arXiv:0710.5063v1 [stat.ME] 26 Oct 2007 tn ro,NwYr 19-36 S e-mail: USA 11794-4356, York, York New New of Brook, University Stony State Sociology, Emerita, Professor of Teaching Department Distinguished is Tanur M. Illinois e-mail: Chicago, USA Chicago, 60637, Studies of Historical University and Science, Conceptual member of on and Committee College, the the of and Statistics of Chairman, Department Burton and Professor DeWitt Service Ernest Distinguished is Stigler M. Stephen Tanur M. Judith 1919–2005 and Stigler M. Legacy: Stephen Fienberg, E. Kruskal Stephen William The 07 o.2,N.2 255–261 2, DOI: No. 22, Vol. 2007, Science Statistical 10.1214/088342306000000411 10.1214/088342306000000402 10.1214/088342306000000385 10.1214/088342306000000367 [email protected] 51-80 S e-mail: USA Carnegie15213-3890, Pennsylvania at Pittsburgh, all University, Cylab, Mellon Automated and Discovery, for and Center Learning the the in Statistics, Science of Social Department and Statistics of Professor

tpe .Febr sMuieFl University Falk Maurice is Fienberg E. Stephen c nttt fMteaia Statistics Mathematical of Institute 1 icse in Discussed 10.1214/088342306000000420 10.1214/088342306000000358 ah n h copnigcmetre eiei atfrom a recollections part others. with Thi in several along friends. derive occasion, other that commentaries on and accompanying presentations family the his and of c raphy and members Chicag colleagues with of Bill’s University along of the spoke several which 2005, followi at 19, April service m May last memorial on away on as passed and well Bill illness, as him. broadly, tended with more Mathematical contact statistics of of in Institute field came the the on on impact and lasting tics a had Unive the who at and career professional entire his virtually spent Abstract. iin sa dtrada nitleta n professional and intellectual an as and editor 1994, an as ticians fascain ersnaiesampling. representative influen association, his of under phrases: fall nev and to words who and Key statisticians him of with generations interact new intr to accomp to to opportunity and and time friends biography first old present the to for the him reintroduce of to purposes p is his commentaries the in events of selected One on back life. looked Bill which in 285–303) [email protected] ilwskonproal oms fa le eeaino st of generation older an of most to personally known was Bill ttsia Science Statistical fi[email protected] . , , . and 10.1214/088342306000000394 10.1214/088342306000000376 2007 , ila rsa Bl)wsadsigihdsaitca wh statistician distinguished a was (Bill) Kruskal William , ulse nitriwb ad ael(o.9, (Vol. Zabell Sandy by interview an published nylpda,KuklWli et measures test, Kruskal–Wallis Encyclopedias, Judith . . , , 1 aer nrltdfils Bl,Mri n l started all I and Martin “Bill, fields. related in careers children.) at Tanur’s origami Judy taught to also camp (She summer paperfolding. of art and the promote origami to appearances on television called numerous books today making co-authoring is USA, what of Origami founder Lil- Oppenheimer, as lian famous became later Kruskal, Vorhaus mother, Lillian Bill’s owned business. the fur Kruskal, decades wholesale many largest Joseph for nation’s boys was father, which three Kruskal, of His & Kruskal oldest girls. the two 1919, and 10, October on City ern iesfo h rgnli aiainand pagination in detail. original typographic the from differs reprint ttsia Science article Statistical original the the of by reprint published electronic an is This h he rsa rtesalwn nt research to on went all brothers Kruskal three The York New in born was Kruskal Henry William .ABIFBIOGRAPHY BRIEF A 1. nttt fMteaia Statistics Mathematical of Institute , 07 o.2,N.2 255–261 2, No. 22, Vol. 2007, st fChicago, of rsity diptfrom input nd ollaborators rofessional dc him oduce edr In leader. rhdan had er ga ex- an ng ce. n who any eda held o biog- s anying Statis- brief atis- o This . 