Francis Anscombe
Encyclopedia
Francis John Anscombe (13 May 1918 – 17 October 2001) was a statistician
.
Born in Hove
in England, Anscombe was educated at Trinity College
at Cambridge University. After serving in the Second World War, he joined Rothamsted Experimental Station
for two years before returning to Cambridge as a lecturer.
In experiment
s, Anscombe emphasized randomization in both the design and analysis phases. In the design
phase, Anscombe argued that the experimenters should randomize
the labels of blocks
. In the analysis phase, Anscombe argued that the randomization plan should guide the analysis of data; Anscombe's approach has influenced John Nelder
and R. A. Bailey in particular.
He moved to Princeton University
in 1956, and became the founding chairman of the statistics
department at Yale University
in 1963.
According to David Cox
, his best-known work may be his 1961 account of formal properties of residuals
in linear regression
.
His earlier suggestion for a variance-stabilizing transformation
for Poisson
data is often known as the Anscombe transform
.
He later became interested in statistical computing, and stressed that "a computer should make both calculations and graphs", and illustrated the importance of graphing data with four data sets now known as Anscombe's quartet
. He later published a textbook on statistical computing in APL.
In economics
and decision theory
he is best known for a 1963 paper with Robert Aumann
which provides the standard basis for the theory of subjective probability.
He was brother-in-law
to another well-known statistician, John Tukey
of Princeton University
; their wives were sisters.
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...
.
Born in Hove
Hove
Hove is a town on the south coast of England, immediately to the west of its larger neighbour Brighton, with which it forms the unitary authority Brighton and Hove. It forms a single conurbation together with Brighton and some smaller towns and villages running along the coast...
in England, Anscombe was educated at Trinity College
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
at Cambridge University. After serving in the Second World War, he joined Rothamsted Experimental Station
Rothamsted Experimental Station
The Rothamsted Experimental Station, one of the oldest agricultural research institutions in the world, is located at Harpenden in Hertfordshire, England. It is now known as Rothamsted Research...
for two years before returning to Cambridge as a lecturer.
In experiment
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...
s, Anscombe emphasized randomization in both the design and analysis phases. In the design
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled experiments...
phase, Anscombe argued that the experimenters should randomize
Random assignment
Random assignment or random placement is an experimental technique for assigning subjects to different treatments . The thinking behind random assignment is that by randomizing treatment assignment, then the group attributes for the different treatments will be roughly equivalent and therefore any...
the labels of blocks
Randomized block design
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups that are similar to one another. Typically, a blocking factor is a source of variability that is not of primary interest to the experimenter...
. In the analysis phase, Anscombe argued that the randomization plan should guide the analysis of data; Anscombe's approach has influenced John Nelder
John Nelder
John Ashworth Nelder FRS was a British statistician known for his contributions to experimental design, analysis of variance, computational statistics, and statistical theory.-Contributions:...
and R. A. Bailey in particular.
He moved 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....
in 1956, and became the founding chairman of the 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....
department at Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
in 1963.
According to David Cox
David Cox (statistician)
Sir David Roxbee Cox FRS is a prominent British statistician.-Early years:Cox studied mathematics at St. John's College, Cambridge and obtained his PhD from the University of Leeds in 1949, advised by Henry Daniels and Bernard Welch.-Career:He was employed from 1944 to 1946 at the Royal Aircraft...
, his best-known work may be his 1961 account of formal properties of residuals
Errors and residuals in statistics
In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
in 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...
.
His earlier suggestion for a variance-stabilizing transformation
Variance-stabilizing transformation
In applied statistics, a variance-stabilizing transformation is a data transformation that is specifically chosen either to simplify considerations in graphical exploratory data analysis or to allow the application of simple regression-based or analysis of variance techniques.The aim behind the...
for Poisson
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...
data is often known as the Anscombe transform
Anscombe transform
In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The Anscombe transform is widely used in photon-limited imaging ...
.
He later became interested in statistical computing, and stressed that "a computer should make both calculations and graphs", and illustrated the importance of graphing data with four data sets now known as Anscombe's quartet
Anscombe's quartet
Anscombe's quartet comprises four datasets that have identical simple statistical properties, yet appear very different when graphed. Each dataset consists of eleven points. They were constructed in 1973 by the statistician F.J...
. He later published a textbook on statistical computing in APL.
In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
and decision theory
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
he is best known for a 1963 paper with Robert Aumann
Robert Aumann
Robert John Aumann is an Israeli-American mathematician and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel...
which provides the standard basis for the theory of subjective probability.
He was brother-in-law
Brother-in-law
A brother-in-law is the brother of one's spouse, the husband of one's sibling, or the husband of one's spouse's sibling.-See also:*Affinity *Sister-in-law*Brothers in Law , a 1955 British comedy novel...
to another well-known statistician, John Tukey
John Tukey
John Wilder Tukey ForMemRS was an American statistician.- Biography :Tukey was born in New Bedford, Massachusetts 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...
of 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....
; their wives were sisters.