Ronald Fisher

R. A. Fisher
Sir Ronald Aylmer Fisher (1890-1962)
Born	17 February 1890(1890-02-17) East Finchley, London , England
Died	29 July 1962 (aged 72) Adelaide, Australia
Residence	England Australia
Nationality	British
Fields	Statistician Evolutionary biologist Geneticist
Institutions	Rothamsted Experimental Station University College London Cambridge University CSIRO
Alma mater	Cambridge University
Academic advisors	Sir James Jeans F.J.M. Stratton
Doctoral students	C.R. Rao D. J. Finney
Known for	Fisher's fundamental theorem Maximum likelihood Fisher information Analysis of variance Fisher-Kolmogorov equation Coining the term 'null hypothesis' Fiducial inference Fisher's exact test Fisher's principle Fisherian runaway F-distribution
Influences	Leonard Darwin
Influenced	Joseph Oscar Irwin A. W. F. Edwards Georg Rasch
Notable awards	Royal Medal (1938) Guy Medal in Gold (1946) Copley Medal (1955) Linnean Society of London's Darwin-Wallace Medal (1958).
Religious stance	Church of England
Notes He was the father-in-law of George E. P. Box.

Sir Ronald Aylmer Fisher, FRS (17 February 1890 – 29 July 1962) was an English statistician, evolutionary biologist, and geneticist. He was described by Anders Hald as "a genius who almost single-handedly created the foundations for modern statistical science"^[1] and Richard Dawkins described him as "the greatest of Darwin's successors".^[2]

Biography

Early life

Fisher was born in East Finchley in London, England, to George and Katie Fisher. His father was a successful fine arts dealer. He had a happy childhood, being doted on by three older sisters, an older brother, and his mother, who died when Fisher was 14. His father lost his business in several ill-considered transactions only 18 months later.^[3]

Although Fisher had very poor eyesight he was a precocious student, winning the Neeld Medal (a competitive essay in Mathematics) at Harrow School at the age of 16. Because of his poor eyesight, he was tutored in mathematics without the aid of paper and pen, which developed his ability to visualize problems in geometrical terms, as opposed to using algebraic manipulations. He was legendary in being able to produce mathematical results without setting down the intermediate steps. He also developed a strong interest in biology, and, especially, evolution.

In 1909 he won a scholarship to Gonville and Caius College, Cambridge. There he formed many friendships and became enthralled with the heady intellectual atmosphere. At Cambridge, Fisher learned of the newly rediscovered theory of Mendelian genetics; he saw biometry—and its growing corpus of statistical methods—as a potential way to reconcile the discontinuous nature of Mendelian inheritance with continuous variation and gradual evolution. However, his foremost concern was eugenics, which he saw as a pressing social as well as scientific issue that encompassed both genetics and statistics. In 1911 he was involved in forming the Cambridge University Eugenics Society with such luminaries as John Maynard Keynes, R. C. Punnett and Horace Darwin (Charles Darwin's son). The group was active, and held monthly meetings, often featuring addresses by leaders of mainstream eugenics organizations, such as the Eugenics Education Society of London, founded by Charles Darwin's half-cousin, Francis Galton in 1909.^[4]

After graduating in 1913, Fisher was eager to join the army in anticipation of Great Britain's entry into World War I; however, he failed the medical examinations (repeatedly) because of his eyesight. Over the next six years, he worked as a statistician for the City of London. For his war work, he took up teaching physics and mathematics at a series of public schools, including Bradfield College in Berkshire, as well as aboard H.M. Training Ship Worcester. Major Leonard Darwin (another of Charles Darwin's sons) and an unconventional and vivacious friend he called Gudruna were almost his only contacts with his Cambridge circle. They sustained him through this difficult period. A bright spot in his life was that Gudruna matched him to her sister Eileen Guinness; they married in 1917 when she was only 17. With the sisters' help, he set up a subsistence farming operation on the Bradfield estate, where they had a large garden and raised animals, learning to make do on very little. They lived through the war without ever using their food coupons.^[5]

During this period, Fisher started writing book reviews for the Eugenic Review and gradually increased his interest in genetic and statistical work. He volunteered to undertake all such reviews for the journal, and was hired to a part-time position by Major Darwin. He published several articles on biometry during this period, including the ground-breaking "The Correlation Between Relatives on the Supposition of Mendelian Inheritance" , written in 1916 and published in 1918. This paper laid the foundation for what came to be known as biometrical genetics, and introduced the very important methodology of the analysis of variance, which was a considerable advance over the correlation methods used previously. The paper showed very convincingly that the inheritance of traits measurable by real values, the values of continuous variables, is consistent with Mendelian principles.^[6]

With the end of the war he went looking for a new job, and was offered one at the famed Galton Laboratory by Karl Pearson. Because he saw the developing rivalry with Pearson as a professional obstacle, however, he accepted instead a temporary job as a statistician with a small agricultural station in the country in 1919.

