Tales of Statisticians
Frank Wilcoxon
2 Sept 1892 - 18 Nov 1965

Frank Wilcoxon and a twin sister were born to recently married wealthy American parents who had rented Glengarriffe Castle near Cork, Ireland for the occasion. He grew up in the family home in Catskill NY, whose beauty made a permanent impression on him. His youth otherwise was difficult. Sometime around 1908 he ran away to sea, jumped ship after a week of chipping paint when the ship failed to sail, and hid out for years from the imagined consequences of this desertion in the back country of West Virginia, first as an oil well worker, then as a tree surgeon. A trip to Boston to hone the latter skills at a forestry school fizzled when it turned out that the school had closed. Finally returning home, he was sent to the Pennsylvania Military College in 1917, another totally incompatible environment. His twin sister died in childbirth in 1918.

After a WW1 job with the Atlas Powder Company in Michigan, Wilcoxon entered Rutgers in 1920, and completed an MS in chemistry in 1921; he then shifted to Cornell and physical chemistry, and got his PhD in 1924. He was then 32; a late start for the sciences. His first position after graduation was a postdoctoral fellowship at the Boyce Thompson Institute for Plant Research in Yonkers, where he was assigned to investigate the use of copper compounds as fungicides. At the Institute, Wilcoxon, Jack Youden, and biologist F E Denny led a group in studying Fisher's newly issued Statistical Methods for Research Workers (1ed 1925). Wilcoxon and Youden both went on to influential careers in statistics.

After the fellowship, he worked briefly (1928-1929) for the sponsoring firm, Nichols Copper, and then returned to the Institute. During WW2 he took a two-year leave to manage the control lab of the Ravenna Ordnance Plant, operated by his old employer Atlas Powder; his control group established an accident-free record of which he remained proud all his life. He next (1943) worked as group leader of the insecticide and fungicide laboratory at American Cyanamid, where he contributed to the development of malathion.

His statistical interests continued to grow. His decisive transition from chemistry to statistics occurred in the middle of 1945. His first paper, published in that year, dealt not surprisingly with dose effect curves in plant pathology. His second, also in 1945, not only addressed his second interest; it was a bombshell which broke new and permanent ground. It contained the rank-sum and signed-rank tests which are still named for him, and which are among the cornerstones in the edifice of nonparametric statistics. The basic idea of these tests, which had first been used by Spearman in 1906 but not widely followed up, was to replace points in the sample data by their respective ranks. Wilcoxon's two tests do much of what the Gosset T test will do, but without the need to assume normal distribution of the population being studied (as the Gosset test properly requires; that requirement is frequently violated in practice).

It is often pointed out that Wilcoxon did not at first see the full importance of what he had done in his 1945 paper. Let it be noted that the much more relevantly trained Dantzig also did not at first see the full power of the simplex method of programming, which he was to invent two years later, in 1947. In both cases, development was rapid. Wilcoxon followed up his 1945 paper by a stratified version of his ranks test, published in 1946 in a mathematically obscure journal. Both results were collected in his 1947 pamphlet, Some Rapid Approximate Statistical Procedures, which was several times later expanded and reprinted. In recognition of this work, Wilcoxon was transferred in 1950 to the company's Lederle Laboratories, where he established a statistical consulting group. He retired in 1957, at the standard age of 65, to a part-time consulting position back at the Boyce Thompson Institute.

Wilcoxon had taught physical chemistry part-time at Brooklyn Polytechnic from 1929 to 1941, when war work ended that dual career. In 1960, after his retirement from industry, he was persuaded by Ralph Bradley to rejoin academe by accepting a half-time Distinguished Lectureship in the new Department of Statistics at Florida State in Tallahassee, which Bradley had just founded.

Wilcoxon, who with his wife was an enthusiastic bicyclist, shifted to a motorcycle for part of his time at Florida. He was a strict teacher. Perhaps bearing in mind the periods in his life when a mistake would destroy the town he was working in, he insisted that the answer not only had to be theoretically right, but also computationally correct. He was regarded with respect and affection by students and colleagues alike. He and others extended his early discoveries to a series of nonparametric sequential ranking procedures; a joint paper appeared in 1963. Academic interest in these developments was shown by the invitation to give a talk at the joint meeting of the Institute of Mathematical Statistics and the Eastern North American Region of the Biometric Society, at Chapel Hill NC in April 1962. Wilcoxon received a standing ovation at the end.

At the time of his death, Wilcoxon was working on a multivariate generalization of his two-sample rank sum test. His proposals were described posthumously (by Bradley, 1967). They have not been taken up by the statistical community. No matter. His place in the history of the subject is secure.

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