Maurice Kendall
Encyclopedia
Sir Maurice George Kendall, FBA
(6 September 1907 – 29 March 1983) was a British statistician
, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.
, Northamptonshire
as the only child of John Roughton Kendall and Georgina Brewer. As a young child he survived a case of cerebral meningitis
, which was at the time frequently fatal. After growing up in Derby, England, he studied mathematics
at St. John's College
, Cambridge
, where he played cricket
and chess
(with future champions Conel Hugh O'Donel Alexander
and Jacob Bronowski
). After graduation as a Mathematics Wrangler in 1929, he joined the British Civil Service
in the Ministry of Agriculture
. In this position he became increasingly interested in using statistics
towards agricultural
questions, and one of his first published papers to the Royal Statistical Society
involved studying crop productivity using factor analysis
. He was elected a Fellow of the Society in 1934.
generation, developing both one of the first early mechanical devices to produce random digits, and formulated a series of tests for statistical randomness
in a given set of digits which, with some small modifications, became fairly widely used. He produced one of the second large collections of random digits (100,000 in total, over twice as many as those published by L. H. C. Tippett in 1927), which was a commonly used tract until the publication of RAND Corporation's A Million Random Digits with 100,000 Normal Deviates
in 1955 (which was developed with a roulette
wheel-like machine very similar to Kendall's and verified as "random" using his statistical tests).
Kendall and Babington-Smith used four separate tests to determine whether a given sequence of digits was "random" (or "unordered"). The first was a frequency test, which looked to make sure that the count of each digit in a sequence was close enough to expected probabilities ("close enough" was determined by the use of a chi square calculation). If one were rolling an ideal six-sided die
, over the long run one would expect to get an equal number of ones, twos, threes, etc. The second test was a serial test, which looked at the expected and observed frequencies of pairs of two digits (01, 11, 12, etc.), which got around the problem of sequences such as "1234512345" which would pass the frequency test but be decidedly non-random. The third test was another type of frequency test, this time for the expected and found set of five-digit sequences, known as a poker test, after the card game
. The fourth test was known as the gap test, which looked for expected gaps between individual digits (usually between zeros) in long sequences, comparing observed counts ("01230" would be a gap of three digits between the zeros, "0120" would be two, etc.) with their statistical probabilities. If a set of numbers passed all four tests, it was considered by Kendall and Babington Smith to be "random enough" for most usage. They also developed the notion of "local randomness", noting that in any sufficiently long sequence of truly random digits there would be sets which would look exceedingly unrandom (such as a string of many zeros together). They concluded that these small cases of local un-randomness in an overall random sequence should not be discarded, but that care must be taken in the uses of random number sequences to make sure such "patches" of data did not overly add bias to the results.
In 1937, he aided the aging statistician G. Udny Yule in the revision of his standard statistical textbook, Introduction to the Theory of Statistics, commonly known for many years as "Yule and Kendall". The two had met by chance in 1935, and were on close terms until Yule's death in 1951 (Yule was godfather
to Kendall's second son).
During this period he also began work on the rank correlation coefficient
which currently bears his name (Kendall's tau), which eventually led to a monograph on Rank Correlation in 1948.
In the late 1930s, he was additionally part of a group of five other statisticians who endeavored to produce a reference work summarizing recent developments in statistical theory, but it was cancelled on account of onset of World War II
.
During the war he also produced a series of papers extending to work of R.A. Fisher on the theory of k-statistics, and developed a number of extensions to this work through the 1950s. After the war, he worked on the theory and practice of time series analysis, and conclusively demonstrated (with the meager computing
resources available at the time) that unsmoothed sample periodogram
s were unreliable estimators for the population spectrum.
, University of London
. Here he worked part-time as the director of the new Research Techniques Division. From 1952 to 1957 he edited a two-volume work on Statistical Sources in the United Kingdom, which was a standard reference until the mid-1970s. In the fifities he also worked on multivariate analysis
, and developed the text Multivariate Analysis in 1957. In the same year he also developed, along with W. R. Buckland, a Dictionary of Statistical Terms, aimed at helping making the tools of statistics more available to potential users in industry and government.
