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Investigations: Stephen Stigler

image: Research headerStephen Stigler's new book challenges researchers to show him the numbers. The statistician argues that people, not numbers, lie. He values opinions and theories that are backed by vetted evidence.

Apple orchards and statistical theories may appear unrelated. But Stephen M. Stigler, the Ernest DeWitt Burton distinguished service professor in statistics and a member of the Committee on the Conceptual Foundations of Science, has found a connection. The topics come up as he explains the purpose of a wooden, rectangular box, filled with beads and rows of tiny pins, that sits atop a filing cabinet in his Eckhart Hall office. Called a quincunx, the first such box was made in 1873 for the scientist Francis Galton, who designed it to provide a lesson in probability.

image: Stephen Stigler (photo by Matthew Gilson)Stigler picks it up and demonstrates how the beads, by chance, consistently form a bell-shaped curve as they fall through the matrix and bounce off the pins. The arrangement of the pins--in groups of five, they form rectangles with one pin at each corner and one in the middle--is the literal definition of "quincunx." It also happens to be the same formation used in planting trees in an orchard.

"The practice, as well as the name," explains Stigler, "goes back to the ancient Romans. It maximizes the number of trees that can be planted in a given area, while maintaining a minimum distance among them."

Stigler overlaps other seemingly divergent worlds with that of statistics in his latest book, Statistics on the Table: The History of Statistical Concepts and Methods (Harvard). The book collects Stigler's essays--some previously published, others fresh or revised--on past debates and discoveries that have involved the use of statistics. While Stigler calls his earlier effort, The History of Statistics: The Measurement of Uncertainty before 1900 (Harvard, 1993), a "treatise" on the development of the discipline, he concedes that in the new book--intended primarily for statisticians and quantitative social scientists--he goes "a little bit afield," discoursing on the temperance movement, fingerprint identification, probability, eponymy, and coin minting.

"I hope the book will spread awareness of the richness of the history of statistics," he says. "I started out in theoretical work and then my interest in the history of the subject grew as I saw how it gives me and my colleagues and students a better understanding of the modern subject. This field touches almost everything."

In the introduction to Statistics on the Table, Stigler explains that the book's title comes from a 1910 letter to the Times of London written by Karl Pearson, a prominent English statistician whose work has always intrigued the professor (one of the original calculators used in Pearson's laboratory is now displayed on Stigler's desk). In the letter, Pearson tells economists critical of his statistical evaluation of how alcohol use affects child--rearing that if they wish to dispute his findings, they must put their own "statistics on the table, please."

In the first essay, Stigler documents the debate that raged among Pearson and other scholars, including John Maynard Keynes, over the validity of Pearson's conclusions that parental alcoholism does not necessarily have disastrous consequences for children's health. The book's other 21 essays continue to underscore Stigler's larger point: Statistics should indeed be on the table--and have been--in not only scientific but also historical, literary, and religious arguments.

"Almost all public debates could benefit from statistical insights," says Stigler. "Anywhere measurements are taken and policies made, statistics come in. People point fingers at the misuse of statistics all the time, but you shouldn't say the numbers are no good. Rather, it's that the lies of the people using them are easier to point out when they're expressed numerically."

Stigler's cumulative research for the book, which ends with a 42-page bibliography, spans decades and took him all over the world. He scoured archives and searched rolls of microfilm records at London's University College and at American universities, including Harvard and the University of California, Berkeley, his doctoral alma mater. He also traveled to Paris and Adelaide, Australia, and corresponded with rare-book dealers who had copies of relevant studies and other manuscripts. "There were a lot of surprises along the way," he says. "Many of these essays were the results of surprises."

For example, Stigler recalls how he came across the word "pyx" while catching up on some reading at the beginning of a winter break in 1975. He wondered why he had never before heard of such a perfect three-letter word for Scrabble. His curiosity was piqued even more when he looked the word up and discovered that it meant, according to Merriam Webster's Collegiate Dictionary, either "a container for the reserved host" or "a box used in a mint for deposit of sample coins reserved for testing weight and fineness."

The words "sample" and "testing" led him into an "intense two-week period" in which he sought all the information he could find on the second meaning of pyx. "It fortunately was during a break, when I could pursue it!" he jokes. He eventually found himself in the vault of the Royal Mint in London, examining materials from an ancient ceremony called the Trial of the Pyx, in which sample coins placed in the pyx at the end of several production cycles are taken out, counted, weighed, and assayed. "Here I was being shown their most sacred treasures from a ceremony that has been going on for 800 years," he recalls, noting that the trial provides a rare example of a long-running quality-control program in which modern statistical concepts such as sampling have been used since the Middle Ages.

Stigler says he is now "trying to come to grips with the tremendous and exciting growth in statistics through the 20th century." He's interested in the relationship between statistical methods and the questions they are designed to answer in economics, genetics, and the social and physical sciences. His current projects include researching the work of geneticist and statistician Ronald A. Fisher, who advanced the design of statistical experiments during the first half of the 20th century. He's also looking at scientific literature to discern whether economists learn more from statisticians or vice versa.

Continuing his practice of finding a statistical angle to just about anything, Stigler is also addressing why golfer Greg Norman fell apart at the end of the 1996 Masters Tournament, after leading most of the way. "He was done in by a century-old statistical concept called regression," posits Stigler. The regression effect, he says, shows up when, for example, tall parents have a child who is closer to average height or when a student scores well on standardized tests but gets only average grades in school.

"It's a problem with measuring the degree to which people are really good or just lucky," he says. "There's a neat example of this effect in golf tournaments. There's a tendency for the measured performance of early leaders to change over the course of a four-day golf tournament." He plans to illustrate this point by gathering data on the scores of all participants in five years of four major tournaments, and then modeling the data to estimate the magnitude of the regression effect.

As for Norman's 1996 loss, Stigler suspects, "his luck just ran out."--C.S.

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