# Martin Bradbury Wilk

At its spring 1988 meeting, the Board of the Statistical Society of Canada elected Martin Wilk an Honorary Member for seminal contributions to the fields of analysis of variance, multivariate analysis, model fitting and validation, for enormous contributions to Statistics Canada as the Chief Statistician, and for insightful guidance of the Society while serving on its Board and as its President.

This tribute originally appeared in *Liaison* Vol. 4 No. 1, November 1989.

## Martin Bradbury Wilk, 1922-2013

If there could ever be an act carried out with the complete unanimity of the Society, it would surely be the naming of Martin Wilk as an Honorary Member. Martin's efforts have affected the lives of a great many Canadians, be they academic, business, government, industrial, or scientific statisticians, or be they honourable citizens.

Martin Wilk was born 18 December 1922 in Montreal. He graduated from Strathcona Academy, Outremont, in 1940. He received a Bachelor's degree in Chemical Engineering from McGill University in 1945. From 1945-1950 he was Research Chemical Engineer at the Atomic Energy Project of the N.R.C.. He next did graduate statistics at Iowa State University, obtaining an M.S. in 1953, followed by a doctorate in 1955. His Ph.D. thesis was titled “Linear Models and Randomized Experiments” and was supervised by Oscar Kempthorne.

Martin moved in 1955 to New Jersey, where he was Research Associate and Assistant Director of the Statistical Techniques Research Group at Princeton University. In 1956 he began his fourteen-year career at Bell Telephone Laboratories, Murray Hill, New Jersey. At Bell Labs he was, in turn: Member of Technical Staff; Head, Statistics and Data Analysis Research Department; Head, Statistical Models and Methods Research Department; and Statistical Director, Management Sciences Research. Meanwhile, between 1959 and 1963, he was Professor of Statistics and Director of Research in Statistics at Rutgers University.

In 1970 Martin moved into the higher management levels of the American Telephone and Telegraph Company, commuting to New York City and occupying a succession of positions culminating as Assistant Vice President- Director of Corporate Planning.

While living in New Jersey, Martin participated in numerous statistical professional society activities, ranging from his Vice Presidency and then Presidency of the local chapter of the American Statistical Association in 1955-56 to his Vice Presidency of the ASA in 1980-82. He is a five-time Fellow: of the ASA, the Institute of Mathematical Statistics, the Royal Statistical Society, the American Association for the Advancement of Science, and the New York Academy of Sciences, and he is an elected Member of the International Statistical Institute.

Throughout the years, Martin retained his Canadian citizenship and ties. To our Society's and country`s great fortune, Martin was prevailed upon in 1980 to return to Canada as Chief Statistician.

He was the first mathematical statistician to occupy the post (and was followed by the second!). Martin's contributions and accomplishments at Statistics Canada were notable, including: negotiating a reinstatement of a Cabinet-cancelled 1986 Census, a shift towards analytic and interpretive studies, creation of a network of advisory committees, and a resurgent international standing for the institution. He resigned as Chief Statistician in January of 1986.

Since “retirement” Martin has maintained a close involvement with Statistics Canada, continued to chair the National Task Force on Tourism Data, become a member of the Council of the Canadian Institute for Advanced Research, and been President of our Society.

Throughout his career, Martin has: edited, refereed, advised, organized, presided, counselled, chaired, lectured, granted, nominated, belonged, been elected, and been rewarded. If anyone has been a complete statistician it is Martin Wilk.

In his scientific career it may be stated that Martin Wilk, as well as writing a succession of influential papers, achieved several scientific breakthroughs, notably the work with Ram Granadesikan on probability plotting for multivariate data (papers 11, 26, 30, 31) and with Sam Shapiro on the W statistic, which tests for normality by regression on order statistics (papers 21, 27, 28, 29, 34). The first W statistic paper (in 1965) was designated as a Citation Classic by Current Contents, having been cited more than 320 times by 1984, and the 1972 W statistic paper received the Jack Youden Prize “for an exceptional expository paper in Technometrics for the year 1972”. A list of Martin's major publications is appended.

Martin is known particularly for his wit, for the forcefulness of his extemporaneous argument, for his piercing questioning, for his ability to recognize the central elements of a problem, for his lateral thinking, and for his leadership. His coined terms “blue collar statistician” and “white collar statistician” are likely to be long made use of. In conversation, he routinely comes out with things like:

“Significance tests are things to do while one is trying to think of something sensible to do.”

“The hallmark of good science is that it uses models and ‘theory' but never believes them.”