Stained glass window in the dining hall of Caius College, in Cambridge, commemorating Ronald Fisher and representing a Latin square.

Early professional years

In 1919 Fisher started work at Rothamsted Experimental Station located at Harpenden, Hertfordshire, England. Here he started a major study of the extensive collections of data recorded over many years. This resulted in a series of reports under the general title Studies in Crop Variation. This began a period of great productivity. Over the next seven years, he pioneered the principles of the design of experiments and elaborated his studies of "analysis of variance". He furthered his studies of the statistics of small samples. Perhaps even more important, he began his systematic approach of the analysis of real data as the springboard for the development of new statistical methods. He began to pay particular attention to the labour involved in the necessary computations, and developed methods that were as practical as they were founded in rigour. In 1925, this work culminated in the publication of his first book, Statistical Methods for Research Workers.^[7] This went into many editions and translations in later years, and became a standard reference work for scientists in many disciplines. In 1935, this was followed by The Design of Experiments, which also became a standard.

In addition to "analysis of variance", Fisher invented the technique of maximum likelihood and originated the concepts of sufficiency, ancillarity, Fisher's linear discriminator and Fisher information. His 1924 article "On a distribution yielding the error functions of several well known statistics" presented Karl Pearson's chi-squared and Student's t in the same framework as the Gaussian distribution, and his own "analysis of variance" distribution z (more commonly used today in the form of the F distribution). These contributions easily made him a major figure in 20th century statistics.

In defending the use of the z distribution when the data were not Gaussian, Fisher introduced the "randomization test". According to biographers Yates and Mather, "Fisher introduced the randomization test, comparing the value of t or z actually obtained with the distribution of the t or z values when all possible random arrangements were imposed on the experimental data."^[8]

However, Fisher wrote that randomization tests were "in no sense put forward to supersede the common and expeditious tests based on the Gaussian theory of errors." Fisher thus effectively began the field of non-parametric statistics, even though he didn't believe it was a necessary move.

His work on the theory of population genetics also made him one of the three great figures of that field, together with Sewall Wright and J. B. S. Haldane, and as such was one of the founders of the neo-Darwinian modern evolutionary synthesis. In addition to founding modern quantitative genetics with his 1918 paper, he was the first to use diffusion equations to attempt to calculate the distribution of gene frequencies among populations. He pioneered the estimation of genetic linkage and gene frequencies by maximum likelihood methods, and wrote early papers on the wave of advance of advantageous genes and on clines of gene frequency. His 1950 paper on gene frequency clines is notable as the first application of computers to biology.

Fisher had a long and successful collaboration with E.B. Ford in the field of ecological genetics. The outcome of this work was the general recognition that the force of natural selection was often much stronger than had been appreciated before, and that many ecogenetic situations (such as polymorphism) were not selectively neutral, they were maintained by the force of selection. Fisher was the original author of the idea of heterozygote advantage, which was later found to play a frequent role in genetic polymorphism.^[9] The discovery of indisputable cases of natural selection in nature was one of the main strands in the modern evolutionary synthesis.

Fisher introduced the concept of Fisher information in 1925, some years before Shannon's notions of information and entropy. Fisher information has been the subject of renewed interest in the last few years, due to B. Roy Frieden's book Physics from Fisher Information, which attempts to derive the laws of physics from a Fisherian starting point.

Fisher's Genetical Theory of Natural Selection

Fisher was an ardent promoter of eugenics, which also stimulated and guided much of his work in the genetics of humans. His book The Genetical Theory of Natural Selection was started in 1928 and published in 1930. It contained a summary of what was already known to the literature. He developed ideas on sexual selection, mimicry and the evolution of dominance. He famously showed that the probability of a mutation increasing the fitness of an organism decreases proportionately with the magnitude of the mutation. He also proved that larger populations carry more variation so that they have a larger chance of survival. He set forth the foundations of what was to become known as population genetics.

