Willcox, Walter F.

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Willcox, Walter F.



Walter Francis Willcox (1861-1964), American statistician, lived 103 years, was a persistent walker, and even after his ninetieth birthday attended meetings of the International Statistical Institute in Rio de Janeiro, New Delhi, and Stockholm. Such durability attracts attention, and Willcox was afraid that he would be remembered more for his feet than for his head. Actually, he deserves an outstanding place among American social scientists and statisticians as a pioneer teacher-scholar in demography.

Willcox played a major role in transforming the academic approach to social questions from one based on law guided by philosophy to one based on factual investigation guided by provisional theory. His work in social science grew out of a revolt against philosophy. Having studied philosophy and law at Amherst College and Columbia University (Amherst awarded him an a.b. in 1884 and an a.m. in 1888; Columbia awarded him an LL.B. in 1887 and a PH.D. in 1891), in 1889 he went to Berlin, where he began a thesis on divorce. He approached the subject in the tradition of natural law, as a study of practical ethics, until he encountered Bertillon’s Étude dèmographique du divorce (1883). Its empirical method opened up a new world to him, and its substance completely overturned his former convictions. After returning to the United States, he applied Bertillon’s method to the American data that Carroll D. Wright, then commissioner of labor, had published in A Report on Marriage and Divorce 1867-1906 in the United States (see U.S. Bureau of the Census 1908-1909). The result was a major work, The Divorce Problem: A Study in Statistics (1891).

In 1891 Willcox joined the faculty of Cornell University, at first teaching statistics in a philosophy course entitled “Applied Ethics.” He remained at Cornell for forty years, becoming professor of economics and statistics in 1901 and retiring in 1931.

Willcox’s writings ranged widely over the field of demography, covering birth, death, marriage, divorce, migration, the composition of population, and problems of method relating both to censuses and to vital statistics. He tended to study topics of practical importance, which he treated carefully with simple, yet imaginative, manipulative faciliity and presented as lucidly as possible without showmanship. Much of his work is dated, as indeed he asserted it would be, but much of it is remarkably fresh. His studies were valuable in themselves, often illuminating for the first time diverse problems of American society. But perhaps more important, the fact that he brought statistics to bear on sociology made it possible for later scholars, with access to vastly improved data, to probe more deeply into social problems and their interrelationships.

Of Willcox’s studies, the two whose relevance is probably the least dated are the one on the population of China (see 1930a) and the one on the measurement of fertility (see 1910-1911). The former study provided the documentation to which most discussions of China’s population continue to refer. In the latter, Willcox’s measurement was based on the ratio of children under age five to women of childbearing age. The United States did not have complete registration of births until 1933, and Willcox used his ratio, which he obtained from the decennial census, to make the point that the birth rate in the United States had been declining, at least since the early years of the nineteenth century. Willcox was probably the first to employ this ratio, which is now widely used as a measure of fertility whenever birth registration data are not available or are incomplete.

Outside the field of demography, Willcox turned his attention to economic productivity, problems of public health and social welfare, the role of social statistics as an aid to the courts, public opinion and Prohibition legislation, the history of statistics and biographical sketches of early statisticians (whom he preferred to call statists, a term that in his time did not have its present meaning), and above all, the perennial problem of apportionment of representation. Willcox first became interested in apportionment in 1900 and retained this interest all his life: as late as June 1959 he testified before a subcommittee of the Committee on the Judiciary of the House of Representatives, and the New York Times printed a letter from him on the subject written in his 101st year. He favored apportionment based on the method of major fractions, a method that had once been used by Congress but that had subsequently been replaced by the method of equal proportions. It was probably more through Willcox’s efforts than through those of any other single person that the law now provides for automatic apportionment when Congress fails to act.

From 1899 to 1901 Willcox was one of five professional statisticians in charge of the twelfth, or 1900, census of the United States. He served as chief of the division of methods and results and was responsible for providing supplementary analyses of the data gathered in the census. These analytical investigations were the prototypes of what are now called census monographs. He and his staff issued reports on such topics as age statistics, proportions of children in the population, Negroes, illiteracy, and teachers; in 1906 the monumental Supplementary Analysis and Derivative Tables, 12th Census (see U.S. Bureau of the Census 1906) appeared.

In addition to serving as a chief statistician for the census, Willcox served on the Board of Health of New York State from 1899 to 1902, as statistical expert for the War Department on the census of Cuba and Puerto Rico during 1899/1900, as dean of the College of Arts and Sciences at Cornell from 1902 to 1907, and as president of the American Statistical Association in 1912 and of the American Economic Association in 1915. He was particularly interested in international statistics and was elected president of the International Statistical Institute in 1947.

Frank W. Notestein

[Directly related are the entriesCensus; Life Tables; Government Statistics; Population; and the biography ofBertillon.]


(1891) 1897 The Divorce Problem: A Study in Statistics. 2d ed. Columbia University, Faculty of Political Science, Studies in History, Economics and Public Law, Vol. 1, No. 1. New York: Columbia Univ. Press.

1894 The Relation of Statistics to Social Science. National Conference of Charities and Correction, Annual Report 21:86-93.

1897 Density and Distribution of Population in the United States at the Eleventh Census. American Economic Association, Economic Studies, Vol. 2, No. 6. New York: Macmillan.

1910-1911 The Change in the Proportion of Children in the United States and in the Birth Rate in France During the Nineteenth Century. American Statistical Association, Publications 12:490-499. → Since 1914 called the Journal of the American Statistical Association.

(1930a) 1931 A Westerner’s Effort to Estimate the Population of China and Its Increase Since 1650. International Statistical Institute, Bulletin 25, Part 3:156-170. → First published in the Journal of the American Statistical Association.

1930b Census. Volume 3, pages 295-300 in Encyclopaedia of the Social Sciences. New York: Macmillan.

1933 Introduction to the Vital Statistics of the United States, 1900 to 1930. Washington: Government Printing Office.

Studies in American Demography. Ithaca, N.Y.: Cornell Univ. Press, 1940. → Contains writings first published in the decades prior to 1940, as well as previously unpublished material. See especially pages 541-547 for a bibliography of the more important writings of Willcox.


Bertillon, Jacques 1883 Étude démographique dè du divorce et de la sèparation de corps dans les diffèrents pays de l’Europe. Paris: Masson.

Leonard, William R. 1961 Walter F. Willcox: Statist. American Statistician 15:16-19.

Rice, Stuart A. 1964 Walter Francis Willcox: March 22, 1861-October 30, 1964. American Statistician 18: 25-26.

U.S. Bureau of the Census 1906 Supplementary Analysis and Derivative Tables: Twelfth Census of the United States. Washington: Government Printing Office.

U.S. Bureau of the Census 1908-1909 A Report on Marriage and Divorce 1867-1906 in the United States, by Carroll D. Wright. 2 vols. Washington: Government Printing Office.

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