#### Statistician, 1919-2005

William Kruskal, an authority on theoretical statistics who helped the U.S. government bring statistical methods to bear on public policy issues, died of pneumonia on Thursday, April 21, at Bernard Mitchell Hospital in Chicago. He was 85.

Kruskal, the Ernest DeWitt Burton Distinguished Service Professor Emeritus in Statistics and the Harris Graduate School of Public Policy Studies at the University of Chicago, had also co-devised a technique that was incorporated into every major statistical package in use today.

President Richard Nixon appointed Kruskal to his Presidential Commission on Federal Statistics in 1970. The 15-member commission conducted a comprehensive review of the compilation and use of statistics by the federal government, the first such review that had taken place in 20 years.

"He talked about creating a permanent committee to address the kinds of problems the president's commission had laid out on an ongoing basis," said Stephen Fienberg, the Maurice Falk university professor of statistics and social science at Carnegie Mellon University. "Bill was the one who carried that idea out and really forcefully brought it to reality. It wasn't quite single-handed, but it was close."

Kruskal subsequently became the first chairman of the National Research Council's Committee on National Statistics, a position he held from 1971 to 1978. The committee was charged with evaluating statistical issues for the U.S. government, including citizens' attitudes and behavior toward the census. Fienberg, who chaired the committee in the early 1980s, said Kruskal introduced him and many others in academia to the field of statistics and public policy. "I owe him a great debt," Fienberg said.

Along with W. Allen Wallis, the founding Chairman of the University of Chicago's Statistics Department, Kruskal devised the Kruskal-Wallis test. "The test is found today under that name as part of every major statistical computation system," said Stephen Stigler, the Ernest DeWitt Burton Distinguished Service Professor of Statistics at the University of Chicago.

"The Kruskal-Wallis test was able to examine a set of data from several groups of subjects and test for potential differences among the groups," Stigler said. "The test had the great advantage of simplicity, in that it depended only upon the rank order of the observations, not upon their exact values." For example, in comparing groups of individuals' responses in a psychological study, it would be enough to say for every pair of responses which was larger. It would not be necessary to determine how much larger.

With another Chicago colleague, Leo Goodman, Kruskal co-authored a series of classic papers that brought a new sophistication to measuring the association between a pair of qualitative attributes--hair color and eye color, for example--that might occur in a given population.

Kruskal also was noted for some purely theoretical work that Stigler characterized as elegant and almost Einsteinian in its co-ordinate-free approach to what are called "linear statistical methods." Albert Einstein provided new insights to physics by showing that measurements of space and time vary relative to their frame of reference. Likewise, Kruskal freed statisticians from relying on vision-clouding frames of reference. "He was able to illuminate the underlying nature of certain statistical problems with a clarity that was not available when tied to a specific arbitrary choice of frame of reference," Stigler explained.

Colleagues characterized Kruskal's academic interests as encyclopedic. Indeed, he put these interests to use as associate editor for statistics of the International Encyclopedia of the Social Sciences from 1962 to 1968, and co-editor of the International Encyclopedia of Statistics in 1978.

"He was interested in everything, and so he read everything that crossed his desk, all kinds of periodicals, and he sent copies to everybody that he thought might be interested," said Judith Tanur, Kruskal's co-editor of the International Encyclopedia of Statistics. "I'm very sad at losing him. It's the ending of an era," said Tanur, the distinguished teaching professor of sociology at the State University of New York at Stony Brook.

Kruskal's wide-ranging interdisciplinary research and leadership reached across three academic divisions at the University of Chicago over the decades. He was a founding faculty member of the Department of Statistics in the Physical Sciences Division and served as department Chairman from 1966 to 1973. "He played a vital role in building up the new Department of Statistics and establishing an unusually effective collegiality within the department that survives him," Stigler said.

Kruskal further served the University as Dean of the Social Sciences Division from 1974 to 1984, and as Interim Dean of the newly established Irving B. Harris Graduate School of Public Policy Studies from 1988 to 1989.

"He was a man utterly committed to the highest standards of academic excellence," said Hanna Gray, President Emeritus and the Harry Pratt Judson Distinguished Service Professor Emeritus in History at the University of Chicago. "The division certainly thrived, as it has ever since in the quality and creativity of its faculty."

Gray lauded Kruskal as "a tremendously good citizen of the University." She noted that he served on the executive committee of the University's governing body in the late 1960s, a time of considerable turmoil at the University of Chicago and other campuses across the country. "He was one of the thoughtful people who helped to make the faculty governance of the institution under the leadership of President Edward Levi, something that really worked in those conditions," Gray said.

Kruskal was born in New York City on Oct. 10, 1919. He was the oldest of three boys and two girls. His father, Joseph Kruskal, owned Kruskal & Kruskal, which was for many decades the nation's largest wholesale fur business.

His mother, Lillian Vorhaus Kruskal, later became famous as Lillian Oppenheimer, founder of what is today called Origami USA, co-authoring books on origami and making numerous television appearances to promote the art of paperfolding.

The three Kruskal sons all went on to research careers in related fields. "Bill, Martin and I all started as mathematicians, but Bill moved completely into statistics, I moved partially into statistics and Martin moved partially into physics," said Joseph Kruskal Jr., now retired from Bell Laboratories.

Martin Kruskal, a professor emeritus of mathematics at Princeton University, now at Rutgers University, in 1993 received the National Medal of Science, the nation's highest award for scientific achievement. Joseph Kruskal is the former president of two scientific societies. In 1956 he formulated a mathematical theorem that has become widely known in computer science as "Kruskal's theorem."

William Kruskal first attended Antioch College and then Harvard University, receiving his bachelor's degree in mathematics and philosophy with summa cum laude honors in 1940. He then received his master's degree in mathematics from Harvard in 1941 and his Ph.D. in mathematical sciences from Columbia University in 1955.

Kruskal was a mathematician at the U.S. Naval Proving Ground in Dahlgren, Va., from 1941 to 1946, and worked for Kruskal & Kruskal from 1946 to 1948. He was a lecturer in mathematics at Columbia University in 1949 and 1950. He joined the University of Chicago faculty as an instructor in statistics in 1950, later taking brief appointments as a visiting professor at the University of California, Berkeley, and at Harvard University. Kruskal was named the Ernest DeWitt Burton Distinguished Service Professor in Statistics in 1973. He retired as Professor Emeritus in 1990.

He was president of the Institute of Mathematical Statistics in 1971, and of the American Statistical Association in 1982. The institute is the major international professional society concerned with theoretical statistics. It publishes The Annals of Mathematical Statistics, which Kruskal edited from 1958 to 1961.

Kruskal, who received many honors, was elected a fellow of the Institute of Mathematical Statistics, the American Statistical Association, the American Association for the Advancement of Science, and the American Academy of Arts and Sciences.

Kruskal married Norma Evans in 1941. She died in 1992. He is survived by their three sons, Vincent of Harrison, N.Y.; Thomas of Sudbury, Mass.; and Jody of New York City; a sister, Rosaly Yevnin of Jerusalem, Israel; two brothers, Martin David of Princeton, N.J., and Joseph of Maplewood, N.J.; and five grandchildren, Lily, Watertown, Mass.; Peter, Sudbury, Mass.; Michael and Elliot, Harrison, N.Y.; and Zachary, New York City.

May 04, 2005 University of Chicago