Category Archives: Visualization

The Elements of Graphing Data, William S. Cleveland

Bill Cleveland is one of the founding figures in statistical graphics and data visualization. His two books, The Elements of Graphing Data and Visualizing Data, are classics in the field, still well-worth reading today.

Visualizing is about the use of graphics as a data analysis tool: how to check model fit by plotting residuals and so on. Elements, on the other hand, is about the graphics themselves and how we read them. Cleveland (co)-authored some of the seminal papers on human visual perception, including the often-cited Cleveland & McGill (1984), “Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods.” Plenty of authors doled out common-sense advice about graphics before then, and some even ran controlled experiments (say, comparing bars to pies). But Cleveland and colleagues were so influential because they set up a broader framework that is still experimentally-testable, but that encompasses the older experiments (say, encoding data by position vs length vs angle vs other things—so that bars and pies are special cases). This is just one approach to evaluating graphics, and it has limitations, but it’s better than many competing criteria, and much better than “because I said so” *coughtuftecough* :)

In Elements, Cleveland summarizes his experimental research articles and expands on them, adding many helpful examples and summarizing the underlying principles. What cognitive tasks do graph readers perform? How do they relate to what we know about the strengths and weaknesses of the human visual system, from eye to brain? How do we apply this research-based knowledge, so that we encode data in the most effective way? How can we use guides (labels, axes, scales, etc.) to support graph comprehension instead of getting in the way? It’s a lovely mix of theory, experimental evidence, and practical advice including concrete examples.

Now, I’ll admit that (at least in the 1st edition of Elements) the graphics certainly aren’t beautiful: blocky all-caps fonts, black-and-white (not even grayscale), etc. Some data examples seem dated now (Cold War / nuclear winter predictions). The principles aren’t all coherent. Each new graph variant is given a name, leading to a “plot zoo” that the Grammar of Graphics folks would hate. Many examples, written for an audience of practicing scientists, may be too technical for lay readers (for whom I strongly recommend Naomi Robbins’ Creating More Effective Graphs, a friendlier re-packaging of Cleveland).

Nonetheless, I still found Elements a worthwhile read, and it made a big impact on the data visualization course I taught. Although the book is 30 years old, I still found many new-to-me insights, along with historical context for many aspects of R’s base graphics.

[Edit: I’ll post my notes on Visualizing Data separately.]

Below are my notes-to-self, with things-to-follow-up in bold:

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Teaching data visualization: approaches and syllabi

While I’m still working on my reflection of the dataviz course I just taught, there were some useful dataviz-teaching talks at the recent IEEE VIS conference.

Jen Christiansen and Robert Kosara have great summaries of the panel on “Vis, The Next Generation: Teaching Across the Researcher-Practitioner Gap.”

Even better, slides are available for some of the talks: Marti Hearst, Tamara Munzner, and Eytan Adar. Lots of inspiration for the next time I teach.

Hearst_ClassDiscussions

Finally, here are links to the syllabi or websites of various past dataviz courses. Browsing these helps me think about what to cover and how to teach it.

Comment below or tweet @civilstat with any others I’ve missed, and I’ll add them to the list.

Statistical Graphics and Visualization course materials

I’ve just finished teaching the Fall 2015 session of 36-721, Statistical Graphics and Visualization. Again, it is a half-semester course designed primarily for students in the MSP program (Masters of Statistical Practice) in the CMU statistics department. I’m pleased that we also had a large number of students from other departments taking this as an elective.

For software we used mostly R (base graphics, ggplot2, and Shiny). But we also spent some time on Tableau, Inkscape, D3, and GGobi.

We covered a LOT of ground. At each point I tried to hammer home the importance of legible, comprehensible graphics that respect human visual perception.

Pie chart with remake

Remaking pie charts is a rite of passage for statistical graphics students

My course materials are below. Not all the slides are designed to stand alone, but I have no time to remake them right now. I’ll post some reflections separately.