In 1953 he published " The Analytics of Economic Time Series, Part 1: Prices" in which he suggested that the movement of shares on the stock market was random i.e. they were as likely to go up on a certain day as they were to go down. These results were disturbing to some financial economists and further debate and research then followed. This ultimately led to the creation of the Random Walk Hypothesis
, and the closely related efficient-market hypothesis which states that random price movements indicate a well-functioning or efficient market.
. In the 1960s he published and co-edited a number of volumes and monographs in statistical theory.
In 1972, he became director of the World Fertility Survey, a project sponsored by the International Statistical Institute
and the United Nations
which aimed to study fertility
in developed and developing nations. He continued this work until 1980, when illness forced him to retire.
in 1980 in recognition for his work on the World Fertility Survey. He was also elected a fellow of the British Academy
and received the highest honor of the Royal Statistical Society
, the Guy Medal
in Gold. He additionally had served as president of the Operational Research Society, the Institute of Statisticians
, and was elected a fellow of the American Statistical Association
, the Institute of Mathematical Statistics
, the Econometric Society
, and the British Computer Society
. At the time of his death in 1983, he was honorary president of the International Statistical Institute.
British Academy
The British Academy is the United Kingdom's national body for the humanities and the social sciences. Its purpose is to inspire, recognise and support excellence in the humanities and social sciences, throughout the UK and internationally, and to champion their role and value.It receives an annual...
(6 September 1907 – 29 March 1983) was a British statistician
Statistics
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....
, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.
Education and early life
Maurice Kendall was born in KetteringKettering
Kettering is a market town in the Borough of Kettering, Northamptonshire, England. It is situated about from London. Kettering is mainly situated on the west side of the River Ise, a tributary of the River Nene which meets at Wellingborough...
, Northamptonshire
Northamptonshire
Northamptonshire is a landlocked county in the English East Midlands, with a population of 629,676 as at the 2001 census. It has boundaries with the ceremonial counties of Warwickshire to the west, Leicestershire and Rutland to the north, Cambridgeshire to the east, Bedfordshire to the south-east,...
as the only child of John Roughton Kendall and Georgina Brewer. As a young child he survived a case of cerebral meningitis
Meningitis
Meningitis is inflammation of the protective membranes covering the brain and spinal cord, known collectively as the meninges. The inflammation may be caused by infection with viruses, bacteria, or other microorganisms, and less commonly by certain drugs...
, which was at the time frequently fatal. After growing up in Derby, England, he studied 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...
at St. John's College
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
, Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, where he played cricket
Cricket
Cricket is a bat-and-ball game played between two teams of 11 players on an oval-shaped field, at the centre of which is a rectangular 22-yard long pitch. One team bats, trying to score as many runs as possible while the other team bowls and fields, trying to dismiss the batsmen and thus limit the...
and chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...
(with future champions Conel Hugh O'Donel Alexander
Conel Hugh O'Donel Alexander
Conel Hugh O'Donel Alexander, CMG, CBE was an Irish-born British cryptanalyst, chess player, and chess writer. He worked on the German Enigma machine at Bletchley Park during World War II, and was later the head of the cryptanalysis division at GCHQ for over 20 years...
and Jacob Bronowski
Jacob Bronowski
Jacob Bronowski was a Polish-Jewish British mathematician, biologist, historian of science, theatre author, poet and inventor...
). After graduation as a Mathematics Wrangler in 1929, he joined the British Civil Service
British Civil Service
Her Majesty's Home Civil Service, also known as the Home Civil Service, is the permanent bureaucracy of Crown employees that supports Her Majesty's Government - the government of the United Kingdom, composed of a Cabinet of ministers chosen by the prime minister, as well as the devolved...
in the Ministry of Agriculture
Ministry of Agriculture
An agriculture ministry or department of agriculture is a ministry or other government agency charged with agriculture. The ministry is often headed by a minister for agriculture....
. In this position he became increasingly interested in using statistics
Statistics
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....
towards agricultural
Agriculture
Agriculture is the cultivation of animals, plants, fungi and other life forms for food, fiber, and other products used to sustain life. Agriculture was the key implement in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that nurtured the...
questions, and one of his first published papers to the Royal Statistical Society
Royal Statistical Society
The Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
involved studying crop productivity using factor analysis
Factor analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...
. He was elected a Fellow of the Society in 1934.
