# Ronald Aylmer Fisher

### Quick Info

London, England

Adelaide, Australia

**Ronald Aylmer Fisher**was a British statistician and geneticist important in developing the use of statistics in genetics and biomathematics.

### Biography

**R A Fisher**'s parents were Katie Heath, the daughter of a solicitor, and George Fisher, of Robinson and Fisher a firm of auctioneers in King Street, St James, London. Katie and George had seven children, four boys and three girls. After the birth of Geoffrey in 1876 and Evelyn in 1877, they named their third child, who was born the following year, Alan. He died at a very young age and Katie, being superstitious, decided that all their children from that time on would have a "y" in their name. Ronald Aylmer Fisher was the second of twins, but the older twin was still-born.

In 1904 Ronald entered Harrow, but this was a difficult time for the fourteen year old boy, for his mother died in that year of acute peritonitis. Despite this, he excelled at Harrow winning the Neeld Medal in 1906 in a mathematical essay competition open to the whole school. Fisher was awarded a £80 scholarship from Caius and Gonville College, Cambridge, which was necessary to finance his studies since his father had lost his fortune. In October 1909 he matriculated at Cambridge.

Although he studied mathematics and astronomy at Cambridge, he was also interested in biology. In his second year as an undergraduate he began consulting senior members of the university about the possibility of forming a Cambridge University Eugenics Society. He graduated with distinction in the mathematical tripos of 1912. His tutor, however, believed he could have done better, writing [3]:-

... if he had stuck to the ropes he would have made a first class mathematician, but he would not.Awarded a Wollaston studentship, he continued his studies at Cambridge under Stratton on the theory of errors reading Airy's manual the

*Theory of Errors*. It was Fisher's interest in the theory of errors that eventually led him to investigate statistical problems.

After leaving Cambridge, Fisher had no means of financial support and worked for a few months on a farm in Canada. He returned to London, taking up a post as a statistician in the Mercantile and General Investment Company. When war broke out in 1914 he enthusiastically tried to enlist in the army, having already trained in the Officers' Training Corps while at Cambridge. His medical test showed him A1 on all aspects except his eyesight, which was rated C5, so he was rejected. He became a teacher of mathematics and physics, teaching at Rugby and other similar schools between 1915 and 1919.

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. Ruth Eileen and Gudruna's father, Dr Henry Gratton Guinness, had died when they were young and Ruth Eileen, only sixteen years of age, 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.

Fisher gave up being a mathematics teacher in 1919 when he was offered two posts simultaneously. Karl Pearson offered him the post of chief statistician at the Galton laboratories and he was also offered the post of statistician at the Rothamsted Agricultural Experiment Station. This was the oldest agricultural research institute in the United Kingdom, established in 1837 to study the effects of nutrition and soil types on plant fertility, and it appealed to Fisher's interest in farming. He accepted the post at Rothamsted where he made many contributions both to statistics, in particular the design and analysis of experiments, and to genetics.

There he studied the design of experiments by introducing the concept of randomisation and the analysis of variance, procedures now used throughout the world. Fisher's idea was to arrange an experiment as a set of partitioned sub-experiments that differ from each other in having one or several factors or treatments applied to them. The sub-experiments were designed in such a way as to permit differences in their outcome to be attributed to the different factors or combinations of factors by means of statistical analysis. This was a notable advance over the existing approach of varying only one factor at a time in an experiment, which was a relatively inefficient procedure.

In 1921 he introduced the concept of likelihood. The likelihood of a parameter is proportional to the probability of the data and it gives a function which usually has a single maximum value, which he called the maximum likelihood. In 1922 he gave a new definition of statistics. Its purpose was, he claimed, the reduction of data, and he identified three fundamental problems. These are:

- specification of the kind of population that the data came from;
- estimation; and
- distribution.

*Statistical Methods for Research Workers*(1925) ran to many editions which he extended throughout his life. It was a handbook for the methods for the design and analysis of experiments which he had developed at Rothamsted. The contributions Fisher made included the development of methods suitable for small samples, like those of Gosset, and the discovery of the precise distributions of many sample statistics. Fisher published

*The design of experiments*(1935) and

*Statistical tables*(1947). His books [3]:-

... revolutionized agricultural research; for they described the methods, now used the world over, for evaluating the results of small sample experiments and for so laying our experimental trials as to minimise the disturbances due to heterogeneity of soils and the unavoidable irregularity of biological material.While at the Agricultural Experiment Station he had conducted breeding experiments with mice, snails and poultry, and the results he obtained led to theories about gene dominance and fitness which he published in

*The Genetical Theory of Natural Selection*(1930).

This work on natural selection led Fisher to question the way that in civilised societies weak and relatively infertile people obtained advantages over strong healthy individuals. He felt that the natural survival of the fittest method of improving the human race was being artificially changed by factors that specifically benefited the less well adapted. A strong advocate of measures to counter this trend, he proposed that family allowances should be proportional to income to support the well-adapted healthy members of society. As one might expect, this policy was very unpopular and he found few supporters.

In 1933 Karl Pearson retired as Galton Professor of eugenics at University College and Fisher was appointed to the chair as his successor. In fact the post was split in two, with Karl Pearson's son Egon Pearson also being appointed to a chair. Fisher held this post for ten years, being appointed as Arthur Balfour professor of genetics at the University of Cambridge in 1943. Before this, however, he had moved away from London when war broke out in 1939, finding temporary accommodation at Harpenden. He retired from his Cambridge chair in 1957 but continued to carry out his duties there for another two years until his successor could be appointed. He then moved to the University of Adelaide where he continued his research for the final three years of his life.