About a third of the book concerned the applications of these ideas to humans, and presented what data there was available at the time. He presented a theory that attributed the decline and fall of civilizations to its arrival at a state where the fertility of the upper classes is forced down. Using the census data of 1911 for Britain, he showed that there was an inverse relationship between fertility and social class. This was partly due, he believed, to the rise in social status of families who were not capable of producing many children but who rose because of the financial advantage of having a small number of children. Therefore he proposed the abolishment of the economic advantage of small families by instituting subsidies (he called them allowances) to families with larger numbers of children, with the allowances proportional to the earnings of the father. He himself had two sons and six daughters. According to Yates and Mather, "His large family, in particular, reared in conditions of great financial stringency, was a personal expression of his genetic and evolutionary convictions."

The book was reviewed, among others, by physicist Charles Galton Darwin, a grandson of Charles Darwin's, and following publication of his review, C. G. Darwin sent Fisher his copy of the book, with notes in the margin. The marginal notes became the food for a correspondence running at least three years.^[10] Fisher's book The Genetical Theory of Natural Selection, also had a major influence on the evolutionary biologist W. D. Hamilton and the development of his later theories on the genetic basis for the existence of kin selection.

Between 1929 and 1934 the Eugenics Society also campaigned hard for a law permitting sterilization on eugenic grounds. They believed that it should be entirely voluntary, and a right, not a punishment. They published a draft of a proposed bill, and it was submitted to Parliament. Although it was defeated by a 2:1 ratio, this was viewed as progress, and the campaign continued. Fisher played a major role in this movement, and served in several official committees to promote it.

In 1934, Fisher moved to increase the power of scientists within the Eugenics Society, but was ultimately thwarted by members with an environmentalist point of view, and he, along with many other scientists, resigned.

Method and personality

The interest in eugenics, and his experiences working on the Canadian farm, made Fisher interested in starting a farm of his own. In these plans he was encouraged by Gudruna, the wife of a college friend, and this led to him meeting Ruth Eileen Gratton Guinness, Gudruna's younger sister. Their father, Dr Henry Gratton Guinness, had died when they were young. Ruth Eileen was only sixteen years of age when she met Fisher. She knew that her mother would not approve of her marrying so young. As a result Fisher married Ruth Eileen at a secret wedding ceremony without her mother's knowledge, on 26 April 1917, only days after Ruth Eileen's 17th birthday. They had two sons and seven daughters, one of whom died in infancy. His daughter Joan married George E. P. Box and wrote a well-received biography of her father.

As an adult, Fisher was noted for his loyalty to his friends. Once he had formed a favourable opinion of any man, he was loyal to a fault. A similar sense of loyalty bound him to his culture. He was a patriot, a member of the Church of England, politically conservative, and a scientific rationalist. Much sought after as a brilliant conversationalist and dinner companion, he very early on developed a reputation for carelessness in his dress and, sometimes, his manners. In later years he was the archetype of the absent-minded professor.

He knew the scriptures well and H. Allen Orr describes him as "deeply devout Anglican who, between founding modern statistics and population genetics, penned articles for church magazines" in the Boston Review ^[11]. But he was not dogmatic in his religious beliefs. In a 1955 broadcast on Science and Christianity^[12], he said, "The custom of making abstract dogmatic assertions is not, certainly, derived from the teaching of Jesus, but has been a widespread weakness among religious teachers in subsequent centuries. I do not think that the word for the Christian virtue of faith should be prostituted to mean the credulous acceptance of all such piously intended assertions. Much self-deception in the young believer is needed to convince himself that he knows that of which in reality he knows himself to be ignorant. That surely is hypocrisy, against which we have been most conspicuously warned."

Later years

It was Fisher who referred to the growth rate r (used in equations such as the logistic function) as the Malthusian parameter, as a criticism of the writings of Thomas Robert Malthus. Fisher referred to "...a relic of creationist philosophy..." in observing the fecundity of nature and deducing (as Darwin did) that this therefore drove natural selection.

He received the recognition of his peers in 1929 when he was inducted into the Royal Society. His fame grew and he began to travel more and lecture to wider circles. In 1931 he spent six weeks at the Statistical Laboratory at Iowa State College in Ames, Iowa. He gave three lectures a week on his work, and met many of the active American statisticians, including George W. Snedecor. He returned again for another visit in 1936.