Work in statistics
In 1938 and 1939 he began work, along with Bernard Babington-Smith, on the question of random numberRandom number
Random number may refer to:* A number generated for or part of a set exhibiting statistical randomness.* A random sequence obtained from a stochastic process.* An algorithmically random sequence in algorithmic information theory....
generation, developing both one of the first early mechanical devices to produce random digits, and formulated a series of tests for statistical randomness
Statistical randomness
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll, or the digits of π exhibit statistical randomness....
in a given set of digits which, with some small modifications, became fairly widely used. He produced one of the second large collections of random digits (100,000 in total, over twice as many as those published by L. H. C. Tippett in 1927), which was a commonly used tract until the publication of RAND Corporation's A Million Random Digits with 100,000 Normal Deviates
A Million Random Digits with 100,000 Normal Deviates
A Million Random Digits with 100,000 Normal Deviates is a 1955 book by the RAND Corporation. The book, consisting primarily of a random number table, was an important 20th century work in the field of statistics and random numbers...
in 1955 (which was developed with a roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
wheel-like machine very similar to Kendall's and verified as "random" using his statistical tests).
Kendall and Babington-Smith used four separate tests to determine whether a given sequence of digits was "random" (or "unordered"). The first was a frequency test, which looked to make sure that the count of each digit in a sequence was close enough to expected probabilities ("close enough" was determined by the use of a chi square calculation). If one were rolling an ideal six-sided die
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
, over the long run one would expect to get an equal number of ones, twos, threes, etc. The second test was a serial test, which looked at the expected and observed frequencies of pairs of two digits (01, 11, 12, etc.), which got around the problem of sequences such as "1234512345" which would pass the frequency test but be decidedly non-random. The third test was another type of frequency test, this time for the expected and found set of five-digit sequences, known as a poker test, after the card game
Poker
Poker is a family of card games that share betting rules and usually hand rankings. Poker games differ in how the cards are dealt, how hands may be formed, whether the high or low hand wins the pot in a showdown , limits on bet sizes, and how many rounds of betting are allowed.In most modern poker...
. The fourth test was known as the gap test, which looked for expected gaps between individual digits (usually between zeros) in long sequences, comparing observed counts ("01230" would be a gap of three digits between the zeros, "0120" would be two, etc.) with their statistical probabilities. If a set of numbers passed all four tests, it was considered by Kendall and Babington Smith to be "random enough" for most usage. They also developed the notion of "local randomness", noting that in any sufficiently long sequence of truly random digits there would be sets which would look exceedingly unrandom (such as a string of many zeros together). They concluded that these small cases of local un-randomness in an overall random sequence should not be discarded, but that care must be taken in the uses of random number sequences to make sure such "patches" of data did not overly add bias to the results.
In 1937, he aided the aging statistician G. Udny Yule in the revision of his standard statistical textbook, Introduction to the Theory of Statistics, commonly known for many years as "Yule and Kendall". The two had met by chance in 1935, and were on close terms until Yule's death in 1951 (Yule was godfather
Godparent
A godparent, in many denominations of Christianity, is someone who sponsors a child's baptism. A male godparent is a godfather, and a female godparent is a godmother...
to Kendall's second son).
During this period he also began work on the rank correlation coefficient
Rank correlation
In statistics, a rank correlation is the relationship between different rankings of the same set of items. A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess its significance....
which currently bears his name (Kendall's tau), which eventually led to a monograph on Rank Correlation in 1948.
In the late 1930s, he was additionally part of a group of five other statisticians who endeavored to produce a reference work summarizing recent developments in statistical theory, but it was cancelled on account of onset of 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...
.
War-time efforts
Kendall became Assistant General Manager to the British Chamber of Shipping by day and had air-raid warden duties by night. Despite these constraints on his time, he managed to produce volume one of The Advanced Theory of Statistics in 1943 and a second volume in 1946.During the war he also produced a series of papers extending to work of R.A. Fisher on the theory of k-statistics, and developed a number of extensions to this work through the 1950s. After the war, he worked on the theory and practice of time series analysis, and conclusively demonstrated (with the meager computing
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...
resources available at the time) that unsmoothed sample periodogram
Periodogram
The periodogram is an estimate of the spectral density of a signal. The term was coined by Arthur Schuster in 1898 as in the following quote:...
s were unreliable estimators for the population spectrum.
