Picturing the Uncertain World by Howard Wainer is a book about statistics and statistical thinking, aided by visual depictions of data. Each article in the collection starts by stating a question or phenomenon, which is then investigated further using some clever statistics.
I bought the book after Scott Murray pointed me to it as the source of his assertion that in order to show uncertainty, the best way was to use blurry dots. I was surprised by that, since my own work had shown people to be pretty bad at judging blurriness, so that didn’t seem to be a particularly good choice (at least if you want people to be able to judge the amount of uncertainty).
I had never heard of Howard Wainer before reading this book. It turns out that he has been an outspoken critic of bad charts for a long time, much longer than blogs have been around to do that. In fact, Wainer wrote an article for American Statistician in 1984 that could have been the blueprint for blogs like junk charts.
And it turns out that there is even a connection between Wainer and Kaiser Fung, who runs junk charts.
@eagereyes Howard introduced me to Tufte principles in my first stats course almost 20 yr ago!
— Kaiser Fung (@junkcharts) December 9, 2014
This is also interesting because the book reminded me of Kaiser’s Numbers Rule Your World and Numbersense. It all makes sense.
After Scott pointing it out, the book immediately intrigued me: had somebody figured out how to show uncertainty well? How did I not know about this? Well, it turns out he hasn’t. But there is a lot of other good stuff in this book that makes it very worthwhile.
Wainer’s idea of uncertainty is much broader than the usual error metrics (though he addresses those as well). In fact, he describes statistics as the science of uncertainty. That makes a lot of sense, and he makes the case repeatedly about how statistics provides means of dealing with uncertainty about facts and observations.
As a consequence, the book is really about statistical thinking, aided by visual depictions of the data. In several chapters, Wainer takes data and either redraws an existing chart, or argues that by simply looking at the data the right way, it becomes much easier to understand what is going on.
The key chapter from my perspective was chapter 13, Depicting Error. Wainer shows a number of ways to depict error, from tables to a number of charts. Some of these are well-known, others not. They are all interesting, though there isn’t much that is surprising (especially after having seen the Error Bars Considered Harmful paper by Michael Correll and Michael Gleicher at InfoVis earlier this year).
There is a lot of other good stuff in the book too, though. Chapter 16, Galton’s Normal, talks about the way the normal distribution drops to very, very small probabilities in the tails. It’s a short chapter, but it really drove home a point for me about how hard it is to intuitively understand distributions, even the ubiquitous normal distribution.
The final chapter, The Remembrance of Things Past, is probably the best. It’s the deepest, most human, and I think it has the best writing. It describes the statistical graphics produced by population of the jewish ghetto in Kovno, Lithuania, during the Holocaust. It’s chilling and fascinating, and the charts they created are incredible. Wainer does an admirable job of framing the entire chapter and navigating between becoming overly sentimental and being too sterile in his descriptions.
The book is really a collection of articles Wainer wrote for Chance Magazine and American Statistician in the mid–2000s (with one exception from 1996). As a result, it isn’t really more than the sum of its parts: it doesn’t have any cohesion between the chapters. But on the other hand, each chapter is a nicely self-contained piece, easy to read, and it’s easy to pick the book up to read a chapter or two. Wainer also writes very well. The chapters are easy to read, and his explanations of statistical phenomena and procedures are very good and easy to follow even if you don’t know much about statistics.
Ultimately, my question about the blurry dots was not answered, because Wainer points to Alan MacEachren’s book How Maps Work as the source of the blurriness argument. I can’t find my copy of that book at the moment though, so following this lead further will have to wait for another day.