Download all materials as a ZIP file (38 MB), or browse individual files:
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Summary sheet of ways to map statistical uncertainty

A few years ago, a team at the Cornell Program on Applied Demographics (PAD) created a really nice demo of several ways to show statistical uncertainty on thematic maps / choropleths. They have kindly allowed me to host their large file here: PAD_MappingExample.pdf (63 MB)

Screenshot of index page from PAD mapping examples

Screenshot of index page from PAD mapping examples

Each of these maps shows a dataset with statistical estimates and their precision/uncertainty for various areas in New York state. If we use color or shading to show the estimates, like in a traditional choropleth map, how can we also show the uncertainty at the same time? The PAD examples include several variations of static maps, interaction by toggling overlays, and interaction with mouseover and sliders. Interactive map screenshots are linked to live demos on the PAD website.

I’m still fascinated by this problem. Each of these approaches has its strengths and weaknesses: Symbology Overlay uses separable dimensions, but there’s no natural order to the symbols. Pixelated Classification seems intuitively clear, but may be misleading if people (incorrectly) try to find meaning in the locations of pixels within an area. Side-by-side maps are each clear on their own, but it’s hard to see both variables at once. Dynamic Feedback gives detailed info about precision, but only for one area at a time, not all at once. And so forth. It’s an interesting challenge, and I find it really helpful to see so many potential solutions collected in one document.

The creators include Nij Tontisirin and Sutee Anantsuksomsri (both since moved on from Cornell), and Jan Vink and Joe Francis (both still there). The pixellated classification map is based on work by Nicholas Nagle.

For more about mapping uncertainty, see their paper:

Francis, J., Tontisirin, N., Anantsuksomsri, S., Vink, J., & Zhong, V. (2015). Alternative strategies for mapping ACS estimates and error of estimation. In Hoque, N. and Potter, L. B. (Eds.), Emerging Techniques in Applied Demography (pp. 247–273). Dordrecht: Springer Netherlands, DOI: 10.1007/978-94-017-8990-5_16 [preprint]

and my related posts:

See also Visualizing Attribute Uncertainty in the ACS: An Empirical Study of Decision-Making with Urban Planners. This talk by Amy Griffin is about studying how urban planners actually use statistical uncertainty on maps in their work.

About to teach Statistical Graphics and Visualization course at CMU

I’m pretty excited for tomorrow: I’ll begin teaching the Fall 2015 offering of 36-721, Statistical Graphics and Visualization. This is a half-semester course designed primarily for students in our MSP program (Masters in Statistical Practice).

A large part of the focus will be on useful principles and frameworks: human visual perception, the Grammar of Graphics, graphic design and interaction design, and more current dataviz research. As for tools, besides base R and ggplot2, I’ll introduce a bit of Tableau, D3.js, and Inkscape/Illustrator. For assessments, I’m trying a variant of “specs grading”, with a heavy use of rubrics, hoping to make my expectations clear and my TA’s grading easier.

Di Cook, LDA and CART classification boundaries on Flea Beetles dataset

Classifier diagnostics from Cook & Swayne’s book

My initial course materials are up on my department webpage.
Here are the

  • syllabus (pdf),
  • first lecture (pdf created with Rmd), and
  • first homework (pdf) with dataset (csv).

(I’ll probably just use Blackboard during the semester, but I may post the final materials here again.)

It’s been a pleasant challenge to plan a course that can satisfy statisticians (slice and dice data quickly to support detailed analyses! examine residuals and other model diagnostics! work with data formats from rectangular CSVs through shapefiles to social networks!) … while also passing on lessons from the data journalism and design communities (take design and the user experience seriously! use layout, typography, and interaction sensibly!). I’m also trying to put into practice all the advice from teaching seminars I’ve taken at CMU’s Eberly Center.

Also, in preparation, this summer I finally enjoyed reading more of the classic visualization books on my list.

