# Ronald Fisher

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**Sir Ronald Aylmer Fisher**, FRS (17 February 1890 – 29 July 1962) was a British eugenicist, evolutionary biologist, geneticist and statistician. He has been described by Richard Dawkins as "The greatest of Darwin’s successors", and the historian of statistics Anders Hald said "Fisher was a genius who almost single-handedly created the foundations for modern statistical science."

## Biography

### Early life

Fisher was born in East Finchley in London, to George and Katie Fisher. His father was a successful businessman, who dealt in fine arts. His boyhood was a happy one, being doted on by his three older sisters, an older brother, and his mother, who died when Fisher was only 14. His father lost his business in several ill-considered transactions only 18 months later. Although Fisher had very bad 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 developed a strong interest in biology, and, especially, evolution.

He obtained a needed scholarship to the University of Cambridge in 1909 as scholar at Gonville and Caius College. He had a very happy time there, forming many friendships and became enthralled with the heady intellectual atmospherics. In 1911 he became heavily involved in the formation of 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 quite active, and held monthly meetings, often featuring addresses by leaders of mainstream eugenics organizations, such as the Eugenics Education Society of London, founded by Francis Galton in 1909. By the time Fisher graduated with a degree in mathematics in 1913, it had over 150 members.

From the time of graduation when he left Cambridge for a mundane job in London, it would be six years before he found a post that could use his abilities to advantage. 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. When the war came, he tried several times to enlist, but was rejected because of his eyesight. For his war work, he took up teaching physics and mathematics at a series of public schools, including Bradfield College in Berkshire. He was miserable, and did poorly at it. A bright spot in his life was that Gudruna matched him to her sister Eileen Guinness. He fell madly in love, and they married when she was only 17 in 1917. 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.

During this period, Fisher started writing book reviews for the *Eugenic Review* and gradually increased his interest in genetical 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 to be Expected Between Relatives on the Supposition of Mendalian Inheritance.* 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 continuous variables were consistent with Mendelian principles.

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.

### Early professional years

In 1919 Fisher started work at Rothamsted Experimental Station located at Harpenden in 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.* He was in his prime, and he began a period of amazing 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 labor involved in the necessary computations, and developed ingenious methods that were as practical as they were founded in rigor. In 1925, this work culminated in the publication of his first book, *Statistical Methods for Research Workers*. 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.

Fisher invented the techniques of maximum likelihood and analysis of variance, 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 normal distribution and his own analysis of variance distribution z. These contributions easily made him a major figure in 20th century statistics.

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.

Fisher introduced the concept of Fisher information in 1925, many years before Shannon's notion of entropy. Fisher information has been the subject of renewed interest in the last few years, both due to the growth of Bayesian inference in artificial intelligence, and due to B. Roy Frieden's book *Physics from Fisher Information*, which attempts to derive the laws of physics from a Fisherian starting point.

### Eugenics

Fisher was an ardent promoter of eugenics, which also stimulated and guided much of his work in genetics of man. 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 chance of a mutation increasing the fitness of an organism decreases 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 man, 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 of 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. 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.

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

As an adult, Fisher was noted for his loyalty to his friends. Once he had formed a favorable 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.

### 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 honor at its 25th anniversary in 1957 when it had grown to 2000 employees. In 1939 when war broke out, the University tried to dissolve the eugenics department, and ordered all of the animals destroyed. Fisher fought back, but he was 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, a pilot, was killed in the war.

In 1943 he was offered the Balfour Chair of Genetics at Cambridge, 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. His re-appointment was denied by the University in the summer of 1950, much to Fisher's dismay. He now realized he could expect little in the way of support, but 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*

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

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

## References

- Fisher, Box Joan (1978) R. A. Fisher: The Life of a Scientist, New York: Wiley, ISBN 0471093009.

## See also

## 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 0050021702.*The Genetical Theory of Natural Selection*(1930) ISBN 0198504403.*The design of experiments*(1935) ISBN 0028446909, ISBN B0000CKL1X-
*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 0122575504, ISBN 0050008730*Contributions to mathematical statistics*(1950) ISBN B0000CHSZU.*Statistical methods and statistical inference*(1956) ISBN 0028447409

### Biographies of Fisher

- Fisher, Box Joan (1978)
*R. A. Fisher: The Life of a Scientist*, New York: Wiley, ISBN 0471093009. - Yates F & Mather K (1963) Ronald Aylmer Fisher.
*Biographical Memoirs of Fellows of the Royal Society of London*9:91-120 Available on University of Adelaide website

## External links

- Biography at MacTutor
- 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

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