Data Theory

Karl Ho

School of Economic, Political and Policy Sciences

University of Texas at Dallas

Data Visualization

Data Literacy

Data generating process
Graphic grammar
Statistical judgement

What to visualize and how?

Data Literacy

Data generating process
1. How data are generated
2. Distribution
3. Missing values
4. Bad data (Quartz guide to bad data | GitHub)

Data are not simply “found” but are produced through social, technical, and methodological processes (Gitelman 2013, Raw Data is an Oxymoron).

Implications for visualization: Every graph carries assumptions from sampling, measurement, and coding decisions.

Example: Census data vs. Twitter API data—each is shaped by institutional and technical design.

“Data do not exist independently of the ideas, instruments, practices, contexts, and knowledge used to generate them” (Kitchin 2014, The Data Revolution).

Data Literacy

Graphic grammar
1. Bad charts deliver incorrect message
2. Poor design
3. Color
4. Label
5. Font
6. Scale
7. Dimensionality

Leland Wilkinson (2005) provides a theoretical foundation:
- Visualization = Mapping data → aesthetic attributes → perceptual objects.

Hadley Wickham’s ggplot2 operationalizes this grammar.

Key idea: A graph is not “just a picture” but a systematic composition of layers.

“A statistical graphic is a visual display that shows quantitative and categorical information” (Wilkinson 2005, p. 22).

Data Literacy

Statistical understanding
1. Size does (not) matter
2. Representativeness does
3. Forecast/prediction minded
4. Explanation
5. Causality vs. correlation

Visualization is inseparable from statistical reasoning.

Gary King et al. (2000): “Statistical analyses do not interpret themselves; interpretation is the substantive act of turning data into knowledge.”

Visualization can mislead if statistical uncertainty, distributions, or context are ignored.

Cleveland (1985) emphasizes exploratory data analysis (EDA) as a form of statistical thinking with graphics.

Data Scales

Measurement levels (Stevens 1946):

Nominal (categories)
Ordinal (rankings)
Interval (equal units, no true zero)
Ratio (absolute zero, full comparability)

Data Scales

Data scales affect visualization choices:

Nominal → bar charts, mosaics
Ordinal → ordered barplots, dot plots
Interval/Ratio → histograms, scatterplots, line charts

Colin Ware (2012): “Perceptual tasks are the foundation for graphical design: what people can and cannot perceive determines what graphics can and cannot do.”

Data Made, Data Found

Small data
Big data

What determines size of data?

What distinguishes types of data?

What is good data?

Data Made, Data Found

Small data: Carefully sampled surveys, experiments.
- Advantage = control, inference. Limitation = scale.
Big data: Sensor logs, social media, administrative records.
- Advantage = volume, real-time analysis. Limitation = bias, lack of representativeness.

Visualization challenge:
- scalability of graphics (e.g., from scatterplots to heatmaps, from static charts to interactive dashboards).

Alberto Cairo (2016): “Big data is not necessarily better data. More is not always more.”

Understanding data theory is essential to effective visualization.

Data literacy grounds us in how data are produced.
Grammar of graphics gives us a structured language for design.
Statistical judgment keeps our visuals honest.
Awareness of scale, type, and size (small vs. big data) ensures clarity and validity.

“Above all else, show the data.”

- Edward Tufte (2001)

Big data and small data:

actions

individuals

interactions

transactions

individuals

Network structure

(Legislative Yuan in Taiwan)

Network structure (Legislative Yuan)

Colors and shapes represent members of parties.
Size indicates importance in terms of number of bills and mobilization of cosigners

Positions indicate distances from other networks and within own network.

Lines between nodes represents interactions (sponsor/cosponsor)

Let the dataset change your mindset.

- Hans Rosling

Hans Rosling

Swedish physician and statistician

Founded Gapminder Foundation
Visualize historical data on public health and poverty

Hal Varian

Chief Economist, Google

Professor of Economics, University of California, Berkeley.

Big Data: New Tricks for Econometrics

Machine Learning and Econometrics

If you’re not doing something different, you’re not doing anything at all.

- Edward Tufte

It comes with the package, to reconcile [yourself] to life’s inevitable trade-offs and heartaches.

Could data analytics add value to your research?

The first thing is "it will do no harm". Visualized data must not obscure the findings or confuse the readers.

Data Theory

Data Visualization

Data Literacy

Data generating process

Graphic grammar

Statistical judgement

What to visualize and how?

Data Literacy

Data generating process

​How data are generated

Distribution

Missing values

Bad data (Quartz guide to bad data | GitHub)

Data Literacy

Graphic grammar

Bad charts deliver incorrect message

Poor design

Color

Label

Font

Scale

Dimensionality

Data Literacy

Statistical understanding

Size does (not) matter

Representativeness does

Forecast/prediction minded

Explanation

Causality vs. correlation

Data Scales

Measurement levels (Stevens 1946):

Nominal (categories)

Ordinal (rankings)

Interval (equal units, no true zero)

Ratio (absolute zero, full comparability)

Data Scales

Data scales affect visualization choices:

Nominal → bar charts, mosaics

Ordinal → ordered barplots, dot plots

Interval/Ratio → histograms, scatterplots, line charts

Data Made, Data Found

Small data

Big data

What determines size of data?

What distinguishes types of data?

What is good data?

Data Made, Data Found

Understanding data theory is essential to effective visualization.

Data literacy grounds us in how data are produced.

Grammar of graphics gives us a structured language for design.

Statistical judgment keeps our visuals honest.

Awareness of scale, type, and size (small vs. big data) ensures clarity and validity.

Big data and small data:

actions

interactions

transactions

Network structure

(Legislative Yuan in Taiwan)

Network structure (Legislative Yuan)

Let the dataset change your mindset.

- Hans Rosling

Hans Rosling

Hal Varian

If you’re not doing something different, you’re not doing anything at all.

- Edward Tufte

It comes with the package, to reconcile [yourself] to life’s inevitable trade-offs and heartaches.

Could data analytics add value to your research?

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