Data Visualization

Lecture 04

January 30, 2026

Review

EDA

EDA: Understand structure of data while making as few assumptions as possible (e.g. look at the raw data, not “smoothed” versions).
You might be asking the “right” questions but have the “wrong” data: be open-minded and rely on domain knowledge.
Quantitative EDA can be a starting point, but EDA also requires visualization.

Data Visualization

Challenges for Effective Visualization

Limits From Cognitive Processes
No “Optimal” Visualization
Temptation To Overload Figures
Easy to “Lie” About The Data

Further Challenges

Following Munzner (2014):

Possible designs are a bad match with human perceptual and cognitive systems;
Possible designs are a bad match with the intended task;
Only a small number of possibilities are reasonable choices;
“Randomly choosing possibilities is a bad idea because the odds of finding a very good solution are very low.”

Remember: Data Never Speaks For Itself

Data must be understood in a particular context. You need to understand your data and what it says (or does not say!) based on your hypotheses.

What question(s) does your data address?
What transformations make the representation of the data as salient as possible?
What scales or channels are most appropriate?

Some Caveats

There is no recipe to effective visualization. Everything depends on your data and the story you want to tell.
This also means that defaults from data visualization packages are usually bad.
Principles are largely based on Western (American/European) norms and may not translate perfectly.
A lot of these guidelines are based on average outcomes, there is likely to be a lot of individual variation.

Some Data Viz Principles

Gestalt Principles

The Gestalt school of psychology identified several principles of perception.

Core idea: Humans are very good at finding structure.

As a result, you need to evaluate the totality of a visual field, not just each component.

Gestalt Principles

Proximity
Similarity
Connection
Common Fate
Continuity
Closure

Illustration of several Gestalt principles. Adapted from Healy (2018).

Impact of Continuity

Code

# create trend for data
x = rand(Uniform(0, 20), 10)
y = 5 .+ 2 * x
# sample and add noise
ε = rand(Normal(0, 5), 10)
y .+= ε

p1 = scatter(x, y, xlabel=L"$x$", ylabel=L"$y$", color=:blue, markersize=8)
p2 = plot(sort(x), sort(y), xlabel=L"$x$", ylabel=L"$y$", color=:blue, marker=:circle, markersize=8)

plot(p1, p2, layout=(1,2), size=(1100, 500))

Figure 1: Illustrating impact of connected points.

Vertical Scales

Worry about the vertical scale
- Are you exaggerating small changes? Downplaying meaningful changes?
- “Adjust vertical scale of data” to reflect meaningful changes and “Vertical scale should always include zero” are conflicting advice.

Principle of Proportional Ink

On the left: 2014 quantity is ~1.1x 2010 value, but due to vertical scale the 2014 bar uses 2.7x the ink.

Can mislead viewers into thinking the difference is larger than it truly is!

Source: Calling Bullshit

What Makes A Good Color Scheme?

Perceptually uniformity: preserve a mapping between changes in perceived colors and changes in attribute values.
Color-blind safe!

Color Schemes

Good news: Most plotting libraries include a wide variety of perceptually uniform, color-blind safe color schemes.

Bad news: These are not usually the defaults (in particular, avoid “rainbow” color schemes).

Good site: Paul Tol’s color schemes.

Sequential Color Schemes

Sequential schemes change in intensity from low to high as the value changes.

Divergent Color Schemes

Divergent schemes intensify in two directions from a zero or mean value.

Unordered Color Schemes

Unordered schemes are appropriate for categorical data.

Avoid Using Two Vertical Axes

Two axis plot

Source: Datawrapper.de

Avoid Using Two Vertical Axes

Illustration of how rescaling axes manipulates impression

Source: Datawrapper.de

Example: Spurious Correlations

Spurious Correlation 5901

Source: Spurious Correlations

Encode Information With Marks and Channels

Marks: Geometric primitives

Points
Segments
Paths
Polygons

Channels: Mark appearance

Color (Hue/Saturation/Luminescence)
Position (1D/2D/3D)
Size (Length/Area/Volume)
Angle

Ordered vs. Categorical Attributes

The channels available depend on the type of attribute:

Ordered attributes can be
- Ordinal: Ranking, no meaning to distance;
- Quantitative: Measure of magnitude which supports arithmetic comparison;
Categorical attributes are unordered.