“Don't make assumptions about unmeasureable random variables.”

“Contemplation of raw observations with an empty mind, even when it is possible, is often hardly more beneficial than not studying them at all.”

“Models must be used but must never be believed.”

“Insightfulness is generally more important than objectivity.”

“In data analysis, as in experimentation, discovery is more important than confirmation.”

“…is somewhere between meaningless and misleading.”

“Most new phenomena turn out to be errors.”

“Attacking factor analysis is like criticizing a pile of cow dropping for the shape it is in.”

Martin Wilk has been the complete Canadian statistician. We have written this article with respect and affection.

David R. Brillinger, Professor of Statistics

*University of California, Berkeley, California*

Jane F. Gentleman , Senior Research Statistician

*Social & Economic Studies Division, Statistics Canada*

### Selected Publications

1. Wilk, M.B. (1949). Preparation and extraction of S35, *Can. J. Res.*, 27, 475-488.

2. Wilk, M.B. (1955). The randomization analysis of a generalized Randomized Block Design, *Biometrika*, 42, 70-79.

3. Wilk, M.B. & Kempthorne, O. (1955). Fixed, mixed, and random models, *J. Amer. Stat. Assoc.*, 50, 1114-1167.

4. Wilk, M.B. & Kempthorne, O. (1956). Some aspects of the analysis of factorial experiments in a completely randomized design, *Ann. Math. Stat.*, 27, 950-985.

5. Wilk, M.B. (1956). Linear models in the analysis of variance, *Proc. 2nd Conference on Design of Experiments in Army Research Development and Testing*, 243-257.

6. Wilk, M.B. & Kempthorne, O. (1957). Non-additivities in a latin square design, *J. Amer. Stat. Assoc.*, 52, 218-236,.

7. Wilk, M.B., Torrey, M.N. & Gohn, G.R. (1958). A study of the variability in the mechanical properties of alloy a phosphor bronze strip, *Proc. Amer. Soc. Testing Materials* 58, 893-910.

8. Lundberg, J.L., Wilk, M.B., & Huyett, M.J. (1960). Solubilities and diffusivities of nitrogen in polyethylene, *J. Applied Physics*, 1131-1132.

9. Wilk, M.B., Gnanadesikan, R. (1961). Graphical analysis of multiresponse experimental data using ordered distances, *Proc. National Academy Science USA*, 47, 1209-1212.

10. Hogben, D., Pinkham, R.S., & Wilk, M.B. (1961). The moments of the non-central t-distribution, *Biometrika*, 48, 465-468.

11. Wilk, M.B., Gnanadesikan, R., & Huyett, M.J. (1962). Probability plots for the gamma distribution, *Technometrics*, 4, 1-20.

12. Lundberg, J.L., Wilk, M.B., & Huyett, M.J. (1962). Estimation of diffusivities and solubilities from sorption studies, *J. Polymer Science*, 57, 275-299.

13. Wilk, M.B., Gnanadesikan, R., & Huyett, M.J. (1962). Estimation of parameters of the gamma distribution using order statistics, *Biometrika*, 49, 525-545.

14. Wilk, M.B., Gnanadesikan, R., & Huyett, M.J. (1963). Separate maximum likelihood estimation of scale or shape parameters of the gamma Distribution using order statistics, *Biometrika*, 50, 217-221.

15. Pinkham, R.S., & Wilk, M.J. (1963). Tail areas of the t-distribution from a mills'-ratio-like expansion, *Ann. Math. Stat.*, 34, 335-337.

16. Wilk, M.B., Gnanadesikan, R., & Freeny, A.E. (1963). Estimation of error variance from smallest ordered contrasts, *J. Amer. Stat. Assoc*. 58, 152-160.

17. Lundberg, John L., Wilk, M.B., & Huyett, M.J. (1963). Sorption studies using automation and computation, *Industrial and Engineering Chemistry Fundamentals*, 2, 37-43.

18. Hogben, D., Wilk, M.B., & Pinkham, R.S. (1964). The moments of a variate related to the non-central t, *Ann. Math. Stat.*, 35, 298-314.

19. Hogben, D., Pinkham, R.S., & Wilk, M.B. (1964). An approximation to the distribution of Q (a variate related to the non-central t), *Ann. Math. Stat.*, 35, 315-318.

20. Wilk, M.B., & Gnanadesikan, R.(1964). Graphical methods for internal comparisons in multiresponse experiments, *Ann. Math. Stat.*, 35, 613-631.

