John Tukey
Encyclopedia
John Wilder Tukey ForMemRS
(June 16, 1915 – July 26, 2000) was an American statistician
.
in 1915, and obtained a B.A.
in 1936 and M.Sc. in 1937, in chemistry, from Brown University
, before moving to Princeton University
where he received a Ph.D.
in mathematics
.
During World War II
, Tukey worked at the Fire Control Research Office and collaborated with Samuel Wilks
and William Cochran
. After the war, he returned to Princeton, dividing his time between the university and AT&T Bell Laboratories
.
Among many contributions to civil society
, Tukey served on a committee of the American Statistical Association
that produced a report challenging the conclusions of the Kinsey Report
, Statistical Problems of the Kinsey Report on Sexual Behavior in the Human Male.
He was awarded the IEEE Medal of Honor
in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform
(FFT) algorithm
."
Tukey retired in 1985. He died in New Brunswick, New Jersey
on July 26, 2000.
interests were many and varied. He is particularly remembered for his development with James Cooley
of the Cooley–Tukey FFT algorithm. In 1970, he contributed significantly to what is today known as the jackknife estimation—also termed Quenouille-Tukey jackknife. He introduced the box plot
in his 1977 book,"Exploratory Data Analysis
".
Tukey's range test, the Tukey lambda distribution, Tukey's test of additivity
and Tukey's lemma
all bear his name. He is also the creator of several little-known methods such as the trimean
and median-median line, an easier alternative to linear regression
.
In 1974, he developed, with Jerome H. Friedman, the concept of the projection pursuit
.
While working with John von Neumann
on early computer designs, Tukey introduced the word "bit
" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948.
The term "software", which Paul Niquette claims he coined in 1953, was first used in print by Tukey in a 1958 article in American Mathematical Monthly
, and thus some attribute the term to him.
and confirmatory data analysis, believing that much statistical methodology placed too great an emphasis on the latter.
Though he believed in the utility of separating the two types of analysis, he pointed out that sometimes, especially in natural science
, this was problematic and termed such situations uncomfortable science
.
1. It is an attitude AND
2. A flexibility AND
3. Some graph paper (or transparencies, or both).
No catalogue of techniques can convey a willingness to look for what can be seen, whether or not anticipated. Yet this is at the heart of exploratory data analysis. The graph paper - and transparencies - are there, not as a technique, but rather as recognition that the picture-examining eye is the best finder we have of the wholly unanticipated.
About John Tukey
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
(June 16, 1915 – July 26, 2000) was an American statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
.
Biography
Tukey was born in New Bedford, MassachusettsNew Bedford, Massachusetts
New Bedford is a city in Bristol County, Massachusetts, United States, located south of Boston, southeast of Providence, Rhode Island, and about east of Fall River. As of the 2010 census, the city had a total population of 95,072, making it the sixth-largest city in Massachusetts...
in 1915, and obtained a B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in 1936 and M.Sc. in 1937, in chemistry, from Brown University
Brown University
Brown University is a private, Ivy League university located in Providence, Rhode Island, United States. Founded in 1764 prior to American independence from the British Empire as the College in the English Colony of Rhode Island and Providence Plantations early in the reign of King George III ,...
, before moving to Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
where he received a Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, Tukey worked at the Fire Control Research Office and collaborated with Samuel Wilks
Samuel S. Wilks
Samuel Stanley Wilks was an American mathematician and academic who played an important role in the development of mathematical statistics, especially in regard to practical applications....
and William Cochran
William Gemmell Cochran
William Gemmell Cochran was a prominent statistician; he was born in Scotland but spent most of his life in the United States....
. After the war, he returned to Princeton, dividing his time between the university and AT&T Bell Laboratories
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...
.
Among many contributions to civil society
Civil society
Civil society is composed of the totality of many voluntary social relationships, civic and social organizations, and institutions that form the basis of a functioning society, as distinct from the force-backed structures of a state , the commercial institutions of the market, and private criminal...
, Tukey served on a committee of the American Statistical Association
American Statistical Association
The American Statistical Association , is the main professional US organization for statisticians and related professions. It was founded in Boston, Massachusetts on November 27, 1839, and is the second oldest, continuously operating professional society in the United States...
that produced a report challenging the conclusions of the Kinsey Report
Kinsey Reports
The Kinsey Reports are two books on human sexual behavior, Sexual Behavior in the Human Male and Sexual Behavior in the Human Female , by Dr. Alfred Kinsey, Wardell Pomeroy and others and published by Saunders...
, Statistical Problems of the Kinsey Report on Sexual Behavior in the Human Male.
He was awarded the IEEE Medal of Honor
IEEE Medal of Honor
The IEEE Medal of Honor is the highest recognition of the Institute of Electrical and Electronics Engineers . It has been awarded since 1917, when its first recipient was Major Edwin H. Armstrong. It is given for an exceptional contribution or an extraordinary career in the IEEE fields of...
in 1982 "For his contributions to the spectral analysis of random processes and the fast Fourier transform
Fast Fourier transform
A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
(FFT) algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
."
Tukey retired in 1985. He died in New Brunswick, New Jersey
New Brunswick, New Jersey
New Brunswick is a city in Middlesex County, New Jersey, USA. It is the county seat and the home of Rutgers University. The city is located on the Northeast Corridor rail line, southwest of Manhattan, on the southern bank of the Raritan River. At the 2010 United States Census, the population of...
on July 26, 2000.
