Samuel Stanley Wilks (June 17, 1906 – March 7, 1964) was an American mathematician and academic who played an important role in the development of
mathematical statistics
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...
, especially in regard to practical applications.
Early life and education
Wilks was born in
Little Elm
Little Elm is a city in Denton County, Texas, United States, and a part of the Dallas–Fort Worth metroplex. It is an extended suburb of Denton; its population was 46,453 as of the 2020 census. In 2000, the census population was at 3,646. By the ...
,
Texas
Texas (, ; Spanish language, Spanish: ''Texas'', ''Tejas'') is a state in the South Central United States, South Central region of the United States. At 268,596 square miles (695,662 km2), and with more than 29.1 million residents in 2 ...
and raised on a farm. He studied Industrial Arts at the North Texas State Teachers College in Denton, Texas, obtaining his bachelor's degree in 1926. He received his master's degree in mathematics in 1928 from the University of Texas. He obtained his Ph.D. at the
University of Iowa
The University of Iowa (UI, U of I, UIowa, or simply Iowa) is a public university, public research university in Iowa City, Iowa, United States. Founded in 1847, it is the oldest and largest university in the state. The University of Iowa is org ...
under
Everett F. Lindquist; his thesis dealt with a problem of statistical measurement in education, and was published in the ''
Journal of Educational Psychology
The ''Journal of Educational Psychology'' is a peer-reviewed academic journal that was established in 1910 and covers educational psychology. It is published by the American Psychological Association.
The current editor-in-chief is Steve Graham ( ...
''.
Career
Wilks became an instructor in mathematics at
Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
in 1933; in 1938 he assumed the editorship of the journal ''
Annals of Mathematical Statistics
The ''Annals of Mathematical Statistics'' was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the ''Annals of Statistics'' and the ''Annals of Probability''. In 1938, ...
'' in place of
Harry C. Carver. Wilks assembled an advisory board for the journal that included major figures in statistics and probability, among them
Ronald Fisher
Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who a ...
,
Jerzy Neyman
Jerzy Neyman (April 16, 1894 – August 5, 1981; born Jerzy Spława-Neyman; ) was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College ...
, and
Egon Pearson.
During
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
he was a consultant with the
Office of Naval Research
The Office of Naval Research (ONR) is an organization within the United States Department of the Navy responsible for the science and technology programs of the U.S. Navy and Marine Corps. Established by Congress in 1946, its mission is to plan ...
. Both during and after the War he had a profound impact on the application of statistical methods to all aspects of military planning.
Wilks was named professor of mathematics and director of the Section of Mathematical Statistics at
Princeton
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...
in 1944, and became chairman of the Division of Mathematics at the university in 1958.
Wilks died in 1964 in
Princeton
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...
.
Work in mathematical statistics
He was noted for his work on multivariate statistics. He also conducted work on
unit-weighted regression, proving the idea that under a wide variety of common conditions, almost all sets of weights will yield composites that are very highly correlated (Wilks, 1938), a result that has been dubbed Wilks's theorem (Ree, Carretta, & Earles, 1998).
Another result, also called “
Wilks' theorem
In statistics Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produce confidence intervals for maximum-likelihood estimates or as a test statistic for performing the likelihood-ratio te ...
” occurs in the theory of
likelihood ratio tests, where Wilks showed the distribution of log likelihood ratios is asymptotically
.
From the start of his career, Wilks favored a strong focus on practical applications for the increasingly abstract field of mathematical statistics; he also influenced other researchers, notably
John Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distributi ...
, in a similar direction. Drawing upon the background of his thesis, Wilks worked with the Educational Testing Service in developing the standardized tests like the
SAT
The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Schol ...
that have had a profound effect on American education. He also worked with
Walter Shewhart
Walter Andrew Shewhart (pronounced like "shoe-heart";
March 18, 1891 – March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the ''father of statistical quality control'' and also related to the Shewhart cycl ...
on statistical applications in quality control in manufacturing.
Wilks's lambda distribution In statistics, Wilks' lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially with regard to the likelihood-ratio test and multivariate analysis of variance (MANOVA).
De ...
is a
probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
related to two
independent
Independent or Independents may refer to:
Arts, entertainment, and media Artist groups
* Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s
* Independ ...
Wishart distributed variables. It is important in
multivariate statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable.
Multivariate statistics concerns understanding the different aims and background of each of the dif ...
and
likelihood-ratio test
In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after im ...
s.
Honors
The
American Statistical Association
The American Statistical Association (ASA) is the main professional organization for statisticians and related professionals in the United States. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest continuousl ...
named its
Wilks Memorial Award
The Wilks Memorial Award is awarded by the American Statistical Association to recognize outstanding contributions to statistics. It was established in 1964 and is awarded yearly. It is named in memory of the statistician Samuel S. Wilks. The awa ...
in his honor.
References
(Reprinton American Statistical Association'
''Statisticians in History'' website.
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External links
{{DEFAULTSORT:Wilks, Samuel S.
20th-century American mathematicians
American statisticians
1906 births
1964 deaths
Presidents of the American Statistical Association
Presidents of the Institute of Mathematical Statistics
Fellows of the American Statistical Association
University of North Texas alumni
Fellows of the Econometric Society
People from Little Elm, Texas