21. Shapiro, S.S., & Wilk, M.B. (1965). An analysis of variance test for normality (complete samples), *Biometrika*, 52, 591-611.

22. Tukey, J.W., & Wilk, M.B. (1965). Data analysis and statistics: techniques and approaches, *Proc. Cal. Tech. Symposium on Information Processing in Sight Sensory Systems*, 7-27. Reprinted in *The Collected Works of John W. Tukey*, Vol. V, Graphics 1965- 1985, 1-22 (1988).

23. Wilk, M.B., Gnanadesikan, R., & Lauh, E. (1966). Scale parameter estimation from the order statistics of unequal gamma components, *Ann. Math. Stat.*, 37, 152-176.

24. Tukey, J.W., & Wilk, M.B., (1966). Data analysis and statistics: An expository overview, *AFIPS Conf. Proceedings* (Spartan Book), 29, 695-709.

25. Gabbe, J.D., Wilk, M.B., & Brown, W.L. (1967). Statistical analysis and modeling of the high-energy proton data from the telstar l satellite, *Bell System Tech. Jour.*, 46, 1301-1450.

26. Wilk, M.B., & Gnanadesikan, R. (1968). Probability plotting methods for the analysis of data, *Biometrika*, 55, 1-17.

27. Shapiro, S.S., Wilk, M.B., & Chen, H.G. (1968). A comparative study of various tests for normality, *J. Amer. Stat. Assoc.*, 63, 1343-1372.

28. Shapiro, S.S., & Wilk, M.B. (1968). Approximations for the null distribution of the W statistic, *Technometrics*, 10, 861-866.

29. Wilk, M.B., & Shapiro, S.S. (1968). The joint assessment of normality of several independent samples, *Technometrics*, 10, 825-839.

30. Gnanadesikan, R., & Wilk, M.B. (1969). Data analytic methods in multivariate statistical analysis, *Multivariate Analysis II*, Academic Press, 593-638.

31. Gnanadesikan, R., & Wilk, M.B. (1969). A probability plotting procedure for general analysis of variance, *J. Roy. Stat. Soc.* B, 32, 88-101.

32. Gnanadesikan, R., & Wilk, M.B. (1970). Use of maximum likelihood for estimating error variance from a collection of analysis of variance mean squares, *Ann. Math. Stat.*, 41, 292-304.

33. Wilk, M.B. (1970). The corporation and the university as social engineers, *Proc. of University of Maryland Seminar on “University, The Corporation and American Priorities in the Seventies”* .

34. Shapiro, S.S., & Wilk, M.B. (1972). An analysis of variance test for the exponential distribution (complete samples), *Technometrics*, 14, 355-370.

35. Wilk, M.B. (1972). Utility prices and allowed rate of return, *Proc. Second Annual Regulatory Information Systems Conference*, St. Louis, Missouri.

36. Wilk, M.B. (1973). The study of complex systems, *Proc. of Computer Science and Statistics: 7th Annual Symposium on the Interface*.

37. Gentleman, J.F., & Wilk, M.B. (1975). Detecting outliers in a two-way table. I. Statistical behavior of residuals, *Technometrics*, 17, 1-14.

38. Wilk, M.B. (1975). Uncertainties in analysis of complex systems, *Proc. Symposium on Statistics and Related Topics*, Carleton University, Ottawa, Canada.

39. Gentleman, J.F., & Wilk, M.B. (1975). Detecting outliers. II. Supplementing the direct analysis of residuals, *Biometrics*, 31, 387-410.

40. Wilk, M.B. (1975). Planning and uncertainty, *Proc. Computer Science and Statistics: 8th Annual Symposium on the Interface*, Los Angeles, 510-516 .

41. Wilk, M.B. (1979). Statistical consulting. Transcript of panel discussion, *Proc. of Computer Science and Statistics: 12th Annual Symposium on the Interface*, 69-95.

42. Wilk, M.B. (1985). The relationship between statisticians and statisticians, *Survey Methodology*, 11, 89-94.

43. Wilk, M.B. (1987). The concept of error in statistical and scientific work, *Proc. Third Annual Research Conf.*, Bureau of the Census, 223-228.

44. Wilk, M.B. (1988). Data analysis and statistics: principles and practice. In *The Collected Works of John W. Tukey*, Vol. V, Graphics 1965- 1985, 23-29. (Based on 1965 invited talk.)

45. Wilk, M.B., & Fellegi, I.P. (1988). Is Statistics singular or plural? *Can. J. Statistics*, 16, Supplement, 1-8.