Tukey, John Wilder, 1915-

Topologist.

One of the most influential statisticians of the twentieth century, John Wilder Tukey (1915-2000) played a key role in both the development and study of statistics. Upon receiving his Ph.D. in mathematics in 1939 from Brown University, he joined the faculty at Princeton; in 1945, he also began work at Bell Laboratories. Equally committed to both Princeton and Bell Labs, Tukey chose to work concurrently at both institutions. He was also a consultant for many companies, such as Merck and Company, Xerox Corporation, and the Educational Testing Service, and was a frequent advisor to the government for such programs as the US Census. From 1960 to 1980 he led the statistical component of NBC’s election night projections. Among other projects Tukey analyzed Alfred Kinsey's research and examined data on ozone depletion. Tukey made many important contributions to the field of statistics, such as work in time series analysis, exploratory data analysis, and multiple comparisons. Through his work, Tukey developed statistical applications including the Box-and-Whisker Plot, the Stem-and-Leaf Diagram, Cooley-Tukey Fast Fourier Transforms, Tukey’s Paired Comparisons and citation and permutated indices. Tukey's influence extends beyond statistics to everyday language: he was the first to use the word "software" in print and coined words such as "bit" and "linear programming." A prolific writer, John W. Tukey penned more than 500 technical papers and reports and published, among numerous other works. His collected papers amount to eight volumes of work.

John Wilder Tukey was born on June 16, 1915 in New Bedford, Massachusetts. His father, Ralph H. Tukey, taught Latin at New Bedford High School. Barred by nepotism rules from teaching at the same school as her husband, Tukey's mother, Adah Tasker Tukey, became a private tutor. Her son showed intellectual promise early; soon, he became her primary pupil. The largely home-schooled John entered Brown University, graduating in 1936 with a degree in chemistry, earning a master's degree in chemistry in 1937. That year he entered Princeton intending to get a doctorate in chemistry but switched to mathematics (he had been studying both subjects), earning his doctorate in 1939. He published three papers before being awarded his doctorate, which itself in 1940 was published as Convergence and Uniformity in Topology.

Hired at Princeton as an instructor after receiving his doctorate, Tukey remained on the faculty throughout World War II. However, his talents for data analysis were recognized as being useful to the war effort. Thus, he joined the Fire Control Research Office, headquartered in Princeton. There, he worked on ballistics, range finding, and other fire control problems. Among his colleagues were Wilfrid Dixon, Merrill Flood, William Cochran, and Stanley Wilks. (Tukey also worked at the Princeton branch of the Frankfort Arsenal Fire Control Design Division.)

Soon after the war, Tukey was made associate professor of mathematics (Frederick Mosteller was his first doctoral student) and steadily rose through the academic ranks: professor of mathematics (1950-65); professor of statistics (1965-85), a department he helped found and served as chair until 1970; Donner Professor of Science (1976-85); Tukey moved to emeritus status in science and statistics in 1985, when he also became Senior Research Statistician. Tukey's amazing mathematical gifts were also put to use by Princeton's administration. From 1945-70 he was chair of the academic scheduling committee. While lying on his back on a table, people would read to him the scheduling complexities. Tukey would solve the problems in his head and quickly call out solutions.

As an academic statistician Tukey made numerous contributions to his field. According to A. D. Gordon, as a practicing statistician, Tukey believed in:

the usefulness and limitation of mathematical statistics; the importance of having methods of statistical analysis that are robust to violations of the assumptions underlying their use; the need to amass experience of the behaviour of specific methods of analysis in order to provide guidance on their use; the importance of allowing the possibility of data's influencing the choice of method by which they are analyzed; the need for statisticians to reject the role of 'guardian of proven truth', and to resist attempts to provide once-for-all solutions and tidy over-unifications of the subject; the iterative nature of data analysis; implications of the increasing power, availability and cheapness of computing facilities; the training of statisticians. 1

One early and continuing interest was in time series analysis, the development of methods to analyze a sequence of data points, measured typically at successive times, spaced at (often uniform) time intervals. Bogert, Healey and Tukey developed cepstral analysis, for instance, to help distinguish an earthquake from an explosion, thus cepstral analysis has applications for the monitoring of nuclear testing.

Tukey explored the problem of robustness of data. For instance, a sample median is more robust than a sample mean, which can be thrown off by one large sample. Tukey recommended medians as a way of smoothing data, which is the capture important patterns in the data, while leaving out noise or other fine-scale phenomena. Smoothing data is very useful in image processing.

One would be hard pressed to find an area of statistics that Tukey did not work on and influence. Analysis of variance (ANOVA) and multiple comparisons were two other areas of interest.

The Fast Fourier Transform (FFT) is perhaps Tukey's most famous and useful contribution to statistics and their application. FFT, developed with James Cooley, is an algorithm that, as the name suggests, speeds data processing. A Discrete Fourier Transform (DFT) decomposes a sequence of values into components of different frequencies. Calculating DFT's is often too slow to be practical. Because the Cooley-Tukey algorithm breaks a particular DFT into smaller DFTs, it can be combined arbitrarily with any other algorithm for the DFT. An FFT (there are others besides Cooley-Tukey, which is the most common) can be applied in digital signal processing and for the quick multiplication of large integers and is a common technique useful in analyzing wave forms in such disciplines as astrophysics.