1 in 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. In this work Bill freed statisticians devised the Kruskal–Wallis test, a now ubiquitous from relying on vision-clouding coordinate frames of rank test for one-way analyses of variance, found reference. Morris Eaton, who was a junior colleague today under that name as part of every major sta- to Bill in the late 1960s and early 1970s, describes tistical computing package. Their original paper ap- the impact of this work in an accompanying com- peared in the Journal of the American Statistical mentary. Association (JASA) in 1952, and it and the test re- Bill co-authored yet another series of landmark main widely cited today (see the discussion in papers with Frederick Mosteller in the 1980s on rep- Stigler’s accompanying commentary). resentative sampling. These papers trace the history With another Chicago colleague, Leo Goodman, of the notion of probability sampling and describe Bill co-authored a series of four classic papers that, how it evolved from the “loose” and not-well-defined THE WILLIAM KRUSKAL LEGACY 5

Fig. 6. Bill and other statistics faculty with Frederick Mosteller in 1973 on the occasion of Mosteller’s receipt of an honorary degree from the University of Chicago. notion of “representativeness.” Bill had a fascination co-editor (with Judith Tanur) of the International with the origins of statistical terminology and ideas. Encyclopedia of Statistics in 1978. His role as editor This fascination also is reflected in his work with is described by Tanur in her accompanying commen- Steve Stigler on the appearance and uses of “nor- tary and also by Stephen Fienberg. mal” in statistics (normal equations, normal distri- When a statistical issue in an unfamiliar setting bution, with senses of both the usual and the ideal), caught his eye, Bill would frequently begin a file and in Bill’s longstanding investigation of the term that would grow over time, as he added the products and idea of “relative importance.” of his library work, correspondence he would initi- President Richard Nixon appointed Bill to his ate with experts in other fields, and clippings from President’s Commission on Federal Statistics in 1970. his voracious reading of newspapers, scholarly mag- The 15-member Commission conducted a compre- azines and professional journals. The topics would hensive review of the data-gathering and compila- range from cloud seeding to casualty counts in the tion and use of statistics by the federal government, Vietnam War to the Dreyfus Affair. These files and the first such review that had taken place in 20 the careful references to the sources he had encoun- years. The subsequent creation of a permanent com- tered added immeasurably to the depth of scholar- mittee to address the kinds of problems the Presi- ship of all entries in the encyclopedias he edited. dent’s Commission had laid out (the National Re- Even those contributing authors who in fact never search Council’s Committee on National Statistics) read beyond narrow specialties acquired through was predominantly due to Bill’s efforts, and he be- Bill’s uncredited editorial intervention the appear- came its first chairman, serving from 1971 to 1978. ance of widely read scientific generalists. As sev- The Committee was charged with evaluating statis- eral of the commentaries note, Bill’s mailing of clip- tical issues for the U.S. government, including citi- pings became a source of amusement, stimulation zens’ attitudes and behavior toward the census. Mar- and an occasional prod to action among his varied garet Martin in an accompanying commentary de- colleagues, friends and acquaintances. scribes her interactions with Bill as they launched Bill received many honors over the course of his the Committee. career. In 1970–1971 he was a Fellow at the Cen- Bill’s academic interests were encyclopedic. In- ter for Advanced Study in the Behavioral Sciences deed, he put these interests to use as the associate and NSF Senior Postdoctoral Fellow, and he was editor for statistics of the International Encyclope- a Fellow of the John Simon Guggenheim Memorial dia of the Social Sciences from 1962 to 1968, and Foundation in 1979–1980. He was elected a Fellow of 6 S. E. FIENBERG, S. M. STIGLER AND J. M. TANUR