  • Cleveland’s The Elements of Graphing Data and Robbins’ Creating More Effective Graphs are chock full of advice on making clear graphics that harness human visual perception correctly.
  • Ware’s Information Visualization adds to this the latest research findings and a ton of useful detail.
  • Cleveland’s Visualizing Data and Cook & Swayne’s Interactive and Dynamic Graphics for Data Analysis are a treasure trove of practical data analysis advice. Cleveland’s many case studies show how graphics are a critical part of exploratory data analysis (EDA) and model-checking. In several cases, his analysis demonstrates that previously-published findings used an inappropriate model and reached poor conclusions due to what he calls rote data analysis (RDA). Cook & Swayne do similar work with more modern statistical methods, including the first time I’ve seen graphical diagnostics for many machine learning tools. There’s also a great section on visualizing missing data. The title is misleading: you don’t need R and GGobi to learn a lot from their book.
  • Monmonier’s How to Lie with Maps refers to dated technology, but the concepts are great. It’s still useful to know just how maps are made, and how different projections work and why it matters. Much of cartographic work sounds analogous to statistical work: making simplifications in order to convey a point more clearly, worrying about data quality and provenance (different areas on the map might have been updated by different folks at different times), setting national standards that are imperfect but necessary… The section on “data maps” is critical for any statistician working with spatial data, and the chapter on bureaucratic mapping agencies will sound familiar to my Census Bureau colleagues.

I hope to post longer notes on each book sometime later.

Dataviz contest on “Visualizing Well-Being”

Someone from OECD emailed me about a data visualization contest for the Wikiprogress website (the deadline is August 24th):

Visualizing Well-Being contest

I am contacting you on behalf of the website Wikiprogress, which is currently running a Data Visualization Contest, with the prize of a paid trip to Mexico to attend the 5th OECD World Forum in Guadalajara in October this year. Wikiprogress is an open-source website, hosted by the OECD, to facilitate the exchange of information on well-being and sustainability, and the aim of the competition is to encourage participants to use well-being measurement in innovative ways to a) show how data on well-being give a more meaningful picture of the progress of societies than more traditional growth-oriented approaches, and b) to use their creativity to communicate key ideas about well-being to a broad audience.

After reading your blog, I think that you and your readers might be interested in this challenge. The OECD World Forums bring together hundreds of change-makers from around the world, from world leaders to small, grassroots projects, and the winners will have their work displayed and will be presented with a certificate of recognition during the event.

You can also visit the competition website here: http://bit.ly/1Gsso2y

It does sound like a challenge that might intrigue this blog’s readers:

  • think about how to report human well-being, beyond traditional measures like GDP;
  • find relevant good datasets (“official statistics” or otherwise);
  • visualize these measures’ importance or insightful trends in the data; and
  • possibly win a prize trip to the next OECD forum in Guadalajara, Mexico to network with others who are interested in putting data, statistics, and visualization to good use.

Two principled approaches to data visualization

Yesterday I spoke at Stat Bytes, our student-run statistical computing seminar.

My goal was to introduce two principled frameworks for thinking about data visualization: human visual perception and the Grammar of Graphics.
(We also covered some relevant R packages: RColorBrewer, directlabels, and a gentle intro to ggplot2.)

These are not the only “right” approaches, nor do they guarantee your graphics will be good. They are just useful tools to have in your arsenal.

Example plot with direct labels and ColorBrewer colors, made in ggplot2.

Example plot with direct labels and ColorBrewer colors, made in ggplot2.

The talk was also a teaser for my upcoming fall course, 36-721: Statistical Graphics and Visualization [draft syllabus pdf].

Here are my

The talk was quite interactive, so the slides aren’t designed to stand alone. Open the slides and follow along using my notes below.
(Answers are intentionally in white text, so you have a chance to think for yourself before you highlight the text to read them.)

If you want a deeper introduction to dataviz, including human visual perception, Alberto Cairo’s The Functional Art [website, amazon] is a great place to start.
For a more thorough intro to ggplot2, see creator Hadley Wickham’s own presentations at the bottom of this page.

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Nice example of a map with uncertainty

OK, back to statistics and datavis.

As I’ve said before, I’m curious about finding better ways to draw maps which simultaneously show numerical estimates and their precision or uncertainty.

The April 2015 issue of Significance magazine includes a nice example of this [subscription link; PDF], thanks to Michael Wininger. Here is his Figure 2a (I think the labels for the red and blue areas are mistakenly swapped, but you get the idea):

Wininger, Fig. 2a

Basically, Wininger is mapping the weather continuously over space, and he overlays two contours: one for where the predicted snowfall amount is highest, and another for where the probability of snowfall is highest.

