Statistical Science

The William Kruskal Legacy: 1919–2005

Stephen E. Fienberg, Stephen M. Stigler, and Judith M. Tanur

Full-text: Open access


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 Statistics 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 extended 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 biography 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 statisticians 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.

Article information

Statist. Sci. Volume 22, Number 2 (2007), 255-261.

First available in Project Euclid: 27 September 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Encyclopedias Kruskal–Wallis test measures of association representative sampling


Fienberg, Stephen E.; Stigler, Stephen M.; Tanur, Judith M. The William Kruskal Legacy: 1919–2005. Statist. Sci. 22 (2007), no. 2, 255--261. doi:10.1214/088342306000000420.

Export citation


  • Advisory Committee on Problems of Census Enumeration (1972). America's Uncounted People. National Academy of Sciences, Washington.
  • Bjerve, P. J. and Kruskal, W. H. (1989). Kiaer, Anders Nicolai. Encyclopedia of Statistical Sciences Suppl. 78. Wiley, New York.
  • Campbell, D. T., Kruskal, W. H. and Wallace, W. P. (1966). Seating aggregation as an index of attitude. Sociometry 29 1--15. (Correction 30 104.)
  • Chayes, F. and Kruskal, W. H. (1966). An approximate statistical test for correlations between proportions. J. Geology 74 692--702. (Correction 78 380.)
  • 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.)
  • Goodman, L. A. and Kruskal, W. H. (1954). Measures of association for cross classifications. J. Amer. Statist. Assoc. 49 732--764.
  • Goodman, L. A. and Kruskal, W. H. (1959). Measures of association for cross classifications. II. Further discussion and references. J. Amer. Statist. Assoc. 54 123--163.
  • Goodman, L. A. and Kruskal, W. H. (1963). Measures of association for cross classifications. III. Approximate sampling theory. J. Amer. Statist. Assoc. 58 310--364.
  • Goodman, L. A. and Kruskal, W. H. (1972). Measures of association for cross classifications. IV. Simplification of asymptotic variances. J. Amer. Statist. Assoc. 67 415--421.
  • Goodman, L. A. and Kruskal, W. H. (1974). Empirical evaluation of formal theory. J. Math. Sociology 3 187--196.
  • Goodman, L. A. and Kruskal, W. H. (1979). Measures of Association for Cross Classifications. Springer, New York.
  • Kruskal, W. H. (1946). Helmert's distribution. Amer. Math. Monthly 53 435--438.
  • Kruskal, W. H. (1952). A nonparametric test for the several sample problem. Ann. Math. Statist. 23 525--540.
  • Kruskal, W. H. (1953). On the uniqueness of the line of organic correlation. Biometrics 9 47--58.
  • Kruskal, W. H. (1954). The monotonicity of the ratio of two noncentral $t$ density functions. Ann. Math. Statist. 25 162--165.
  • Kruskal, W. H. (1957). Historical notes on the Wilcoxon unpaired two-sample test. J. Amer. Statist. Assoc. 52 356--360.
  • Kruskal, W. H. (1958). Ordinal measures of association. J. Amer. Statist. Assoc. 53 814--861.
  • Kruskal, W. H. (1960). Some remarks on wild observations. Technometrics 2 1--3.
  • Kruskal, W. H. (1961). The coordinate-free approach to Gauss--Markov estimation and its application to missing and extra observations. Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1 435--451. Univ. California Press, Berkeley.
  • Kruskal, W. H. (1965). Statistics, Molière and Henry Adams. The Centennial Review 9 79--96.
  • Kruskal, W. H., assoc. ed. for Statistics (1968). International Encyclopedia of the Social Sciences. Macmillan and Free Press, New York.
  • Kruskal, W. H. (1968). When are Gauss--Markov and least squares estimators identical? A coordinate-free approach. Ann. Math. Statist. 39 70--75.
  • Kruskal, W. H. (1971). Mathematical sciences and social sciences: Excerpts from the report of a panel of the Behavioral and Social Sciences Survey. Amer. Statist. 25(1) 27--31.
  • Kruskal, W. H. (1973). The Committee on National Statistics. Science 180 1256--1258.
  • Kruskal, W. H. (1974). The ubiquity of statistics. Amer. Statist. 28 3--6.
  • Kruskal, W. H. (1975). The geometry of generalized inverses. J. Roy. Statist. Soc. Ser. B 37 272--283. (Correction 48 258.)
