Wilks, S.S. (Samuel Stanley), 1906-1964

Samuel Stanley Wilks was a mathematician and statistician. He taught at Princeton University.

educator and editor. He stressed the close relationship of theoretical and applied statistics, and was concerned that the American public understand mathematics as a large body of theory and applications woven into engineering, the sciences and practical affairs. He had a long love affair with multivariate analysis and developed the notion of tolerance limits in order statistics; but he also set up quality control courses and prepared reports that led to better techniques of pre-election forecasting. Interested in testing and measurement, he spent thirty years working with the College Entrance Examination Board and the Educational Testing Service.

Wilks was the son of Chance C. Wilks and Bertha May Gammon. His father was a banker, who later turned to farming; and his mother was a talented musician, who instilled her strong sense of curiosity into her sons. He was raised on a 250-acre Texas farm near Little Elm, Texas with his two younger brothers Syrrel and William. Hunting and fishing were his favorite childhood pastimes, but he also built a radio at the age of twelve in 1918, when the technology was new. Wilks attended a rural one-room school and a larger high school in nearby Denton, Texas. During his senior year, Wilks took an advanced placement class in mathematics at North Texas State Teachers College. He matriculated at the North Texas State Teachers College in Denton, Texas, and graduated with an A.B. degree in architecture in 1926. Because his eyesight was poor, Wilks decided to pursue mathematics instead of architecture. While teaching mathematics and industrial arts at an Austin, Texas high school, he did graduate work in mathematics at the University of Texas at Austin, and earned a master’s degree in 1928. At the University of Texas his first course in advanced mathematics was on set theory taught by R.L. Moore, who was known for his research in topology, his unusual pedagogy, and his disdain for applied mathematics. Given a strong practical bent, Wilks held greater interest in the fields of probability and statistics taught by Professor Edward L. Dodd. Dodd recommended that Wilks pursue further study in these fields with Professor Henry L. Reitz at the University of Iowa, at the time the center for statistical studies in America. Wilks’s doctoral dissertation at the University of Iowa concerned the sampling distribution of the statistics of a variable in which a matching sample had been drawn so as to match an initial sample on a correlated variable. In 1931 he married Gena Orr of Denton, Texas. They had a son named Stanley.

Upon receiving his doctorate from University of Iowa in 1931, Wilks was awarded a (postdoctoral) National Research Council (NRC) Fellowship in mathematics at Columbia University, where he studied with Harold Hotelling, whose name is associated with the T-square statistic, a generalization of Student’s t statistic used in multivariate hypothesis testing. The following year he was appointed an NRC International Research Fellow and worked at the University of London and at Cambridge University. While in London, he worked with British statistician and eugenicist Karl Pearson and Scottish agricultural statistician John Wishart, who would later become the first director of the Cambridge University Statistical Laboratory. Wilks’s year of study in the United Kingdom was a busy one, since he completed at least six papers. Also, while in London, Wilks’s only child Stanley Neal was born. Among the publications that resulted from his NRC International Research fellowship were “Moments and distributions of estimates of population parameters from fragmentary samples” for Annals of Mathematical Statistics and “Certain generalizations in the analysis of variance” for Biometrika. These early works, together with his dissertation, demonstrate Wilks’s fondness for problems of multivariate analysis that gave him pleasure throughout his career; but they also show his concern “to get new results into print.” In his 1932 Biometrika paper Wilks proposed multivariate criteria, among them one denoted by “W,” that is still used today.

Following two years of postdoctoral work, Wilks was called as an instructor in the Department of Mathematics at Princeton University in 1933. Subsequently, he would be promoted to assistant professor in 1936 and associate professor in 1938. In 1944 he became Professor of Mathematics, heading the section on mathematical statistics, after his wartime service. He would stay at Princeton for the remainder of his life.

From the start of his teaching career at Princeton, Wilks showed great interest in developing the undergraduate program in mathematics, slowly developing courses on mathematical statistics. The field was still young, and statistical publications were limited. Harald Cramér’s Mathematical Methods of Statistics, the first modern textbook in the field, only appeared in 1946. Although Wilks’s various sets of course notes eventually appeared as textbooks such as Statistical Inference (1937), Mathematical Statistics (1943) and Elementary Statistical Analysis (1948), Wilks was criticized for holding back, failing to apply his principles about publishing new findings to textbooks, despite the needs of the times. Later in 1954 he began co-editing the John Wiley Series in Statistics with Walter Shewhart, a major publication effort that transformed statistics for a field that in 1931 had only a few books into one that by 1964 had a large and solid body of literature.

