During 1913–1919, Fisher worked as a statistician in the City of London and taught physics and maths at a sequence of public schools, at the Thames Nautical Training College, and at Bradfield College. There he settled with his new bride, Eileen Guinness, with whom he had two sons and six daughters.<ref name=box>Box, R. A. Fisher, pp. 35–50</ref>
In 1919, he began working at the Rothamsted Experimental Station in Hertfordshire, where he would remain for 14 years.<ref name=russ/> He had been offered a position at the Galton Laboratory in University College London led by Karl Pearson, but instead accepted a temporary role at Rothamsted to investigate the possibility of analysing the vast amount of crop data accumulated since 1842 from the "Classical Field Experiments". He analysed the data recorded over many years, and in 1921 published Studies in Crop Variation I, his first application of the analysis of variance (ANOVA).<ref>Template:Cite journal</ref> Studies in Crop Variation II written with his first assistant, Winifred Mackenzie, became the model for later ANOVA work.<ref>Template:Cite journal</ref> Later assistants who mastered and propagated Fisher's methods were Joseph Oscar Irwin, John Wishart and Frank Yates. Between 1912 and 1922 Fisher recommended, analysed (with heuristic proofs) and vastly popularized the maximum likelihood estimation method.<ref>Template:Cite book</ref>
In 1925 he published Statistical Methods for Research Workers, one of the 20th century's most influential books on statistical methods.<ref name=Conniffe>Template:Cite journal</ref> Fisher's method<ref>Template:Cite book</ref><ref>Template:Cite journal</ref> is a technique for data fusion or "meta-analysis" (analysis of analyses). Fisher formalized and popularized use of the p-value in statistics, which plays a central role in his approach. Fisher proposes the level p=0.05, or a 1 in 20 chance of being exceeded by chance, as a limit for statistical significance, and applies this to a normal distribution (as a two-tailed test), yielding the rule of two standard deviations (on a normal distribution) for statistical significance.<ref>Template:Cite book</ref> The significance of 1.96, the approximate value of the 97.5 percentile point of the normal distribution used in probability and statistics, also originated in this book.
"The value for which P = 0.05, or 1 in 20, is 1.96 or nearly 2; it is convenient to take this point as a limit in judging whether a deviation is to be considered significant or not."<ref>
Template:Cite book</ref>
In Table 1 of the work, he gave the more precise value 1.959964.<ref>
Template:Cite book, Table 1</ref>
One of Fisher's favourite aphorisms was "Natural selection is a mechanism for generating an exceedingly high degree of improbability."<ref>The Genetical Theory of Natural Selection. It was first reported in 1936 by Julian Huxley and often repeated in Huxley's work (e.g., 1942, 1954) until it finally passed into the language unattributed through the writings of C. H. Waddington, Gavin de Beer, Ernst Mayr, and Richard Dawkins.</ref>
Fisher's fame grew, and he began to travel and lecture widely. In 1931, he spent six weeks at the Statistical Laboratory at Iowa State College where he gave three lectures per week, and met many American statisticians, including George W. Snedecor. He returned there again in 1936.Template:Citation needed
In 1935, he published The Design of Experiments, which was "also fundamental, [and promoted] statistical technique and application... The mathematical justification of the methods was not stressed and proofs were often barely sketched or omitted altogether .... [This] led H.B. Mann to fill the gaps with a rigorous mathematical treatment".<ref name=Conniffe/><ref>Template:Cite book</ref>
In this book Fisher also outlined the Lady tasting tea, now a famous design of a statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis.<ref>Fisher, R. A. (1971) The Design of Experiments. Chapter II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment, Section 8. The Null Hypothesis</ref><ref>OED quote: 1935 R. A. Fisher, The Design of Experiments ii. 19, "We may speak of this hypothesis as the 'null hypothesis'...the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."</ref>
In his 1937 paper The wave of advance of advantageous genes he proposed Fisher's equation in the context of population dynamics to describe the spatial spread of an advantageous allele, and explored its travelling wave solutions.<ref>Template:Cite journal</ref> Out of this also came the Fisher–Kolmogorov equation.<ref>Template:Cite web</ref>
In 1937, he visited the Indian Statistical Institute in Calcutta, and its one part-time employee, P. C. Mahalanobis, often returning to encourage its development. He was the guest of honour at its 25th anniversary in 1957, when it had 2000 employees.<ref>Box, R. A. Fisher, p. 337</ref>
In 1938, Fisher and Frank Yates described the Fisher–Yates shuffle in their book Statistical tables for biological, agricultural and medical research.<ref>Template:Cite book Note: the 6th edition, Template:Isbn, is available on the web, but gives a different shuffling algorithm by C. R. Rao.</ref> Their description of the algorithm used pencil and paper; a table of random numbers provided the randomness.
