Samuel S. Wilks

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, especially in regard to practical applications.

Born in Little Elm, Texas and raised on a farm, Wilks was educated at the University of Iowa, where he acquired his Ph.D. under Everett F. Lindquist; his thesis dealt with a problem of statistical measurement in education, and was published in the Journal of Educational Psychology. Wilks became an instructor in mathematics at Princeton University in 1933; in 1938 he assumed the editorship of the journal Annals of Mathematical Statistics 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, Jerzy Neyman, and Egon Pearson.

Wilks was named professor of mathematics and director of the Section of Mathematical Statistics at Princeton in 1944, and became chairman of the Division of Mathematics at the university in 1958. 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 set 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 use of the phrase "Wilks' Theorem" 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, 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 that have had a profound effect on American education. He also worked with Walter Shewhart on statistical applications in quality control in manufacturing.

During World War II he was a consultant with the Office of Naval Research. Both during and after the War he had a profound impact on the application of statistical methods to all aspects of military planning.

Wilks died in 1964 in Princeton.

The American Statistical Association named its Wilks Memorial Award in his honor.

Wilks's lambda distribution is a probability distribution related to two independent Wishart distributed variables. It is important in multivariate statistics and likelihood-ratio tests.

References

• Mosteller, Frederick. "Samuel S. Wilks: Statesman of Statistics." American Statistician, Vol. 18, No. 2 (April 1964), pp. 11–17. (Reprint on American Statistical Association's Statisticians in History website).
• Ree, M. J., Carretta, T. R., & Earles, J. A. (1998). "In top-down decisions, weighting variables does not matter: A consequence of Wilks's theorem. Organizational Research Methods, volume 1(4), pages 407–420. doi:10.1177/109442819814003
• Salsburg, David. The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. New York, W. H. Freeman, 2001.
• Stephan, Frederick F. et al. "Samuel S. Wilks." Journal of the American Statistical Association, Vol. 60, No. 312 (Dec. 1965), pp. 939–66.
• Wilks, S. S. (1938). "Weighting systems for linear functions of correlated variables when there is no dependent variable". Psychometrika, volume 3, pages 23–40. doi:10.1007/BF02287917

External links

• Wilks at Princeton