Channel Effectiveness: Ordered Data

Channels for ordered data, arranged top-to-bottom from more to less effective (channels in the right column are less effective than those in the left). Modified from Healy (2018) after Munzner (2014).

Channel Effectiveness: Categorical Data

Channels for categorical data, arranged top-to-bottom from more to less effective. Modified from Healy (2018) after Munzer (2014).

Preattentive Popout

Try to make your key features “pop out” to the viewer during the pre-attentive scan.

Searching for the blue circle becomes harder. Adapted from Healy (2018).

Code

npt = 20
dist = Distributions.Product(Uniform.([0, 0], [1, 1]))
pts = Tuple.(eachcol(rand(dist, npt)))
blueidx = rand(1:npt)
p1 = scatter(pts[1:end .!= blueidx], color=:red, xticks=:false, yticks=:false, legend=:false, markersize=5, title="Color Only, N=20", framestyle=:box)
scatter!(p1, pts[blueidx, :], color=:blue, markersize=5)

npt = 100
pts = Tuple.(eachcol(rand(dist, npt)))
blueidx = rand(1:npt)
p2 = scatter(pts[1:end .!= blueidx], color=:red, xticks=:false, yticks=:false, legend=:false, markersize=5, title="Color Only, N=100", framestyle=:box)
scatter!(p2, pts[blueidx, :], color=:blue, markersize=5)

npt = 20
pts = Tuple.(eachcol(rand(dist, npt)))
blueidx = rand(1:npt)
p3 = scatter(pts[1:end .!= blueidx], color=:blue, markershape=:utriangle, xticks=:false, yticks=:false, legend=:false, markersize=5, title="Shape Only, N=20", framestyle=:box)
scatter!(p3, pts[blueidx, :], color=:blue, markersize=5, markershape=:circle)

npt = 100
pts = Tuple.(eachcol(rand(dist, npt)))
blueidx = rand(1:npt)
p4 = scatter(pts[1:end .!= blueidx], color=:blue, markershape=:utriangle, xticks=:false, yticks=:false, legend=:false, markersize=5, title="Shape Only, N=100", framestyle=:box)
scatter!(p4, pts[blueidx, :], color=:blue, markersize=5, markershape=:circle)

plot(p1, p2, p3, p4, layout=(2, 2), size=(800, 500))

Visualization Examples

Thoughts On This Plot?

First Street Foundation Return Period Trends

Source: Shu et al. (2023)

How About This One?

Trump Polling Average vs. Employment in Swing States

Source: Joe Weisenthal

Or This One?

Impacts of Climate Mitigation on Air Pollution

Source: Huang et al. (2023)

Or…

Source: Errickson et al. (2021)

Last One!

Source: Bakkensen & Barrage (2022)

Key Points

Data Visualization

No “cookbook”: be thoughtful and honest with your data.
Defaults from software packages (scales, colors, etc.) are usually bad.
Think carefully about if you’re creating artifacts which might mislead others, even if unintentional.

Upcoming Schedule

Next Classes

Next Week: Probability Models and Linear Regression

Assessments

Homework 1 Due Friday, 2/6.

Exercises: This week’s involves some simple computations.

Reading: Franconeri et al (2024)

Quiz 1: Friday, 2/13.

References

References (Scroll for Full List)

Bakkensen, L. A., & Barrage, L. (2022). Going Underwater? Flood Risk Belief Heterogeneity and Coastal Home Price Dynamics. Rev. Financ. Stud., 35, 3666–3709. https://doi.org/10.1093/rfs/hhab122

Errickson, F. C., Keller, K., Collins, W. D., Srikrishnan, V., & Anthoff, D. (2021). Equity is more important for the social cost of methane than climate uncertainty. Nature, 592, 564–570. https://doi.org/10.1038/s41586-021-03386-6

Healy, K. (2018). Data visualization: A practical introduction. Princeton University Press.

Huang, X., Srikrishnan, V., Lamontagne, J., Keller, K., & Peng, W. (2023). Effects of global climate mitigation on regional air quality and health. Nature Sustainability, 1–13. https://doi.org/10.1038/s41893-023-01133-5

Munzner, T. (2014). Visualization analysis and design. CRC Press.

Shu, E., Hauer, M., & Porter, J. (2023, November). Future population exposure to flood risk: A decomposition approach across Shared-Socioeconomic pathways (SSPs). Research Square. https://doi.org/10.21203/rs.3.rs-3628132/v1