In 1933 he left Rothamsted to become a Professor of Eugenics at University College London. In 1937 he visited the Indian Statistical Institute (in Calcutta), which at the time consisted of one part-time employee, Professor P. C. Mahalanobis. He revisited there often in later years, encouraging its development. He was the guest of honour at its 25th anniversary in 1957 when it had grown to 2000 employees^[13] . In 1939, when World War II broke out, the University tried to dissolve the eugenics department, and ordered all of the animals destroyed. Fisher fought back, but he was then exiled back to Rothamsted with a much reduced staff and resources. He was unable to find any suitable war work, and though he kept very busy with various small projects, he became discouraged of any real progress. His marriage disintegrated. His oldest son, George, an aeroplane pilot^[14], was killed in the war.

In 1943 he was offered the Balfour Chair of Genetics at Cambridge University, his alma mater. During the war, this department was also pretty much destroyed, but the University promised him that he would be charged with rebuilding it after the war. He accepted the offer, but the promises were largely unfilled, and the department grew very slowly. A notable exception was the recruitment in 1948 of the Italian researcher Cavalli-Sforza, who established a one man unit of bacterial genetics. He continued his work on mouse chromosome mapping and other projects. They culminated in the publication in 1949 of the idiosyncratic (?) The Theory of Inbreeding. In 1947 he co-founded with Cyril Darlington the journal Heredity: An International Journal of Genetics.

Ronald Fisher was opposed to the UNESCO Statement of Race. He believed that evidence and everyday experience showed that human groups differ profoundly “in their innate capacity for intellectual and emotional development” and concluded that the “practical international problem is that of learning to share the resources of this planet amicably with persons of materially different nature,” and that “this problem is being obscured by entirely well-intentioned efforts to minimize the real differences that exists.” The revised 1951 statement titled "The Race Concept: Results of an Inquiry" was accompanied by Fisher's dissenting commentary.^[15]

He eventually received many awards for his work and was dubbed a Knight Bachelor by Queen Elizabeth II in 1952.

Fisher was opposed to the conclusions of Richard Doll and A.B. Hill that smoking caused lung cancer. He compared the correlations in their papers to a correlation between the import of apples and the rise of divorce in order to show that correlation does not imply causation.^[16] To quote Yates and Mather again, "It has been suggested that the fact that Fisher was employed as consultant by the tobacco firms in this controversy casts doubt on the value of his arguments. This is to misjudge the man. He was not above accepting financial reward for his labours, but the reason for his interest was undoubtedly his dislike and mistrust of puritanical tendencies of all kinds; and perhaps also the personal solace he had always found in tobacco."

After retiring from Cambridge University in 1957 he spent some time as a senior research fellow at the CSIRO in Adelaide, Australia. He died of colon cancer there in 1962.

He was awarded the Linnean Society of London's prestigious Darwin-Wallace Medal in 1958.

Fisher's important contributions to both genetics and statistics are emphasized by the remark of L.J. Savage, "I occasionally meet geneticists who ask me whether it is true that the great geneticist R.A. Fisher was also an important statistician" (Annals of Statistics, 1976).

See also

Notes

1. ↑ Hald, Anders (1998). A History of Mathematical Statistics. New York: Wiley. 
2. ↑ Dawkins, Richard (1995). River out of Eden. 
3. ↑ Box, R. A. Fisher, pp 8-16
4. ↑ Box, R. A. Fisher, pp 17-34
5. ↑ Box, R. A. Fisher, pp 35-50
6. ↑ Box, R. A. Fisher, pp 50-61
7. ↑ Box, R. A. Fisher, pp 93-166
8. ↑ Frank Yates & Kenneth Mather (1963) "Ronald Aylmer Fisher." Biographical Memoirs of Fellows of the Royal Society of London 9:91-120 Available on University of Adelaide website
9. ↑ Fisher R. 1930. The Genetical Theory of Natural Selection.
10. ↑ Fisher, R. A. 1999. The Genetical Theory of Natural Selection. Complete Variorum Edition. Oxford University Press. Appendix 2.
11. ↑ Gould on God Can religion and science be happily reconciled?
12. ↑ Yates, F., and Mather, K. (1963). Ronald Aylmer Fisher. 1890-1962. Biographical Memoirs of Fellows of the Royal Society 9: 91-129. [1]
13. ↑ Box, R. A. Fisher, p 337
14. ↑ Box, R. A. Fisher, p 396
15. ↑ http://unesdoc.unesco.org/images/0007/000733/073351eo.pdf “The Race Concept: Results of an Inquiry”, p. 27. UNESCO 1952
16. ↑ Marston, Jean (08 March 2008). "Smoking gun (letter)". New Scientist 30 (2646): 21. doi:10.1111/j.1467-9477.2007.00176.x. http://www.newscientist.com/article/mg19726460.900-smoking-gun.html. 