Tukey invented ways to display and to test datasets: stem-and-leaf diagrams, which substitute digits for frequency counts used in constructing histograms, allowing for quicker, more suggestive analysis; the box-and-whisker plot, a way of showing quartiles, extremes, and the median in one representation that can show the spread, skewness, and extremes of a dataset; and a paired comparison test, used to find which means are significantly different from one another by comparing all possible pairs of means and is called Tukey's HSD (Honestly Significant Difference) test.

Working at Bell Labs helped to support Tukey's academic work. Projects specifically at Bell Labs were often defense-related. One important project was the development of the Nike missile system; with B. D. Holbrook he did the aerodynamics, trajectory, and warhead designs. With Ralph Blackburn Tukey wrote two papers, published in the Bell System Technical Journal (1958), that introduced spectrum analysis to engineering and scientific practice. Tukey left Bell in 1985, his final position being Associate Executive Director, Research and Information Services.

An active consultant for government and business, Tukey served on many committees and commissions and worked for a number of corporations. Whenever Tukey joined a committee or panel, he was invariably an active participant.

Among the corporations Tukey worked for were Merck (for over 40 years), and after his retirement, Xerox PARC. Most publicly, Tukey developed for the National Broadcasting System ways of projecting election results from partial counts. Tukey achieved some renown in 1960 when he prevented an early call of the election for Richard Nixon. Tukey remained with NBC until 1980, when refined exit polling replaced statistical analysis.

Public service occupied much of Tukey's career. He served as chairman of the Analytical Advisory Committee of the National Assessment of Educational Progress and its successor committee from 1963-1982. While on the President's Science Advisory Committee, he chaired the Panel on Chemicals and Health (1971-72) and the Panel on Environmental Pollution (1964-65) which issued the report, Restoring the Quality of Air. He was chairman of the National Research Council's Committee on Impacts of Stratospheric Change (1975-79) which issued three important reports on the deterioration of the ozone by fluorocarbons.

Another government agency for which Tukey consulted was the Census Bureau. On the politically-charged issue of using statistical adjustments to the census, Tukey favored using such methods because errors would be fewer than with individual enumeration.

National security matters were part of Tukey's career as well. In 1959 he was a delegate to Technical Working Group 2 of the Conference on the Discontinuance of Nuclear Weapons Tests, where his expertise in time series analysis was important in discussing monitoring tests. James Killian was appointed by Eisenhower to examine the nation’s intelligence gathering ability and recommend ways it could be enhanced. Project 3 of Killian's Committee looked into the technology of intelligence gathering; Edwin Land chaired Project 3, whose members included Tukey. The U-2 spy plane came out of Project 3’s recommendation to enhance intelligence gathering using the latest science and technology.

Two other important projects bear mentioning. Seeing a need for a comprehensive bibliography of the literature on statistics and probability, Tukey, enlisting the help of eminent colleagues, developed a citation index for the field. Another significant project was to review at the behest of the American Statistical Association the work of Alfred Kinsey (included on the review committee were Mosteller and Cochran). The statisticians and sex researchers did not get along well, Mrs. Kinsey wishing she could have poisoned them at a dinner at her house ("Tukey was the worst" she said) and Dr. Kinsey annoying Tukey by requesting he cease whistling Gilbert and Sullivan. The committee's report found statistical flaws in Kinsey's work, specifically problems with sampling methods and controlling randomness. Tukey stated that a random selection of three people would provide a better sample than three hundred chosen by Kinsey, who tended to select people known to each other.2

Tukey made many contributions to the development of computers and computing. His work with algorithms and robustness of data has software applications. Indeed, Tukey is credited with coining the work "software," which he first used in print in 1958, and "bit", short for "binary digit." The first computer on Princeton's campus was probably an IBM 650 belonging to the Statistical Techniques Research Group.

Tukey was a member of many professional and scientific societies: Institute of Mathematical Statistics (president, 1960); American Statistical Association (vice-president, 1955-57); American Society for Quality Control; American Association for the Advancement of Science; Biometric Society (council member); National Academy of Sciences (council, 1969-72, 1975-78); American Academy of Arts and Sciences; The Royal Society, London (foreign member); Royal Statistical Society; and the American Philosophical Society (vice-president, 1975-77). He also served on Board of Fellows of Brown University (1974-88).

Many awards came to Tukey during his career: first recipient of the S. S. Wilks Award from the American Statistical Association (1965); Shewhart Medal (1977) and Deming Medal (1983) from the American Society of Quality Control; James Madison Medal (1984) from Princeton University; Educational Testing (ETS) Service Award for Distinguished Service to Measurement(1990); and in 1973, the National Medal of Science "for his studies in mathematical and theoretical statistics . . . and for his outstanding contributions to the applications of statistics to the physical, social, and engineering sciences."

Tukey married Elizabeth Rapp, who at the time worked at ETS, in 1950. They were married for 48 years, Elizabeth dying in 1998. They had no children. Outside his professional work, Tukey had a couple of passionate interests. One was folk dancing. Another was reading science fiction.

1 Quoted in http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Tukey.html, MacTutor History of Mathematics at St. Andrews University, Scotland.

2 The New York Times, obituary, quoted in http://www-groups.dcs.st-and.ac.uk/~history/Obits2/Tukey_NYTimes.html; David R. Brillinger, "John Wilder Tukey (1915-2000), Notices of the American Mathematical Society, vol. 49, no. 2 (Feb. 2002).

Another reference consulted was Tukey's CV.