## “Picturing the Uncertain World” – A New Book on Statistical Graphics by Howard Wainer

I try to read every new book that’s written about data visualization. This is possible because the field is still represented by a relatively small number of experts who take the time to write books. The most recent addition to my library is Howard Wainer’s new book titled *Picturing the Uncertain World: How to Understand, Communicate, and Control Uncertainty through Graphical Display*. Wainer is a longtime expert in statistical graphics who works as a research scientist for the National Board of Medical Examiners and as an adjunct professor of statistics at the Wharton School of the University of Pennsylvania.

Picturing the Uncertain World. Howard Wainer,

Princeton University Press, 2009.

The first thing I should say about this book is that you shouldn’t misunderstand the title as I did initially. Without giving it enough thought, I excitedly assumed that the book focused specifically on visual means to represent levels of uncertainty in graphs. People quite often ask me if there are better ways to do this than error bars, which is a great question that I haven’t taken the time to thoroughly investigate. I was hoping that Wainer had done this for me. It is probably no surprise to those of you who are statisticians, however, that Wainer is using the term “uncertainty” in the sense that all statistical information is uncertain—statistics after all is the “science of uncertainty”. The book isn’t specific in any sense; it addresses a broad, disparate set of issues pertaining to the graphical representation of statistical data.

Similar to Tufte’s books, this is a collection of Wainer’s ideas, stories, and examples, which meanders freely through the landscape of statistical graphics. Both Tufte and Wainer are exceptional thinkers and writers who sprinkle their books with marvelous insights, but neither write books to address a specific topic in a cohesive way. *Picturing the Uncertain World* is a compilation of articles that Waimer wrote over the course of 11 years (1996 through 2007), mostly for the statistics journal *Chance*.

Before commenting further on the content of Wainer’s book, I’d like to mention that, unlike many books in the field, at $29.95 this book is quite affordable. Princeton University Press resisted the temptation to which academic publishers often succumb, which is to price the book beyond the reach of all but university libraries. They accomplished this, however, by paying less attention to the book’s design and printing than a book about graphics deserves. Unlike my books and Tufte’s, Princeton University Press produced Wainer’s book on the cheap. One example of the difference is that Tufte and I both work hard to place figures as close as possible to the text that references them, which involves a lot of time and expense. This prevents the annoying experience of readers having to flip through pages to find the figure and then having to find their way back to the place they left off in the text, which undermines the learning experience.

Now, on to the book’s content. This book is for statisticians. It assumes a fairly high level of statistical fluency, yet I’m not sure that Wainer fully appreciates this fact. About two-thirds of the way into the book in a chapter on statistical error, after using statistical terms and concepts throughout, Wainer includes a section titled “A Brief Tutorial on Statistical Error.” It struck me as odd that he didn’t recognize the need for any tutorials until then. In this sole attempt to inform the uninitiated (that is, readers who either never took “an introductory statistics course” or took one but no longer remember the material), he exclusively covers the calculation of statistical error (hypothesis testing, Type 1 and Type 2 errors, the problem of multiplicity, the Bonferroni method, sensitivity analysis, resampling, multiple imputation, and standard error). Wainer’s rapid tour of statistical error left my head spinning. I felt as if I’d been stomped on by the “Bonferonni method,” which left me in need of some “sensitivity analysis.”

The inside flap of the book jacket concludes with these words: “We live in a world full of uncertainty, yet it is within our grasp to take its measure. Read *Picturing the Uncertain World* and learn how.” This is a bit misleading. Only those who already possess a fairly good understanding of statistics will find this book accessible. Those who don’t will be left gasping like fish on dry land. Statisticians will no doubt enjoy Wainer’s examples and insights, but others will need to take a course (or two or three) before learning much other than how uninformed they are about statistics.

Please don’t misunderstand me. I’m not saying don’t buy this book. I’m merely trying to define the audience that will find it most worthwhile. Although I struggled a bit, I found several sections fascinating and useful. More than the articles, the two parts of the book that spoke to me most compellingly were the “Introduction and Overview” in the beginning and the “Epilogue” at the end, where Wainer the man shines through with grace, warmth, humility, and passion. The fact that he cares deeply about his work and longs to leave the world better off than he found it is evident. I appreciate this and Wainer’s fine service to the world and the statistical graphics community in particular.

Take care,

## 2 Comments on ““Picturing the Uncertain World” – A New Book on Statistical Graphics by Howard Wainer”

Steve,

I read your review with interest, and was inspired to buy a copy of Picturing the Uncertain World. I thought I’d drop you a line to let you know how I’ve got on.

I have enjoyed the first half of the book, but am becoming frustrated by it. I’ve just finished chapter 11, Improving Data Displays. This is a rich field but this chapter has been the weakest so far.

The chapter concludes with an analysis of a graphic from the NY Times in which the value of acquisitions by China and the number of acquisitions by China are displayed over a period of seventeen years. The value of acquisitions rises exponentially over the period, whilst the volume rises in a roughly linear way.

I felt cheated by the two scatter plots that Wainer has produced to replace the original. The log of the value is plotted over time, and we see a linear relationship emerge, but how, from this, are we to derive “a quantitative measure of how China’s acquisitiveness has changed.”

Another criticism would be the parochialism of the examples, almost all of which are drawn from the US. I don’t object to this, and if the audience for his aricles was American, then this makes sense. As an English reader, though, I found that a couple of chapters on SATs left me feeling bored, and wishing that he could have drawn upon evidence from further afield.

Finally, I would agree that the book lacks cohesion or fluency between chapters. I suspect that this is because the book is adapted from articles, but presented in book form.

Half way through the book I worry that I’ve been spoilt by reading Tufte first. Wainer shows little of the dramatic flair or global breadth of reading evident in Tufte’s books. I suppose this is to be expected: in a class with someone as exceptional as Tufte, regression to the mean suggests that is unlikely that another above average author will be better.

Perhaps that sounds a little harsh, I’m glad to have bought the book, and will endeavour to finish it.

I’d be interested to hear what any other of your readers have made of it, especially any who have not read Tufte first, or who have preferred it to Tufte,

Robert Meekings

I’ve now read the whole book, and thought it was only fair to come and update my earlier comment. A book of two halves: and I found the second half much the more enjoyable. I’m reminded of Umberto Eco who apparently made the first hundred pages impenetrable to deter unworthy readers from the riches in store later. Worth persevering with.

Robert

PS: I had the thought of displaying Minard’s chart of Napoleon’s march on Russia using a gapminder.org motion chart, but found that it had been done before: http://understandinguncertainty.org/node/208. It’s just a shame the motion chart doesn’t allow a backgound image of the map to be displayed.