PARTIAL LIST OF PUBLICATIONS [1] Advisory Committee on Problems of Census Enu- meration (1972). America’s Uncounted People. National Academy of Sciences, Washington. [2] Bjerve, P. J. and Kruskal, W. H. (1989). Kiaer, Anders Nicolai. Encyclopedia of Statistical Sciences Suppl. 78. Wiley, New York. [3] Campbell, D. T., Kruskal, W. H. and Wallace, W. P. (1966). Seating aggregation as an index of atti- tude. Sociometry 29 1–15. (Correction 30 104.) [4] Chayes, F. and Kruskal, W. H. (1966). An approxi- mate statistical test for correlations between pro- portions. J. Geology 74 692–702. (Correction 78 380.) [5] David, H. T. and Kruskal, W. H. (1956). The WAGR sequential t-test reaches a decision with probability one. Ann. Math. Statist. 27 797–805. (Correction 29 936.) MR0081045 [6] Goodman, L. A. and Kruskal, W. H. (1954). Mea- sures of association for cross classifications. J. Amer. Statist. Assoc. 49 732–764. [7] Goodman, L. A. and Kruskal, W. H. (1959). Mea- sures of association for cross classifications. II. Fur- ther discussion and references. J. Amer. Statist. As- soc. 54 123–163. [8] Goodman, L. A. and Kruskal, W. H. (1963). Mea- sures of association for cross classifications. III. Ap- Fig. 7. Bill and Norma, circa 1949. proximate sampling theory. J. Amer. Statist. Assoc. 58 310–364. MR0156400 [9] Goodman, L. A. and Kruskal, W. H. (1972). Mea- the Institute of Mathematical Statistics, the Amer- sures of association for cross classifications. IV. Sim- ican Statistical Association, the American Associa- plification of asymptotic variances. J. Amer. Statist. tion for the Advancement of Science and the Amer- Assoc. 67 415–421. ican Academy of Arts and Sciences, and he was an [10] Goodman, L. A. and Kruskal, W. H. (1974). Empir- honorary Fellow of the Royal Statistical Society. In ical evaluation of formal theory. J. Math. Sociology 1978, he served as the Committee of Presidents of 3 187–196. [11] Goodman, L. A. and Kruskal, W. H. (1979). Statistical Societies Fisher Lecturer and received the Measures of Association for Cross Classifications. Samuel S. Wilks Memorial Medal from the Ameri- Springer, New York. MR0553108 can Statistical Association. In 1992 the American [12] Kruskal, W. H. (1946). Helmert’s distribution. Amer. Statistical Association recognized Bill’s long run- Math. Monthly 53 435–438. MR0017490 ning fundamental contributions by giving him its [13] Kruskal, W. H. (1952). A nonparametric test for the Founders Award. several sample problem. Ann. Math. Statist. 23 525– 540. MR0050850 Bill married Norma Evans in 1941. She died in [14] Kruskal, W. H. (1953). On the uniqueness of the 1992. They had three sons, Vincent of Harrison, New line of organic correlation. Biometrics 9 47–58. York, Thomas of Sudbury, Massachusetts and Jody MR0054224 of New York City. Bill died in Chicago on April 22, [15] Kruskal, W. H. (1954). The monotonicity of the ratio 2005. of two noncentral t density functions. Ann. Math. Statist. 25 162–165. MR0061320 ACKNOWLEDGMENT [16] Kruskal, W. H. (1957). Historical notes on the Wilcoxon unpaired two-sample test. J. Amer. We are indebted to Steve Koppes of the University Statist. Assoc. 52 356–360. of Chicago News Office who prepared an official obit- [17] Kruskal, W. H. (1958). Ordinal measures of as- uary of Bill that was released by the University and sociation. J. Amer. Statist. Assoc. 53 814–861. from which we have borrowed extensively. The list of MR0100941 [18] Kruskal, W. H. (1960). Some remarks on wild obser- references that follows comprises a partial bibliogra- vations. Technometrics 2 1–3. MR0110157 phy of William Kruskal. A full listing may be found [19] Kruskal, W. H. (1961). The coordinate-free approach at www.stat.uchicago.edu/people/inmemoriam.html. to Gauss–Markov estimation and its application to THE WILLIAM KRUSKAL LEGACY 7

missing and extra observations. Proc. Fourth Berke- [38] Kruskal, W. H. (1989). Hooker and Yule on relative ley Symp. Math. Statist. Probab. 1 435–451. Univ. importance: A statistical detective story. Internat. California Press, Berkeley. MR0137222 Statist. Rev. 57 83–88. [20] Kruskal, W. H. (1965). Statistics, Moli`ere and Henry [39] Kruskal, W. H. (1990). Contributions to “Fred as a sci- Adams. The Centennial Review 9 79–96. entific generalist.” In A Statistical Model: Frederick [21] Kruskal, W. H., assoc. ed. for Statistics (1968). In- Mosteller’s Contributions to Statistics, Science and ternational Encyclopedia of the Social Sciences. Public Policy (S. E. Fienberg, D. C. Hoaglin, W. Macmillan and Free Press, New York. H. Kruskal, J. M. Tanur and C. Youtz, eds.) 45–54. [22] Kruskal, W. H. (1968). When are Gauss–Markov and least squares estimators identical? A coordinate- Springer, New York. free approach. Ann. Math. Statist. 