There was a certain irony in the fact that Fisher succeeded Pearson in 1933 for the two had a long running dispute. The dispute began in 1917 when Pearson published a paper claiming that Fisher had failed to distinguish likelihood from inverse probability in a paper he wrote in 1915. Although at this stage Fisher was only starting out on his career, he felt angry that Pearson had published an article which was critical of his results without telling him that he was about to do so. Moreover, he did not accept Pearson's criticism, feeling that he was correct.

In fact the reasons for the feud were not nearly as simple as those usually given. The standard explanation is that Fisher became bitter because he suffered serious injustice having his papers rejected by mathematicians who did not understand biology and biologists who did not understand mathematics. Let us take an example to show that in fact this is an over-simplification. In 1918 Fisher submitted his very important paper

*On the correlation between relatives on the supposition of Mendelian inheritance*to the Royal Society. Two referees, R C Punnett and Pearson, were appointed and reported on the paper. Neither referee rejected the paper, however, they both merely expressed reservations and stated clearly that there were aspects of the paper that they were not competent to judge. In the event Fisher withdrew the paper and submitted it to the

*Transactions of the Royal Society of Edinburgh*where it was accepted. It is not surprising that Fisher's novel ideas took time to become accepted.

The feud became bitter, however, when Pearson used his position as editor of

*Biometrika*to attack Fisher's use of the chi-squared test in a 1922 paper. Pearson went much further, however, and claimed that Fisher had done a disservice to statistics by widely publishing erroneous results. The Royal Statistical Society then refused to publish Fisher's papers and he resigned from the Society in protest. Of course Fisher also took every opportunity to attack Pearson, and it would be fair to say that each showed hatred towards the other. Even after Pearson died in 1936, Fisher continued his attack on him, which made the atmosphere in University College a very difficult one with Pearson's son Egon Pearson also holding a chair there.

Fisher was elected a Fellow of the Royal Society in 1929, was awarded the Royal Medal of the Society in 1938, and was awarded the Darwin Medal of the Society in 1948:-

... in recognition of his distinguished contributions to the theory of natural selection, the concept of its gene complex and the evolution of dominance.Then, in 1955, he was awarded the Copley Medal of the Royal Society:-

... in recognition of his numerous and distinguished contributions to developing the theory and application of statistics for making quantitative a vast field of biology.He was elected to the American Academy of Arts and Sciences in 1934, the American Philosophical Society in 1941, the International Society of Haematology in 1948, the National Academy of Sciences of the United States in 1948, and the Deutsche Akademie der Naturforscher Leopoldina in 1960. Various institutions awarded him an honorary degree including Harvard University (1936), University of Calcutta (1938), University of London (1946), University of Glasgow (1947), University of Adelaide (1959), University of Leeds (1961), and the Indian Statistical Institute (1962). He was knighted in 1952.

Fisher's character is described in [3] as follows:-

He was capable of tremendous charm, and warmth in friendship. But he also was the victim, as he himself recognised, of an uncontrollable temper; and his devotion to scientific truth as he saw it being literally passionate, he was an implacable enemy of those whom he judged guilty of propagating error.He had other strengths and weaknesses too [3]:-

As a penetrating thinker Fisher was outstanding; but his writings are difficult for many readers. Indeed, some of his teachings have been most effectively conveyed by the books of others who have been able to simplify their expression. As a lecturer also, Fisher was too difficult for the average student; his classes would rapidly fall away until only two or three students who could stand the pace remained as fascinated disciples. Nor was he particularly successful as an administrator; he perhaps failed to appreciate the limitations of the ordinary man. But with his wide interests and penetrating mind he was a most stimulating and sympathetic conversationalist.

### References (show)

- N T Gridgeman, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - Biography in
*Encyclopaedia Britannica.*http://www.britannica.com/biography/Ronald-Aylmer-Fisher - J H Bennett (ed.),
*Statistical inference and analysis : selected correspondence of R A Fisher*(Oxford, 1989). - J F Box,
*R A Fisher, The life of a scientist*(New York, 1978). - Ronald Aylmer Fisher,
*Biometrics***18**(1962). - Ronald Aylmer Fisher,
*Biometrics***20**(1964). - J C Gower, Ronald Aylmer Fisher 1890-1962,
*Mathematical Spectrum***23**(1990-91), 76-86. - E S Pearson, Some early correspondence between W S Gosset, R A Fisher and Karl Pearson,
*Biometrika***55**(1968), 445-457. - E S Pearson, Some early correspondence between W S Gosset, R A Fisher and Karl Pearson, in E S Pearson and M G Kendall,
*Studies in the History of Statistics and Probability*(London, 1970), 405-418. - E S Pearson, Some reflections on continuity in the development of mathematical statistics 1890-94,
*Biometrika***54**(1967), 341-355. - Ronald Aylmer Fisher,
*Biographical Memoirs of Fellows of the Royal Society of London***9**(1963), 92-129. - Ronald Aylmer Fisher,
*J. Royal Statistical Society***126A**(1963), 159-170. - Ronald Aylmer Fisher,
*Science***156**(1967), 1456-1462.

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- History Topics: Statistics index
- Other: Earliest Known Uses of Some of the Words of Mathematics (B)
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- Other: Earliest Known Uses of Some of the Words of Mathematics (I)
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Written by J J O'Connor and E F Robertson

Last Update October 2003

Last Update October 2003