Scientific contributions
His statisticalStatistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
interests were many and varied. He is particularly remembered for his development with James Cooley
James Cooley
Dr. James W. Cooley is an American mathematician. James William Cooley received a B.A. degree in 1949 from Manhattan College, Bronx, NY, an M.A. degree in 1951 from Columbia University, New York, NY, and a Ph.D. degree in 1961 in applied mathematics from Columbia University...
of the Cooley–Tukey FFT algorithm. In 1970, he contributed significantly to what is today known as the jackknife estimation—also termed Quenouille-Tukey jackknife. He introduced the box plot
Box plot
In descriptive statistics, a box plot or boxplot is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation , lower quartile , median , upper quartile , and largest observation...
in his 1977 book,"Exploratory Data Analysis
Exploratory data analysis
In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...
".
Tukey's range test, the Tukey lambda distribution, Tukey's test of additivity
Tukey's test of additivity
In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way anova to assess whether the factor variables are additively related to the expected value of the response variable...
and Tukey's lemma
Tukey's lemma
In mathematics, Tukey's lemma, named after John Tukey, states that every nonempty collection of finite character has a maximal element with respect to inclusion. It is equivalent to the Axiom of Choice.- References :* Brillinger, David R. "John Wilder Tukey"...
all bear his name. He is also the creator of several little-known methods such as the trimean
Trimean
In statistics the trimean , or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles:This is equivalent to the average of the median and the midhinge:...
and median-median line, an easier alternative to linear regression
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
.
In 1974, he developed, with Jerome H. Friedman, the concept of the projection pursuit
Projection pursuit
Projection pursuit is a type of statistical technique which involves finding the most "interesting" possible projections in multidimensional data. Often, projections which deviate more from a Normal distribution are considered to be more interesting...
.
Statistical terms
Tukey coined many statistical terms that have become part of common usage, but the two most famous coinages attributed to him were related to computer science.While working with John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
on early computer designs, Tukey introduced the word "bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...
" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948.
The term "software", which Paul Niquette claims he coined in 1953, was first used in print by Tukey in a 1958 article in American Mathematical Monthly
American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America....
, and thus some attribute the term to him.
Statistical practice
He also contributed to statistical practice and articulated the important distinction between exploratory data analysisExploratory data analysis
In statistics, exploratory data analysis is an approach to analysing data sets to summarize their main characteristics in easy-to-understand form, often with visual graphs, without using a statistical model or having formulated a hypothesis...
and confirmatory data analysis, believing that much statistical methodology placed too great an emphasis on the latter.
Though he believed in the utility of separating the two types of analysis, he pointed out that sometimes, especially in natural science
Natural science
The natural sciences are branches of science that seek to elucidate the rules that govern the natural world by using empirical and scientific methods...
, this was problematic and termed such situations uncomfortable science
Uncomfortable science
Uncomfortable science is the term coined by statistician John Tukey for cases in which there is a need to draw an inference from a limited sample of data, where further samples influenced by the same cause system will not be available...
.
Quotes
- If we need a short suggestion of what exploratory data analysis is, I would suggest that
1. It is an attitude AND
2. A flexibility AND
3. Some graph paper (or transparencies, or both).
No catalogue of techniques can convey a willingness to look for what can be seen, whether or not anticipated. Yet this is at the heart of exploratory data analysis. The graph paper - and transparencies - are there, not as a technique, but rather as recognition that the picture-examining eye is the best finder we have of the wholly unanticipated.
- A D Gordon offered the following summary of Tukey's principles for statistical practice:
- ... 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 analysed; 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.
- ...Far better an approximate answer to the right question, than the exact answer to the wrong question, which can always be made precise....
- Once upon a time statisticians only explored. Then they learned to confirm exactly - to confirm a few things exactly, each under very specific circumstances. As they emphasized exact confirmation, their techniques inevitably became less flexible. The connection of the most used techniques with past insights was weakened. Anything to which a confirmatory procedure was not explicitly attached was decried as 'mere descriptive statistics', no matter how much we had learned from it.
- There is no data that can be displayed in a pie chart, that cannot be displayed BETTER in some other type of chart.
Publications
The collected works of John W Tukey, edited by William S ClevelandAbout John Tukey
External links
- John W. Tukey: His Life and Professional Contributions published in The Annals of Statistics
- John Wilder Tukey (1915–2000) in Notices of the American Mathematical SocietyNotices of the American Mathematical SocietyNotices of the American Mathematical Society is a membership magazine of the American Mathematical Society, published monthly except for the combined June/July issue. It is the world's most widely read mathematics magazine, sent to the approximately 30,000 AMS members worldwide...
- Memories of John Tukey
- Short biography by Mary Bittrich
- Obituary from The New York TimesThe New York TimesThe New York Times is an American daily newspaper founded and continuously published in New York City since 1851. The New York Times has won 106 Pulitzer Prizes, the most of any news organization...
- "Remembering John W. Tukey", special issue of Statistical ScienceStatistical ScienceStatistical Science is a review journal published by the Institute of Mathematical Statistics. The founding editor was Morris H. DeGroot.-External links:*...