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Agendas on Display

Michael Goodchild

PICTURING THE UNCERTAIN WORLD: How to Understand, Communicate, and Control Uncertainty through Graphical Display. Howard Wainer. xx + 244 pp. Princeton University Press, 2009. $29.95.

From time to time, most scientists experience the frustrations of trying to engage with policymaking. “Evidence-based policy” sounds fine in principle, but in practice it may be difficult, if not impossible, to come up with the kinds of evidence that point unequivocally to one policy option over another. The temptation to be selective, or to present data in a form that invites a particular interpretation, can sometimes be overwhelming. To quote Winston Churchill, “When I call for statistics about the rate of infant mortality, what I want is proof that fewer babies died when I was Prime Minister.”

Uncertainty is endemic in science. The uncertainties that result from measurement error sometimes pale in comparison to those introduced by varying interpretations, poorly defined terms, incomplete documentation or ineffective or misleading presentation of data. This problem can only get worse as the Internet increases our ability to share information across vast distances and cultures. If uncertainty is defined as the degree to which a communication leaves its recipient in doubt about the true nature of the world, then it is a property both of the communication and of the recipient. It is hard for the originator to control or minimize uncertainty, particularly when the recipient, like Churchill, has a political agenda.

In Picturing the Uncertain World, Howard Wainer approaches this problem through stories, and every one is a gem. This is territory that has long been dominated by the books of Edward Tufte—particularly The Visual Display of Quantitative Information (1983), Envisioning Information (1990), Visual Explanations (1997) and Beautiful Evidence (2006)—but Wainer’s approach is refreshingly different. He has himself been involved in many policy debates and understands well that the same information can be interpreted in a variety of ways to support widely divergent positions. As an employee of the National Board of Medical Examiners, he is particularly familiar with debates over the large-scale testing of scholastic aptitude and its political ramifications.

Wainer devotes the book’s first chapter to the consequences of varying sample size and to what he calls de Moivre’s equation. Named for Abraham de Moivre (1667–1754), the equation yields the standard deviation of the sampling distribution of the mean. Wainer provides several examples of misunderstandings that can arise from ignorance of this equation. A map showing U.S. counties with low death rates from kidney cancer reveals that many of them are located in the High Plains. One might infer that these low rates are the result of the region’s cleaner air and water or the rural lifestyle of its inhabitants—but as Wainer explains, a map showing counties with high rates of kidney cancer reveals that many of them are also in the High Plains, right alongside the counties with low rates. This is just what one would expect: Both of the extremes are likely to be found in small, low-density populations such as those of the Plains counties. Wainer also argues that the Small Schools Movement of the late 1990s, which invested billions in breaking up large schools, was based in part on a similar misinterpretation of evidence: Much was made of the fact that small schools were overrepresented among the schools that had the highest scores on certain tests, whereas it was little remarked that small schools were also overrepresented among the lowest-scoring schools (as would be expected, because smaller schools will show greater variation in performance).

This first chapter establishes the pattern of the book: Wainer provides well-written and well-illustrated anecdotes, some of which are grounded in the theory of statistics, but most of which rely on intuition. Some center on graphical display, and the general principles Wainer extracts from these stories pay homage not just to Tufte but also to the earlier work of the French graphical theorist Jacques Bertin and the even earlier work of William Playfair and Francis Galton.

Not all of these narratives address uncertainty, however. Chapter 18, “When Form Violates Function,” recalls a 2003 article in Wired magazine that included a graph patterned after Charles Joseph Minard’s well-known plot of Napoleon’s 1812 campaign (described by Tufte as “the best graph ever produced”). The purpose of the graph in Wired was to illustrate the corporate disaster that followed the AOL–Time Warner merger of 2000. None of the information presented is uncertain, but Wainer shows that it could have been communicated more effectively with different graphics.

Despite its title, Picturing the Uncertain World is not a book solely about graphical display and uncertainty. And despite its subtitle, it does not offer much in the way of guidance on controlling uncertainty. Instead, the reader is left largely to his or her own devices regarding the general principles to be extracted and the lessons to be learned. But communication is both art and science, and principles are few and far between. The value of the book lies elsewhere, in the themes and rhetorical questions that crop up throughout. Why, for example, did William Playfair (1759–1823) invent many of the types of graphical display now in use but miss the scatter plot? And why, asks Wainer, citing the New York Times, do the news media often produce graphs and plots that are better—that is, less open to misinterpretation—than those produced by academics?

Line charts drawn by the Jewish residentsClick to Enlarge ImageThe final chapter, “Numbers and the Remembrance of Things Past,” provides the book’s capstone: the story told by the data collected by inhabitants of the Kovno ghetto in Lithuania during the Nazi occupation in 1941. Uncertainty is not the issue raised by their meticulous demographic statistics; the tables and graphs they produced were equally effective at communicating, and memorializing, the awful history. Rather, this is a story about the interplay between fact and emotion, about the human need to create a factual record even in the direst of circumstances, when the creators of the record knew full well that they were about to become statistics themselves. Emotions do not necessarily scale with objective measures of the magnitude of an event; the memorial to the 168 victims of the Oklahoma City bombing of 1995 may be every bit as moving as the Vietnam memorial with its 58,261 names. As Wainer writes,

Worthy memorials draw on both fact and emotion. We should not underestimate the power of even simple numerical displays to help bridge the gap between a statistic and a tragedy.

In the final analysis, then, this book is not so much about uncertainty or graphical display as about the communication of facts, and the interplay of that information with interpretation, emotion and the many other subjective dimensions of the human experience. Picturing the Uncertain World will appeal to a wide audience, because its arguments are accessible and intuitive, and the occasional references to statistical theory are handled very gently. Like two of Wainer’s earlier books—Visual Revelations: Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot (1997) and Graphic Discovery: A Trout in the Milk and Other Visual Adventures (2005)—this one makes for very fine reading and would be an excellent text for a general-education seminar.

Michael Goodchild is professor of geography and director of the Center for Spatial Studies at the University of California, Santa Barbara. Much of his recent research has focused on the description and modeling of uncertainty in maps and geospatial information.

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