Graphic Discovery

Howard Wainer is Distinguished Research Scientist for the National Board of Medical Examiners and Adjunct Professor of Statistics at the Wharton School of the University of Pennsylvania. He is the author of fifteen other books.

Preface xiii Introduction 1 In the sixteenth century, the bubonic plague provided the motivation for the English to begin gathering data on births, marriages, and deaths. These data, the Bills of Mortality, were the grist that Dr. John Arbuthnot used to prove the existence of God. Unwittingly, he also provided strong evidence that data graphs were not yet part of a scientist's tools. Part I: William Playfair and the Origins of Graphical Display Chapter 1: Why Playfair? 9 All of the pieces were in place for the invention of statistical graphics long before Playfair was born. Why didn't anyone else invent them? Why did Playfair? Chapter 2: Who Was Playfair? 20 by Ian Spence and Howard Wainer William Playfair (1759-1823) was an inventor and ardent advocate of statistical graphics. Here we tell a bit about his life. Chapter 3: William Playfair: A Daring Worthless Fellow 24 by Ian Spence and Howard Wainer Audacity was an important personality trait for the invention of graphics because the inventor had to move counter to the Cartesian approach to science. We illustrate this quality in Playfair by describing his failed attempt to blackmail one of the richest lords of Great Britain. Chapter 4: Scaling the Heights (and Widths) 28 The message conveyed by a statistical graphic can be distorted by manipulating the aspect ratio, the ratio of a graph's width to its height. Playfair deployed this ability in a masterly way, providing a guide to future display technology. Chapter 5: A Priestley View of International Currency Exchanges 39 A recent plot of the operating hours of international currency exchanges confuses matters terribly. Why? We find that when we use a different graphical form, developed by Joseph Priestley in 1765, the structure becomes clear. We also learn how Priestley discovered the latent graphicacy in his (and our) audiences. Chapter 6: Tom's Veggies and the American Way 44 European intellectuals were not the only ones graphing data. During a visit to Paris (and prompted by letters from Benjamin Franklin), Thomas Jefferson learned of this invention and he later put it to a more practical use than the depiction of the life spans of heroes from classical antiquity. Chapter 7: The Graphical Inventions of Dubourg and Ferguson: Two Precursors to William Playfair 47 Although he developed the line chart independently, Priestley was not the first to do so. The earliest seems to be the Parisian physician Jacques Barbeau-Dubourg (1709-1779), who created a wonderful graphical scroll in 1753. Graphical representation must have been in the air, for the Scottish philosopher Adam Ferguson (1723-1816) added his version of time lines to the mix in 1780. Chapter 8: Winds across Europe: Francis Galton and the Graphic Discovery of Weather Patterns 52 In 1861, Francis Galton organized weather observatories throughout Western Europe to gather data in a standardized way. He organized these data and presented them as a series of ninety-three maps and charts, from which he confirmed the existence of the anticyclonic movement of winds around a low-pressure zone. Part II: Using Graphical Displays to Understand the Modern World Chapter 9: A Graphical Investigation of the Scourge of Vietnam 59 During the Vietnam War, average SAT scores went down for those students who were not in the military. In addition, the average ASVAB scores (the test used by the military to classify all members of the military) also declined. This Lake Wobegon-like puzzle is solved graphically. Chapter 10: Two Mind-Bending Statistical Paradoxes 63 The odd phenomenon observed with test scores during the Vietnam War is not unusual. We illustrate this seeming paradox with other instances, show how to avoid them, and then discuss an even subtler statistical pitfall that has entrapped many illustrious would-be data analysts. Chapter 11: Order in the Court 72 How one orders the elements of a graph is critical to its comprehensibility. We look at a New York Times graphic depicting the voting records of U.S. Supreme Court justices and show that reordering the graphic provides remarkable insight into the operation of the court. Chapter 12: No Order in the Court 78 We examine one piece of the evidence presented in the 1998 murder trial of State v. Gibbs and show how the defense attorneys, by misordering the data in the graph shown to the judge, miscommunicated a critical issue in their argument. Chapter 13: Like a Trout in the Milk 81 Thoreau pointed out that sometimes circumstantial evidence can be quite convincing, as when you find a trout in the milk. We examine a fascinating graph that provides compelling evidence of industrial malfeasance. Chapter 14: Scaling the Market 86 We examine the stock market and show that different kinds of scalings provide the answers to different levels of questions. One long view suggests a fascinating conjecture about the trade-offs between investing in stocks and investing in real estate. Chapter 15: Sex, Smoking, and Life Insurance: A Graphical View 90 We examine two risk factors for life insurance--sex and smoking--and uncover the implicit structure that underlies insurance premiums. Chapter 16: There They Go Again! 97 The New York Times is better than most media sources for statistical graphics, but even the Times has occasional relapses to an earlier time in which confusing displays ran rampant over its pages. We discuss some recent slips and compare them with prior practice. Chapter 17: Sex and Sports: How Quickly Are Women Gaining? 103 A simple graph of winning times in the Boston Marathon augmented by a fitted line provides compelling, but incorrect, evidence for the relative gains that women athletes have made over the past few decades. A more careful analysis provides a better notion of the changing size of the sex differences in athletic performances. Chapter 18: Clear Thinking Made Visible: Redesigning Score Reports for Students 109 Too often communications focus on what the transmitter thinks is important rather than on what the receiver is most critically interested in. The standard SAT score report that is sent to more than one million high school students annually is one such example. Here we revise this report using principles abstracted from another missive sent to selected high school students. Part III: Graphical Displays in the Twenty-first Century The three chapters of this section grew out of a continuing conversation with John W. Tukey, the renowned Princeton polymath, on the graphical tools that were likely to be helpful when data were displayed on a computer screen rather than a piece of paper. These conversations began shortly after Tukey's eighty-fourth birthday and continued for more than a year, ending the night before he died. Chapter 19: John Wilder Tukey: The Father of Twenty-first-Century Graphical Display 117 Chapter 20: Graphical Tools for the Twenty-first Century: I. Spinning and Slicing 125 Chapter 21: Graphical Tools for the Twenty-first Century: II. Nearness and Smoothing Engines 134 Chapter 22: Epilogue: A Selection of Selection Anomalies 142 Graphical displays are only as good as the data from which they are composed. In this final chapter we examine an all too frequent data flaw. The effects of nonsampling errors deserve greater attention, especially when randomization is absent. Formal statistical analysis treats only some of the uncertainties. In this chapter we describe three examples of how flawed inferences can be made from nonrandomly obtained samples and suggest a strategy to guard against flawed inferences. Conclusion 150 Dramatis Personae 151 This graphical epic has more than one hundred characters. Some play major roles, but most are cameos. To help keep straight who is who, this section contains thumbnail biographies of all the players. Notes 173 References 177 Index 185