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The William Kruskal Legacy 3 Statistical Science 2007, Vol. 22, No. 2, 255–261 DOI: 10.1214/088342306000000420 c Institute of Mathematical Statistics, 2007 The William Kruskal Legacy: 1919–20051 Stephen E. Fienberg, Stephen M. Stigler and Judith M. Tanur Abstract. William Kruskal (Bill) was a distinguished statistician who spent virtually his entire professional career at the University of Chicago, and who had a lasting impact on the Institute of Mathematical Statis- tics and on the field of statistics more broadly, as well as on many who came in contact with him. Bill passed away last April following an ex- tended illness, and on May 19, 2005, the University of Chicago held a memorial service at which several of Bill’s colleagues and collaborators spoke along with members of his family and other friends. This biog- raphy and the accompanying commentaries derive in part from brief presentations on that occasion, along with recollections and input from several others. Bill was known personally to most of an older generation of statis- ticians as an editor and as an intellectual and professional leader. In 1994, Statistical Science published an interview by Sandy Zabell (Vol. 9, 285–303) in which Bill looked back on selected events in his professional life. One of the purposes of the present biography and accompanying commentaries is to reintroduce him to old friends and to introduce him for the first time to new generations of statisticians who never had an opportunity to interact with him and to fall under his influence. Key words and phrases: Encyclopedias, Kruskal–Wallis test, measures of association, representative sampling. 1. A BRIEF BIOGRAPHY Stephen E. Fienberg is Maurice Falk University William Henry Kruskal was born in New York Professor of Statistics and Social Science in the Department of Statistics, the Center for Automated City on October 10, 1919, the oldest of three boys Learning and Discovery, and Cylab, all at Carnegie and two girls. His father, Joseph Kruskal, owned arXiv:0710.5063v1 [stat.ME] 26 Oct 2007 Mellon University, Pittsburgh, Pennsylvania Kruskal & Kruskal, which was for many decades the 15213-3890, USA e-mail: fi[email protected]. nation’s largest wholesale fur business. Bill’s mother, Stephen M. Stigler is Ernest DeWitt Burton Lillian Vorhaus Kruskal, later became famous as Lil- Distinguished Service Professor and Chairman, lian Oppenheimer, founder of what is today called Department of Statistics and the College, and member Origami USA, co-authoring books on origami and of the Committee on Conceptual and Historical Studies making numerous television appearances to promote of Science, University of Chicago, Chicago, Illinois the art of paperfolding. (She also taught origami at 60637, USA e-mail: [email protected]. Judith M. Tanur is Distinguished Teaching Professor Emerita, summer camp to Judy Tanur’s children.) Department of Sociology, State University of New York, The three Kruskal brothers all went on to research Stony Brook, New York 11794-4356, USA e-mail: careers in related fields. “Bill, Martin and I all started [email protected]. 1Discussed in 10.1214/088342306000000358, This is an electronic reprint of the original article 10.1214/088342306000000367, 10.1214/088342306000000376, 10.1214/088342306000000385, 10.1214/088342306000000394, published by the Institute of Mathematical Statistics in 10.1214/088342306000000402 and Statistical Science, 2007, Vol. 22, No. 2, 255–261. This 10.1214/088342306000000411. reprint differs from the original in pagination and typographic detail. 1 2 S. E. FIENBERG, S. M. STIGLER AND J. M. TANUR Fig. 2. “Bill, save this picture. You were so very proud of your cowboy suit with the gun.” Fig. 1. William H. Kruskal: 1919–2005. University in 1949–1950. He joined the University of Chicago faculty as an instructor in statistics in 1950 as mathematicians, but Bill moved completely into and progressed through the ranks to full professor. statistics, I moved partially into statistics and Martin Along the way, he took brief appointments as a visit- moved partially into physics,” noted Bill’s brother ing professor at the University of California, Berke- Joseph Kruskal, Jr., widely known for “Kruskal’s ley in 1955–1956, and at Harvard University in the theorem” in computer science and his work on multi- summer of 1959. Bill was named the Ernest DeWitt dimensional scaling, and now retired from Bell Lab- oratories. Bill’s other brother, Martin Kruskal, a professor emeritus of mathematics at Princeton Uni- versity and now at Rutgers University, in 1993 re- ceived the National Medal of Science, the nation’s highest award for scientific achievement. Bill first attended Antioch College and then trans- ferred to Harvard University, receiving his bachelor’s degree in mathematics and philosophy summa cum laude in 1940. He then received his master’s degree in mathematics