References

• Aldrich, John (1997). "R.A. Fisher and the making of maximum likelihood 1912-1922". Statistical Science 12 (3): 162–176. doi:10.1214/ss/1030037906. http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ss/1030037906. 

• Box, Joan Fisher (1978) R. A. Fisher: The Life of a Scientist, New York: Wiley, ISBN 0-471-09300-9.

• David Howie, "Interpreting Probability: Controversies and Developments in the Early Twentieth Century" (Cambridge University Press, 2002)

• Salsburg, David (2002) The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, ISBN 0-8050-7134-2

Bibliography

A selection from Fisher's 395 articles

These are available on the University of Adelaide website:

• "Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population." Biometrika, 10: 507-521. (1915)
• "The correlation between relatives on the supposition of Mendelian inheritance" Trans. Roy. Soc. Edinb., 52: 399-433. (1918). It was in this paper that the word variance was first introduced into probability theory and statistics.
• "On the mathematical foundations of theoretical statistics" Philosophical Transactions of the Royal Society, A, 222: 309-368. (1922)
• "On the dominance ratio. Proc. Roy. Soc. Edinb., 42: 321-341. (1922)
• "On a distribution yielding the error functions of several well known statistics" Proc. Int. Cong. Math., Toronto, 2: 805-813. (1924)
• "Theory of statistical estimation" Proceedings of the Cambridge Philosophical Society, 22: 700-725 (1925)
• "Applications of Student's distribution" Metron, 5: 90-104 (1925)
• "The arrangement of field experiments" J. Min. Agric. G. Br., 33: 503-513. (1926)
• "The general sampling distribution of the multiple correlation coefficient" Proceedings of Royal Society, A, 121: 654-673 (1928)
• "Two new properties of mathematical likelihood" Proceedings of Royal Society, A, 144: 285-307 (1934)

Books by Fisher

Full publication details are available on the University of Adelaide website:

• Statistical Methods for Research Workers (1925) ISBN 0-05-002170-2.
• The Genetical Theory of Natural Selection (1930) ISBN 0-19-850440-3.
• The design of experiments (1935) ISBN 0-02-844690-9
• The use of multiple measurements in taxonomic problems (in Annals of Eugenics 7/1936)
• Statistical tables for biological, agricultural and medical research (1938, coauthor:Frank Yates)
• The theory of inbreeding (1949) ISBN 0-12-257550-4, ISBN 0-05-000873-0
• Contributions to mathematical statistics, John Wiley, (1950)
• Statistical methods and scientific inference (1956) ISBN 0-02-844740-9
• Collected Papers of R.A. Fisher (1971-1974). Five Volumes. University of Adelaide.

Biographies of Fisher

• Box, Joan Fisher (1978) R. A. Fisher: The Life of a Scientist, New York: Wiley, ISBN 0-471-09300-9. Preface
• Frank Yates & Kenneth Mather (1963) "Ronald Aylmer Fisher" in Biographical Memoirs of Fellows of the Royal Society of London 9: 91-120.

Secondary literature

• Edwards, A.W.F., 2005, "Statistical methods for research workers" in Grattan-Guiness, I., ed., Landmark Writings in Western Mathematics. Elsevier: 856-70.

External links

• O'Connor, John J.; Robertson, Edmund F., "Ronald Fisher", MacTutor History of Mathematics archive 
• A Guide to R. A. Fisher by John Aldrich
• Earliest Known Uses of Some of the Words of Mathematics for Fisher’s contribution to the language of statistics
• University of Adelaide Library for bibliography, biography, 2 volumes of correspondence and many articles
• Classics in the History of Psychology for the first edition of Statistical Methods for Research Workers
• A collection of Fisher quotations compiled by A. W. F. Edwards
• Ronald Fisher at the Mathematics Genealogy Project
• Sawilowsky, Shlomo S. (2002). Fermat, Schubert, Einstein, and Behrens-Fisher: The Probable Difference Between Two Means When σ₁ ≠ σ₂ Journal of Modern Applied Statistical Methods, 1(2).