London School of Economics
In 1949 he accepted the second chair of statistics at the London School of EconomicsLondon School of Economics
The London School of Economics and Political Science is a public research university specialised in the social sciences located in London, United Kingdom, and a constituent college of the federal University of London...
, University of London
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
. Here he worked part-time as the director of the new Research Techniques Division. From 1952 to 1957 he edited a two-volume work on Statistical Sources in the United Kingdom, which was a standard reference until the mid-1970s. In the fifities he also worked on multivariate analysis
Multivariate analysis
Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...
, and developed the text Multivariate Analysis in 1957. In the same year he also developed, along with W. R. Buckland, a Dictionary of Statistical Terms, aimed at helping making the tools of statistics more available to potential users in industry and government.
In 1953 he published " The Analytics of Economic Time Series, Part 1: Prices" in which he suggested that the movement of shares on the stock market was random i.e. they were as likely to go up on a certain day as they were to go down. These results were disturbing to some financial economists and further debate and research then followed. This ultimately led to the creation of the Random Walk Hypothesis
Random walk hypothesis
The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the prices of the stock market cannot be predicted. It is consistent with the efficient-market hypothesis....
, and the closely related efficient-market hypothesis which states that random price movements indicate a well-functioning or efficient market.
CEIR and WFS
In 1961 he left the University of London and took a position as the managing director (later chairman) of a consulting company, CEIR (later known as Scientific Control Systems), and in the same year began a two-year term as president of the Royal Statistical SocietyRoyal Statistical Society
The Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
. In the 1960s he published and co-edited a number of volumes and monographs in statistical theory.
In 1972, he became director of the World Fertility Survey, a project sponsored by the International Statistical Institute
International Statistical Institute
The International Statistical Institute is a professional association of statisticians. The Institut International de Statistique or International Statistical Institute was founded in 1885 although there had been international congresses from 1853.. The Institute publishes a variety of books and...
and the United Nations
United Nations
The United Nations is an international organization whose stated aims are facilitating cooperation in international law, international security, economic development, social progress, human rights, and achievement of world peace...
which aimed to study fertility
Fertility
Fertility is the natural capability of producing offsprings. As a measure, "fertility rate" is the number of children born per couple, person or population. Fertility differs from fecundity, which is defined as the potential for reproduction...
in developed and developing nations. He continued this work until 1980, when illness forced him to retire.
Honours
He was knighted by the British government in 1974 for his services to the theory of statistics, and received the Peace Medal of the United NationsUnited Nations
The United Nations is an international organization whose stated aims are facilitating cooperation in international law, international security, economic development, social progress, human rights, and achievement of world peace...
in 1980 in recognition for his work on the World Fertility Survey. He was also elected a fellow of the British Academy
British Academy
The British Academy is the United Kingdom's national body for the humanities and the social sciences. Its purpose is to inspire, recognise and support excellence in the humanities and social sciences, throughout the UK and internationally, and to champion their role and value.It receives an annual...
and received the highest honor of the Royal Statistical Society
Royal Statistical Society
The Royal Statistical Society is a learned society for statistics and a professional body for statisticians in the UK.-History:It was founded in 1834 as the Statistical Society of London , though a perhaps unrelated London Statistical Society was in existence at least as early as 1824...
, the Guy Medal
Guy Medal
The Guy Medals are awarded by the Royal Statistical Society in three categories; Gold, Silver and Bronze. The Gold Medal is awarded triennially, the other two are awarded annually...
in Gold. He additionally had served as president of the Operational Research Society, the Institute of Statisticians
Institute of Statisticians
The Institute of Statisticians was a British professional organization founded in 1948 to protect the interests of professional statisticians. It was originally named The Association of Incorporated Statisticians Limited, but this was later changed...
, and was elected a fellow 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...
, the Institute of Mathematical Statistics
Institute of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world...
, the Econometric Society
Econometric Society
The Econometric Society is an international society for the advancement of economic theory in its relation with statistics and mathematics. It was founded on December 29, 1930 at the Stalton Hotel in Cleveland, Ohio....
, and the British Computer Society
British Computer Society
The British Computer Society, is a professional body and a learned society that represents those working in Information Technology in the United Kingdom and internationally...
. At the time of his death in 1983, he was honorary president of the International Statistical Institute.