During World War II, Wilks served on the Applied Mathematics Panel of the National Defense Research Committee. A consultant to the Office of Naval Research (ONR), he also organized and directed the Princeton Statistical Research Group to help improve the weaponry and fire doctrine of the U.S. armed forces.

From his first year at Princeton, Wilks was also involved in the work of the College Entrance Examination Board (CEEB) and later the Educational Testing Service (ETS). For over thirty years he worked with the CEEB and ETS, advising them on research design and analysis, on College Board test score scaling and equating, on the development of mathematics tests and on studies of mathematical education. But he also made other contributions to education generally and mathematics education specifically. In 1947 he published a report in the American Mathematical Monthly for the National Research Council on the state of statistics instruction in the U.S., that influenced a reorganization of statistics instruction at the college level. From 1950 he served continuously as the chairman of the ETS Graduate Record Examination’s Mathematics Test committee. During the years 1955-58, he served on the CEEB’s Commission on mathematics, a group that made important recommendations for the revision of the nation’s secondary school mathematics curriculum. In 1957 Wilks coauthored the Commission’s experimental book for secondary schools on probability and statistics. Following completion of the Commission’s work, he served on the Advisory Board of the School Mathematics Study Group.

Another field in which Wilks made major contributions was quality control. He helped to establish many quality control courses during and after World War II. As a result, Princeton became the site of the annual meeting for the Metropolitan Section of the American Society for Quality Control.

Later in his career, beginning in the 1950’s Wilks had opportunities to travel as a researcher and visiting lecturer within the United States and internationally. In 1950-51, he received a Fulbright Scholarship to again do research at Cambridge. In the spring of 1956 he visited universities and research centers in India, Japan and Australia with the assistance of the Ford and Carnegie Foundations. In 1958-59 he toured Texas and Oklahoma as a visiting lecturer for the Mathematical Association of America, specifically requesting these states because of a long-standing interest in their scientific development. In 1963-64 he was a visiting lecturer at the Institute of Mathematical Statistics.

Wilks was one of a small number of statisticians, who helped to create the Institute of Mathematical Statistics in 1935, and negotiated the transfer of its journal, the Annals of Mathematical Statistics, from the hands of its founding editor Henry Carver to the Institute. Wilks assumed the editorship of the Annals in 1938 and held this post through 1949.

From 1945 he also served on the Social Science Research Council (SSRC), founded to advance research in the social sciences. It accomplished this goal by developing and administering programs to assist in training scientists, promoting new fields of research, and relating people and organizations in the context of research problems and the public interest. From 1945-54 he was vice-chairman of the SSRC’s Joint Committee on Measurement of Opinion, Attitudes and Consumer Wants, and head of its Committee on Problems and Policy in 1952-54. In 1954-55 he was Chairman of the SSRC Board of Directors and Chairman of the Executive Committee from 1961 until his death.

Wilks also served the Russell Sage Foundation on its Board of Trustees from 1953, and from 1955 until his death he was a member of its Executive Council. These were not pro forma positions for him, since he spent hours examining the Foundation’s programs, projects, plans and manuscripts.

Among the honors Wilks enjoyed in his lifetime, were the presidency of American Statistical Association in 1950 and the presidency of the Institute of Mathematical Statistics in 1940. In 1959 he was invited to give the Institute’s Rietz Lectures. In 1947 the University of Iowa honored him with a Centennial Alumni Award. He was elected a member of the American Philosophical Society in 1948 and in 1963 was elected to the American Academy of Arts and Sciences.

Wilks, who was always in the best of health, died suddenly in his sleep in his Princeton home on March 7, 1964. His funeral service was held in Denton, Texas on March 11, and he was buried at Little Elm cemetery near Little Elm, Texas. He was survived by his wife Gena, his son Stanley and three granddaughters.

In an obituary written by his Harvard colleague Frederick Mosteller (1916-2006, APS 1961), the author called Wilks a “Statesman of Statistics”. Indeed, he considered the relation of statistics and mathematics to the sciences and the nation matters of strong concern.