from Harvard in 1941 and his Ph.D. in mathematical statistics from Columbia University in 1955. Bill was a mathematician at the U.S. Naval Prov- ing Ground in Dahlgren, Virginia, from 1941 to 1946, and worked for Kruskal & Kruskal from 1946 to Fig. 3. The Kruskal siblings: Bill, Molly, Rosaly, Martin 1948. He was a lecturer in mathematics at Columbia David and Joe. THE WILLIAM KRUSKAL LEGACY 3 Fig. 4. Western Union telegram from Kruskal to Wallis, accepting the initial appointment at the University of Chicago. Burton Distinguished Service Professor in Statistics (master’s degree in mathematics from Har- in 1973. His wide-ranging interdisciplinary research vard). Very well equipped and capable for and leadership reached across two academic divi- theoretical work in statistics, but prob- sions and a professional school at the University of ably more interested in applications. He Chicago over the decades. He was a founding fac- was at the Naval Proving Ground at ulty member of the Department of Statistics in the Dahlgren, Virginia during the war and, Physical Sciences Division and served as department therefore, had experience in the applica- Chairman from 1966 to 1973, playing a vital role in tion of mathematics to practical problems. building the new Department of Statistics and es- He is mature, conscientious and industri- tablishing an unusually effective collegiality within ous and has a pleasant personality. He has the department. He further served the University as made a good beginning on his Ph.D. the- dean of the Social Sciences Division from 1974 to sis work. Doubtful whether he can finish 1984, and as dean pro tempore of the newly estab- it by the end of this academic year. Age: 30 years. lished Irving B. Harris Graduate School of Public Policy Studies from 1988 to 1989. He retired as pro- [Wald died December 13, 1950.] Bill was appointed fessor emeritus in 1990. In separate commentaries, originally as instructor for a one-year period, Octo- Stephen Stigler comments on Bill’s role within the ber 1, 1950 to September 30, 1951. The formal offer department and Norman Bradburn focuses on Bill’s letter from Wallis (March 6, 1950) makes no refer- role as a citizen of the university and of the broader ence to a Ph.D. degree. Bill’s acceptance came just statistical and social science community. over a week later by telegram, reproduced here as A reference letter dated February 16, 1950 from Figure 4. Abraham Wald to W. Allen Wallis, founding chair- Bill was appointed an assistant professor for a man of the then Committee on Statistics (which three-year term as of October 1, 1951 and reap- later became the Department of Statistics), included pointed on December 14, 1953 for another three-year the following comments: term. There is no mention of his Ph.D. degree in the proposal letter from Wallis or in the Dean’s ap- Very gifted and intelligent. Belongs in the pointment letter. Bill was a perfectionist and it was upper 5 percent of our graduate students. not until 1955 that he submitted the final version Has a very good mathematical background of his thesis and received his Ph.D. (Departments 4 S. E. FIENBERG, S. M. STIGLER AND J. M. TANUR Fig. 5. Bill and other statistics faculty with Jerzy Neyman in 1959 on the occasion of Neyman’s receipt of an honorary degree from the University of Chicago. were then clearly more forgiving of such matters returning to first principles, brought new insight to than they are today.) Bill went on leave to Berkeley measuring the association between pairs of qualita- for the 1955–1956 academic year and Wallis initiated tive attributes. These appeared over a 18-year pe- his promotion to associate professor with indefinite riod in JASA, beginning in 1954, and were later re- tenure that fall, informing the dean of the threat published in book form in 1979. Goodman describes that Bill might stay at Berkeley. Bill’s promotion some of their work and interactions in an accompa- became official in December 1956 and took effect on nying commentary. Bill also wrote a separately au- October 1, 1957. thored piece in JASA on ordinal measures of associ- Bill became editor of The Annals of Mathemati- ation which dovetailed with the Goodman–Kruskal cal Statistics in 1958 and he served in that capacity work. until 1961. This, however, was only the beginning Throughout this period, Bill worked on and off of Bill’s career as an editor, an activity to which he on his coordinate-free approach to linear statistical returned repeatedly throughout his career. He was models. Although he published only three brief pa- president of the Institute of Mathematical Statistics pers on the topic, he also developed what became in 1970–1971 and of the American Statistical Asso- a legendary set of unpublished class notes elaborat- ciation in 1982. Along with senior colleague W. Allen Wallis, Bill ing on the ideas.
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