental Results

Objective Result Analysis —— H3Correlation Cluster SeparationNumerosity

E3 (6

3%)

E3 (2

52%

)

Experimental Results

Objective Result Analysis —— H3Correlation Cluster SeparationNumerosity

E3 (6

3%)

E3 (2

52%

)

Experimental Results

Subjective Result Analysis

Experimental Results

Summary• Geometric scaling causes a bias on the perception of the three visual

features.

• No significant difference occurs between the biases measured from normally and uniformly distributed scatterplots.

• Changing the point radius can correct the bias.

• Limited experimental content• High-level perceptions of scatterplot• Diverse data distributions• More visual channels• Different display devices and screen resolutions

• No quantitative model• To describe the bias• To guide the bias correction

Limitation

1Evaluation Experiment

2Instructive findings

Conclusion

Thank you!

This work is supported by:The National Key Research and Development Program of China (No. 2018YFB1700403) The National Natural Science Foundation of China (No. 61772456, 61761136020, U1609217, 61672538 and 61872388).

Yating Wei, Honghui Mei, Ying Zhao, Shuyue Zhou, Bingru Lin, Haojing Jiang, Wei Chen

Evaluating Perceptual Bias During Geometric Scaling of Scatterplots