*Investigations:
Stephen Stigler*

**Stephen
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.

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.
**