In 1936, Fisher used a Pearson's chi-squared test to analyze Mendel's data and concluded that Mendel's results were far too perfect, suggesting that adjustments (intentional or unconscious) had been made to the data to make the observations fit the hypothesis.<ref>Template:Cite journal</ref> Later authors have claimed Fisher's analysis was flawed, proposing various statistical and botanical explanations for Mendel's numbers.<ref>Template:Cite book</ref><ref>Template:Cite book</ref> In 1947, Fisher co-founded the journal Heredity with Cyril Darlington and in 1949 he published The Theory of Inbreeding.
In 1950, he published "Gene Frequencies in a Cline Determined by Selection and Diffusion".<ref name=":1">Template:Cite journal</ref> He developed computational algorithms for analyzing data from his balanced experimental designs,<ref>Box, R. A. Fisher, pp. 93–166</ref> with various editions and translations, becoming a standard reference work for scientists in many disciplines. In ecological genetics he and E. B. Ford showed that the force of natural selection was much stronger than had been assumed, with many ecogenetic situations (such as polymorphism) being maintained by the force of selection.
During this time he also worked on mouse chromosome mapping, breeding the mice in laboratories in his own house.<ref>Template:Cite journal</ref>
Fisher publicly spoke out against the 1950 study showing that smoking tobacco causes lung cancer, arguing that correlation does not imply causation.<ref>Template:Citation</ref><ref>Template:Citation</ref><ref>Template:Citation</ref><ref>Template:Citation</ref><ref>Template:Citation</ref><ref>Template:Citation</ref> To quote his biographers Yates and Mather, "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."<ref name="frs">Template:Cite journal</ref> Others have suggested that his analysis was biased by professional conflicts and his own love of smoking;<ref>Template:Cite journal</ref> he was a heavy pipe smoker.<ref name="Keane 2022"/>
In the winter of 1954–1955 Fisher met Debabrata Basu, the Indian statistician who wrote in 1988, "With his reference set argument, Sir Ronald was trying to find a via media between the two poles of Statistics – Berkeley and Bayes.<ref>The term "Berkeley" has several meanings, here. Basu refers to the leadership of Jerzy Neyman's department of statistics at the University of California at Berkeley in the world of frequentist statistics. Secondly, Basu alludes to the British philosopher George Berkeley who criticized the use of infinitesimals in mathematical analysis; Berkeley's criticisms were answered by Thomas Bayes in a pamphlet.</ref> My efforts to understand this Fisher compromise led me to the likelihood principle".<ref>p. xvii in Ghosh (ed.)</ref>
Sexy son hypothesis, which hypothesizes that females may choose arbitrarily attractive male mates simply because they are attractive, thus increasing the attractiveness of their sons who attract more mates of their own. This is in contrast to theories of female mate choice based on the assumption that females choose attractive males because the attractive traits are markers of male viability.<ref>Template:Cite journal</ref>
Mimicry, a similarity of one species to another that protects one or both.
Heterozygote advantage<ref>Fisher R. A. 1930. The Genetical Theory of Natural Selection.</ref> which was later found to play a frequent role in genetic polymorphism.
Demonstrating that the probability of a mutation increasing the fitness of an organism decreases proportionately with the magnitude of the mutation and that larger populations carry more variation so that they have a greater chance of survival.
