Creating the right visuals for your data

By George Spencer

Statistician Howard Wainer and psychologist Michael Friendly are numbers magicians — they make the invisible visible. Two of the world's leading figures in the field of data visualization, they are co-authors of a new book, A History of Data Visualization & Graphic Communication.

Wainer, now retired, was principal research scientist at Educational Testing Service, distinguished research scientist at the National Board of Medical Examiners, and professor of statistics at the University of Pennsylvania. Friendly is a professor of psychology at York University in Toronto and a leading scholar of the history of data visualization.

In the following Q&A, they explain how CPAs can best use visual depictions of numbers and how history's "heroes of visual thinking" transformed numbers into images that carry ideas and meaning. They responded to the questions jointly via email.

What questions should CPAs ask themselves when creating visual information such as charts and graphs for clients?

Ask yourself three questions. First, what claims will my clients want to make? Second, what evidence do I have to support those claims? Third, who is the audience? What kinds of data displays do they understand?

You write that good graphical displays of data, like good writing, express ideas with clarity, precision, and efficiency. What rules of visual "grammar" should CPAs follow?

They should think clearly, think precisely, and depict the resulting ideas minimally and avoid irrelevancies. Develop a display that shows only what is needed and nothing more. Moreover, it is essential you think of a data display as a means of communication to human eyes and human minds. Any display is more easily understood if it has a meaningful title that answers this question for the viewer: "Why do I need to understand this?" And make sure all labels are legible.

How have computers made data visualization better — and worse?

On the plus side, computers have made a huge range of potentially helpful graphical depictions available to nearly anyone. On the negative side, computers have made a huge range of potentially meaningless or misleading graphical depictions available to nearly anyone.

What are some of the most common ways charts "lie"? Are there rules of thumb to prevent this?

The short answer is, tell the visual truth as artfully as you can, and then show it to trusted parties and ask them, "What are the messages that the data carry?" If they fail to grasp your intended message, you have failed.

For more details on this in an easy-to-understand form, interested readers are immodestly referred to the first chapter in Wainer's book Visual Revelations, titled "How to Display Data Badly."

How are scatterplots better than bar charts and pie graphs? How can CPAs use them?

Scatterplots gracefully show the relation between two variables such as income earned vs. taxes paid. The other two formats can't do that. Scatterplots also make it possible to show trends, uncertainty, and unusual observations that would go undetected in numerical summaries.

Are there software programs for data visualizations you recommend?

There are dozens. Each has its own advantages and disadvantages. High-level languages like R and Python are the most flexible but require the most knowledge to use fully. Low-level packages are easy but restrictive. Tableau software is a popular intermediate option. It combines flexible graphics with an easy-to-use interface.

The most flexible and powerful graphical tool may be the most old-fashioned — a hand-drawn picture or a picture drawn freehand with a stylus on a tablet. If you go that route, hire both a gifted designer and good artist — the former to decide what to draw, the latter to execute it.

In your book, you say the late 1800s became a "Golden Age" for advances in data depiction while the early 1900s were a "Dark Age." You suggest some dark corners may be lurking in our current age. Why?

From the 1860s to 1890s, statisticians and governments eagerly adopted graphical representations. Then the costs associated with government-sponsored statistical albums outweighed the enthusiasm of those who paid the bills, and experts reverted to relying on numbers and tables.

Today we may be becoming slaves of our tools. Those who want to display data rely too heavily on what's easiest and can become prisoners of their software's default options. It's easy to plot data points on custom charts with high-level software. But good taste in drawing graphs has lagged the ability to make them. We need fewer cookbooks on how to draw graphs and more guides to gastronomy telling us what graphs we should draw.

The good news is that there are now excellent sources of good taste for graphic design and communication that can serve as inspiration and guidance. I recommend the books The Functional Art: An Introduction to Information Graphics and Visualization and The Truthful Art: Data, Charts, and Maps for Communication by Alberto Cairo and Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures by Claus Wilke.

As graduate students, you both studied under a statistics professor at Princeton named John Tukey. You say he revolutionized data visualization. How so?

He believed the goal of data analysis is insight, not numbers. As a result, he changed modern science. He drilled into us his fundamental belief that "the greatest value of a graph is when it forces us to notice what we never expected to see." For example, Tukey taught us all that subtracting the standard statistical summary (e.g., a fitted line) from the data left the opportunity to discover something new. Our history of data visualization highlights scientific discoveries that would not have occurred without a graph.

In the 1780s, one man — William Playfair — invented bar charts, line graphs, and pie charts, as well as framing, titles, labeling of axes, time-period indicators, and other standard embellishments. Who was this visual genius?

Playfair was a Scot trained as a practical engineer by giants of the Industrial Revolution like steam engine innovator James Watt. Playfair was, by turns, an engineer, draftsman, economist, statistician, and silversmith. He was crafty and sometimes unscrupulous, but a genius in advancing the idea that economic trends could be seen in charts.

His advances in data visualization were so astounding that when French King Louis XVI first saw his visual inventions, he said, "They clearly spoke all languages."

In 1786, he produced the first skyrocketing national debt chart. It brilliantly integrated historical collateral information. For example, it showed that in 1775, when what he called the "American War" began, England's debt was £135 million, but at the war's end in 1784 it had nearly doubled to £250 million.

More important, he introduced the idea of visual reasoning and thinking about economic data to an audience that was more accustomed to looking at numbers in tables. Playfair said, "[To give insight to statistical information] it occurred to me that making an appeal to the eye when proportion and magnitude are concerned is the best and readiest method of conveying a distinct idea."

How did scientific and social problems drive innovations in the presentation of visual information?

Problems like widespread epidemics of smallpox, cholera, and other diseases have existed for as long as humans lived together in large towns and cities. Each age had its own tools for dealing with such problems, but they had to coincide with the prevailing epistemological view of the time.

The profound growth of empiricism in the 18th century led to gathering data that reflected the public's health. It was only natural that once experts had data in hand, they would seek methods to understand them. As Tukey observed, graphs emerged as the best way to find the unexpected and hence point to potential solutions.

Does the relation between war and data collection parallel that of disease and data collection?

Yes. In war, lives and treasure are lost at breakneck pace, and it was only natural that war-related data would be gathered and analyzed using the same methods that had proved so successful fighting disease.

The British nurse Florence Nightingale had a flair for mathematics. Some called her the "passionate statistician." Her meticulous records of the causes of death in British field hospitals during the Crimean War quickly revealed that poor sanitation and disease, most notably cholera, killed far more British soldiers than the enemy's guns.

Small wedges in the chart (usually called a "Nightingale Rose" after its designer) that are closest to the vertex show combat deaths. They are consistently dwarfed by larger blue wedges, which are deaths from disease.

Her skillful visual depiction of data led to massive changes in battlefield hygiene. She changed medical practices in war and peace forever.

George Spencer is a freelance writer based in North Carolina. To comment on this article or to suggest an idea for another article, contact Chris Baysden, a JofA associate director, at


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