39 70–75. [40] Kruskal, W. H. (1997). Thermometers with detach- MR0222998 able scales. Thomas Mann and the silent sisters [23] Kruskal, W. H. (1971). Mathematical sciences and so- of his Magic Mountain. In Natur, Mathematik und cial sciences: Excerpts from the report of a panel of Geschichte: Beitr¨age zur Alexander-von-Humboldt- the Behavioral and Social Sciences Survey. Amer. Forschung und zur Mathematikhistoriographie (H. Statist. 25(1) 27–31. Beck, R. Siegmund-Schultze, C. Suckow and M. [24] Kruskal, W. H. (1973). The Committee on National Folkerts, eds.) 315–318. Deutsche Akademie der Statistics. Science 180 1256–1258. Naturforscher Leopoldina, Halle an der Saale. [25] Kruskal, W. H. (1974). The ubiquity of statistics. [41] Kruskal, W. H. and Mosteller, F. (1979). Repre- Amer. Statist. 28 3–6. sentative sampling. I. Non-scientific literature. In- Kruskal, W. H. [26] (1975). The geometry of generalized ternat. Statist. Rev. 47 13–24. inverses. J. Roy. Statist. Soc. Ser. B 37 272–283. [42] Kruskal, W. H. and Mosteller, F. (1979). Represen- (Correction 48 258.) MR0379522 tative sampling. II. Scientific literature, excluding [27] Kruskal, W. H. (1978). Taking data seriously. In To- Internat. Statist. Rev. 47 ward a Metric of Science: The Advent of Science statistics. 111–127. Indicators (Y. Elkana, J. Lederberg, R. K. Merton, [43] Kruskal, W. H. and Mosteller, F. (1979). Represen- A. Thackray and H. Zuckerman, eds.) 139–169. Wi- tative sampling. III. The current statistical litera- ley, New York. ture. Internat. Statist. Rev. 47 245–265. [28] Kruskal, W. H. (1978). Leonard Jimmie Savage and [44] Kruskal, W. H. and Mosteller, F. (1980). Repre- Richard Price. Biographies in International Ency- sentative sampling. IV. The history of the concept clopedia of Statistics (W. H. Kruskal and J. M. Ta- in statistics, 1895–1939. Internat. Statist. Rev. 48 nur, eds.). Free Press, New York. 169–195. MR0586104 [29] Kruskal, W. H. (1978). Formulas, numbers, words: [45] Kruskal, W. H. and Neyman, J. (1995). Stochastic Statistics in prose. The American Scholar 47 223– models and their applications to social phenomena. 229. Probab. Math. Statist. 15 21–27. Kruskal, W. H. [30] (1980). First interactions with Harold [46] Kruskal, W. H. and Stigler, S. M. (1997). Normative Hotelling; testing the Norden bombsight. J. Amer. terminology: “Normal” in statistics and elsewhere. Statist. Assoc. 75 331–333. In Statistics and Public Policy (B. Spencer, ed.) 85– [31] Kruskal, W. H. (1980). The significance of Fisher: A review of R. A. Fisher. The Life of a Scientist, by 111. Oxford Univ. Press. Joan Fisher Box. J. Amer. Statist. Assoc. 75 1019– [47] Kruskal, W. H. and Tanur, J. M., eds. (1978). Inter- 1030. national Encyclopedia of Statistics. Free Press, New [32] Kruskal, W. H. (1982). Criteria for judging statistical York. graphics. Utilitas Math. 21B 283–310. MR0683928 [48] Kruskal, W. H. and Telser, L. G. (1960). Food prices [33] Kruskal, W. H. (1984). The census as a national cere- and the Bureau of Labor Statistics. J. Business 33 mony. In Federal Statistics and National Needs 177– 258–279, 285. 180. U.S. Government Printing Office, Washington. [49] Kruskal, W. H. and Wallis, W. A. (1952). Use of [34] Kruskal, W. H. (1986). Evaluating social science re- ranks in one-criterion variance analysis. J. Amer. search. In Advances in the Social Sciences, 1900– Statist. Assoc. 47 583–621. (Correction 48 907–911.) 1980. (K. W. Deutsch, A. S. Markovits and J. Platt, [50] President’s Commission on Federal Statistics eds.) 231–247. Abt Books, Cambridge, MA. (1971). Federal Statistics: Report of the Presi- [35] Kruskal, W. H. (1986). Terms of reference: Singular dent’s Commission. U.S. Government Printing Of- confusion about multiple causation. J. Legal Studies fice, Washington. 15 427–436. [36] Kruskal, W. H. (1987). Relative importance by aver- [51] Tanur, J. M., Mosteller, F., Kruskal, W. H., aging over orderings. Amer. Statist. 41 6–10. (Cor- Link, R. F., Pieters, R. S. and Rising, G. R., rection 41 341.) eds. (1972). Statistics: A Guide to the Unknown. [37] Kruskal, W. H. (1988). The n cultures. In Proc. Fourth Holden-Day, San Francisco. Annual Research Conference 231–236. Bureau of [52] Zabell, S. (1994). A conversation with William the Census, Washington. Kruskal. Statist. Sci. 9 285–303. MR1293298