I can imagine people would also enjoy an interactive version of this map, where you have sliders for the two cutoffs (how many inches of snow? what level of certainty?). You could also just show more levels of the contours on one static map, by adding extra lines, though that would get messy fast.

I think Wininger’s approach looks great and is easy to read, but it works largely because he’s mapping spatially-continuous data. The snowfall levels and their certainties are estimated at a very fine spatial resolution, unlike say a choropleth map of the average snowfall by county or by state. The other thing that helps here is that certainty is expressed as a probability (which most people can interpret)… not as a measure of spread or precision (standard deviation, margin of error, coefficient of variation, or what have you).

Could this also work on a choropleth map? If you only have data at the level of discrete areas, such as counties… Well, this is not a problem with weather data, but it does come up with administrative or survey data. Say you have survey estimates for the poverty rate in each county (along with MOEs or some other measure of precision). You could still use one color to fill all the counties with high estimated poverty rates. Then use another color to fill all the counties with highly precise estimates. Their overlap would show the areas where poverty is estimated to be high and that estimate is very precise. Sliders would let the readers set their own definition of “high poverty” and “highly precise.”

I might be wrong, but I don’t think I’ve seen this approach before. Could be worth a try.

Dataclysm, Christian Rudder

In between project deadlines and homework assignments, I enjoyed taking a break to read Christian Rudder’s Dataclysm. (That’s right, my pleasure-reading break from statistics grad school textbooks is… a different book about statistics. I think I have a problem. Please suggest some good fiction!)

So, Rudder is one of the founders of dating site OkCupid and its quirky, data-driven research blog. His new book is very readable—each short, catchy chapter was hard to put down. I like how he gently alludes to the statistical details for nerds like myself, in a way that shouldn’t overwhelm lay readers. The clean, Tufte-minimalist graphs work quite well and are accompanied by clear writeups. Some of the insights are basically repeats of material already on the blog, but with a cleaner writeup, though there’s plenty of new stuff too. Whether or not you agree with all of his conclusions [edit: see Cathy O’Neil’s valid critiques of the stats analyses here], the book sets a good example to follow for anyone interested in data- or evidence-based popular science writing.

Most of all, I loved his description of statistical precision:

Ironically, with research like this, precision is often less appropriate than a generalization. That’s why I often round findings to the nearest 5 or 10 and the words ‘roughly’ and ‘approximately’ and ‘about’ appear frequently in these pages. When you see in some article that ‘89.6 percent’ of people do x, the real finding is that ‘many’ or ‘nearly all’ or ‘roughly 90 percent’ of them do it, it’s just that the writer probably thought the decimals sounded cooler and more authoritative. The next time a scientist runs the numbers, perhaps the outcome will be 85.2 percent. The next time, maybe it’s 93.4. Look out at the churning ocean and ask yourself exactly which whitecap is ‘sea level.’ It’s a pointless exercise at best. At worst, it’s a misleading one.

I might use that next time I teach.

The description of how academics hunt for data is also spot on: “Data sets move through the research community like yeti—I have a bunch of interesting stuff but I can’t say from where; I heard someone at Temple has tons of Amazon reviews; I think L has a scrape of Facebook.

Sorry I didn’t take many notes this time, but Alberto Cairo’s post on the book links to a few more detailed reviews.

Winter is coming (to the Broad Street pump)

We live in an amazing future, where an offhand Twitter joke about classic data visualizations and Game of Thrones immediately turns into a real t-shirt you can buy.

You know nothing (about cholera), John Snow

Hats off to Alberto Cairo (whose book The Functional Art and blog are the best introductions to data visualization that I can recommend—but you already knew that).

If you don’t already know the story of John Snow and the Broad Street pump—or if you think you do but haven’t heard the full details—then The Ghost Map is a great telling.

Update: Alberto continues to kick this up a notch, adding two more Game Of Thrones-themed classic dataviz jokes, and making the images/captions available under the Creative Commons license. Awesome.

Winter is coming (for Napoleon)