You are here

Graphic Discovery: A Trout in the Milk and Other Visual Adventures

Howard Wainer
Princeton University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Raymond N. Greenwell
, on

During a dairyman's strike in 19th century New England, when there was suspicion of milk being watered down, Henry David Thoreau wrote, "Sometimes circumstantial evidence can be quite convincing; like when you find a trout in the milk." Howard Wainer uses this as metaphor in his entertaining, informative, and persuasive book on graphs, or the visual communication of information. Sometimes a well-designed graph tells a very convincing story.

Wainer's book is in the spirit of Edward R. Tufte's The Visual Display of Quantitative Information, to which Wainer acknowledges a debt of gratitude. Both books explore what makes makes a graphic good or bad, with lots of examples from the last two centuries. In his preface, Wainer claims that "no one else has stirred together this mixture of historical and future graphical practice with a nuage of modern statistics to produce a visual pudding whose breadth of theme is more than made up for by its rich texture and its savory tang." His claim is valid; this book is a significant contribution to the genre that Tufte has pioneered.

The book is divided into three parts. Part I is historical, focusing on the critical role played by William Playfair (brother of mathematician John Playfair) in introducing the world to the value of graphics. We learn of several predecessors to Playfair (Pliny, Christiaan Huygens, Robert Plot, Joseph Priestley, Jacque Barbeau-Dubourg, and Adam Ferguson), one contemporary of Playfair (Thomas Jefferson), and one successor of Playfair (Francis Galton) who created exemplary graphics that were noteworthy for their time. But it's Playfair whose Commercial and Political Atlas, according to Wainer, "forever changed the way that we look at data." Playfair had a knack for portraying data in a way that made a point clearly and convincingly. He invented the pie chart (which Tufte loathes) and was the first to apply the line and bar graph to economic data. Wainer creates an intriguing portrait of a creative and practical man who was also a bit of a rogue.

Skipping for a moment to Part III of the book, we find another innovator portrayed, the great statistician John Wilder Tukey, who died in 2000 while Wainer was working on the book. Wainer had numerous conversations with Tukey during the last year of Tukey's life, and his fondness and admiration for Tukey make some of the reading poignant and touching. Tukey is most well-known for his work in "Exploratory Data Analysis" (one of the many phrases and terms he coined, along with bit, software, ANOVA, and stem-and-leaf diagram). Wainer pursued with Tukey the future of graphical display. The greatest promise comes from the use of the computer in interactive analysis, which allows motion to convey meaning. Wainer gives four examples: rotatable scatterplots (so that the varying viewpoint might reveal hidden patterns), slicing engines (a complicated idea which Wainer makes clear by an example), nearness engines (to measure how close points are to each other in various dimensions), and smoothing engines (to filter out noise).

In between these two parts is Part II, an assortment of observations on descriptive statistics. Some topics are not specifically visual, such as Simpson's paradox, but Wainer uses graphical analysis to help illustrate what's happening with this paradox. Similarly, he uses graphics when explaining regression to the mean, with controversial conclusions regarding affirmative action. Wainer rejoices in controversy, taking on The New York Times (which he admittedly loves) and the Educational Testing Service (for which he once worked). His prose is witty and persuasive.

Wainer can't seem to stop himself from fulminating, nor would we want him to. In the midst of a discussion of Playfair's use of scale, he takes on the controversy of whether the Supreme Court decision on Brown v. Board of Education resulted in an increase in private elementary schools. At the end of the book, after his tribute to Tukey, Wainer tacks on one last chapter providing four statistical anomalies that should be in every statistics teacher's bag of tricks.

Some of the chapters seem in random order; some seem to assume that the reader didn't read earlier chapters. It may be tempting to skip the footnotes, since many contain minor details, but a few containing interesting anecdotes, and one contains three figures that surely should have been included in the main text.

At the end is a section entitled "Dramatis Personae" containing brief biographical sketches of the many people mentioned in the book, from playwright Edward Albee to fictional Alexis Zorba (the Greek). Even Peter Lawrence ("Yogi") Berra makes the list because of his quote, "You can see a lot just by looking." True enough, but as Tukey once said, "A picture may be worth a thousand words, but it may take a hundred words to do it."


Edward R. Tufte, The Visual Display of Quantitative Information (2nd ed.), Graphics Press, 1983, ISBN 0-9613921-4-2.

Raymond N. Greenwell ( is Professor of Mathematics at Hofstra University in Hempstead, New York. His research interests include applied mathematics and statistics, and he is coauthor of the texts Finite Mathematics and Calculus with Applications, both published by Addison Wesley.

The table of contents is not available.