  • Kruskal, W. H. (1978). Taking data seriously. In Toward a Metric of Science: The Advent of Science Indicators (Y. Elkana, J. Lederberg, R. K. Merton, A. Thackray and H. Zuckerman, eds.) 139--169. Wiley, New York.
  • Kruskal, W. H. (1978). Leonard Jimmie Savage and Richard Price. Biographies in International Encyclopedia of Statistics (W. H. Kruskal and J. M. Tanur, eds.). Free Press, New York.
  • Kruskal, W. H. (1978). Formulas, numbers, words: Statistics in prose. The American Scholar 47 223--229.
  • Kruskal, W. H. (1980). First interactions with Harold Hotelling; testing the Norden bombsight. J. Amer. Statist. Assoc. 75 331--333.
  • Kruskal, W. H. (1980). The significance of Fisher: A review of R. A. Fisher. The Life of a Scientist, by Joan Fisher Box. J. Amer. Statist. Assoc. 75 1019--1030.
  • Kruskal, W. H. (1982). Criteria for judging statistical graphics. Utilitas Math. 21B 283--310.
  • Kruskal, W. H. (1984). The census as a national ceremony. In Federal Statistics and National Needs 177--180. U.S. Government Printing Office, Washington.
  • Kruskal, W. H. (1986). Evaluating social science research. In Advances in the Social Sciences, 1900--1980. (K. W. Deutsch, A. S. Markovits and J. Platt, eds.) 231--247. Abt Books, Cambridge, MA.
  • Kruskal, W. H. (1986). Terms of reference: Singular confusion about multiple causation. J. Legal Studies 15 427--436.
  • Kruskal, W. H. (1987). Relative importance by averaging over orderings. Amer. Statist. 41 6--10. (Correction 41 341.)
  • Kruskal, W. H. (1988). The $n$ cultures. In Proc. Fourth Annual Research Conference 231--236. Bureau of the Census, Washington.
  • Kruskal, W. H. (1989). Hooker and Yule on relative importance: A statistical detective story. Internat. Statist. Rev. 57 83--88.
  • Kruskal, W. H. (1990). Contributions to ``Fred as a scientific generalist.'' In A Statistical Model: Frederick Mosteller's Contributions to Statistics, Science and Public Policy (S. E. Fienberg, D. C. Hoaglin, W. H. Kruskal, J. M. Tanur and C. Youtz, eds.) 45--54. Springer, New York.
  • Kruskal, W. H. (1997). Thermometers with detachable scales. Thomas Mann and the silent sisters of his Magic Mountain. In Natur, Mathematik und Geschichte: Beiträge zur Alexander-von-Humboldt-Forschung und zur Mathematikhistoriographie (H. Beck, R. Siegmund-Schultze, C. Suckow and M. Folkerts, eds.) 315--318. Deutsche Akademie der Naturforscher Leopoldina, Halle an der Saale.
  • Kruskal, W. H. and Mosteller, F. (1979). Representative sampling. I. Non-scientific literature. Internat. Statist. Rev. 47 13--24.
  • Kruskal, W. H. and Mosteller, F. (1979). Representative sampling. II. Scientific literature, excluding statistics. Internat. Statist. Rev. 47 111--127.
  • Kruskal, W. H. and Mosteller, F. (1979). Representative sampling. III. The current statistical literature. Internat. Statist. Rev. 47 245--265.
  • Kruskal, W. H. and Mosteller, F. (1980). Representative sampling. IV. The history of the concept in statistics, 1895--1939. Internat. Statist. Rev. 48 169--195.
  • Kruskal, W. H. and Neyman, J. (1995). Stochastic models and their applications to social phenomena. Probab. Math. Statist. 15 21--27.
  • Kruskal, W. H. and Stigler, S. M. (1997). Normative terminology: ``Normal'' in statistics and elsewhere. In Statistics and Public Policy (B. Spencer, ed.) 85--111. Oxford Univ. Press.
  • Kruskal, W. H. and Tanur, J. M., eds. (1978). International Encyclopedia of Statistics. Free Press, New York.
  • Kruskal, W. H. and Telser, L. G. (1960). Food prices and the Bureau of Labor Statistics. J. Business 33 258--279, 285.
  • Kruskal, W. H. and Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. J. Amer. Statist. Assoc. 47 583--621. (Correction 48 907--911.)
  • President's Commission on Federal Statistics (1971). Federal Statistics: Report of the President's Commission. U.S. Government Printing Office, Washington.
  • Tanur, J. M., Mosteller, F., Kruskal, W. H., Link, R. F., Pieters, R. S. and Rising, G. R., eds. (1972). Statistics: A Guide to the Unknown. Holden-Day, San Francisco.
  • Zabell, S. (1994). A conversation with William Kruskal. Statist. Sci. 9 285--303.