Fisher information, see also scoring algorithm also known as Fisher's scoring, and Minimum Fisher information, a variational principle which, when applied with the proper constraints needed to reproduce empirically known expectation values, determines the best probability distribution that characterizes the system.<ref>B. R. Frieden, Science from Fisher Information, Cambridge University Press, Cambridge, England, 2004.</ref>
F-distribution, arises frequently as the null distribution of a test statistic, most notably in the analysis of variance
Inverse probability, a term Fisher used in 1922, referring to "the fundamental paradox of inverse probability" as the source of the confusion between statistical terms which refer to the true value to be estimated, with the actual value arrived at by estimation, which is subject to error.<ref>Template:Cite journal</ref>
Sufficient statistic, when a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".<ref name="Fisher1922">Template:Cite journal</ref>
Fisher married Eileen Guinness, with whom he had two sons and six daughters.<ref name=box/>
His marriage disintegrated during World War II, and his older son George, an aviator, was killed in combat.<ref>Box, R. A. Fisher, p. 396</ref> His daughter Joan, who wrote a biography of her father, married the statistician George E. P. Box.<ref>Box, Joan Fisher (1978) R. A. Fisher: The Life of a ScientistPreface, Template:ISBN</ref>
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."<ref name="frs"/> Fisher was noted for being loyal, and was seen as a patriot, a member of the Church of England, politically conservative, as well as a scientific rationalist. He developed a reputation for carelessness in his dress and was the archetype of the absent-minded professor. H. Allen Orr describes him in the Boston Review as a "deeply devout Anglican who, between founding modern statistics and population genetics, penned articles for church magazines".<ref>Gould on God: Can religion and science be happily reconciled? bostonreview.net</ref> In a 1955 broadcast on Science and Christianity,<ref name="frs"/> he said:
Between 1950 and 1951, Fisher, along with other leading geneticists and anthropologists of his time, was asked to comment on a statement that UNESCO was preparing on the nature of race and racial differences, which was published in 1950 as the UNESCO Statement on Race. The statement, along with the comments and criticisms of a large number of scientists including Fisher, is published in "The Race Concept: Results of an Inquiry" (1952).<ref name=UNESCO1952>Template:Cite web</ref>
Fisher was one of four scientists who opposed the statement. In his own words, Fisher's opposition is based on "one fundamental objection to the Statement", which "destroys the very spirit of the whole document." He believes that human groups differ profoundly "in their innate capacity for intellectual and emotional development" and concludes from this 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 exist."<ref>Template:Cite book</ref><ref>Template:Cite book</ref><ref>Template:Cite book</ref>
Fisher's opinions are clarified by his more detailed comments on Section 5 of the statement, which are concerned with psychological and mental differences between the races. Section 5 concludes as follows:
Of the entire statement, Section 5 recorded the most dissenting viewpoints. It was recorded that "Fisher's attitude … is the same as Muller's and Sturtevant's".<ref name= UNESCO1952/>Template:Rp Muller's criticism was recorded in more detail and was noted to "represent an important trend of ideas":
Fisher's writings nearly all discuss human populations or humanity as a whole without reference to race or specific racial groups, and none of his work explicitly supports the idea of racial superiority or white supremacy.<ref name="bodmer21" /> Fisher had a close personal relationship with Indian statistician P.C. Mahalanobis, and significantly contributed to the development of the Indian Statistical Institute; and Fisher's graduate students included Walter Bodmer, a child of Jewish-German parents who fled from Nazi Germany while he was young, and Ebenezer Laing, an African geneticist from Ghana.<ref name="bodmer21" /> Daniel Kevles, an American historian of science, described Fisher as an "anti-racist conservative".<ref name="bodmer21" /> However, British historian Richard J. Evans, writing in The New Statesman, argued that Fisher's views on eugenics and his opposition to UNESCO's statement about genetic racial differences were indicative of racism.<ref>Template:Cite web</ref>
Template:Eugenics sidebar
In 1911, Fisher became founding Chairman of the University of Cambridge Eugenics Society, whose other founding members included John Maynard Keynes, R. C. Punnett, and Horace Darwin. After members of the Cambridge Society – including Fisher – stewarded the First International Eugenics Congress in London in summer 1912, a link was forged with the Eugenics Society (UK).<ref>Template:Cite book</ref> He saw eugenics as addressing pressing social and scientific issues that encompassed and drove his interest in both genetics and statistics. During World War I Fisher started writing book reviews for The Eugenics Review and volunteered to undertake all such reviews for the journal, being hired for a part-time position.
The last third of The Genetical Theory of Natural Selection focused on eugenics, attributing the fall of civilizations to the fertility of their upper classes being diminished, and used British 1911 census data to show an inverse relationship between fertility and social class, which was partly due, he claimed, to the lower financial costs and hence increasing social status of families with fewer children. He proposed the abolition of extra allowances to large families, with the allowances proportional to the earnings of the father.<ref name=Adelaide>Template:Cite web</ref><ref name=NewScientist>Template:Cite journal</ref><ref name=Cruz>Template:Cite journal</ref> He served in several official committees to promote eugenics, including the Committee for Legalizing Eugenic Sterilization which drafted legislation aiming to limit the fertility of "feeble minded high-grade defectives ... comprising a tenth of the total population". It was proposed that this policy would allow for voluntary sterilisation. Fisher was against the idea of forced sterilisation.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>
Beginning in 1934, Fisher became disillusioned with the Eugenics Society over concerns that its activities were increasingly aimed in a political rather than scientific direction; he formally dissociated with the Society in 1941.<ref name="bodmer21" />
Fisher wrote a testimony on behalf of the eugenicist Otmar Freiherr von Verschuer. He wrote that, although the Nazis used Verschuer's work to give scientific support for their ideology, it was "[Verschuer's] misfortune rather than his fault that racial theory was a part of the Nazi ideology."<ref name="bodmer21" /><ref>Template:Cite journal</ref> He conducted extensive correspondence with von Verschuer over decades, which is held at the University of Adelaide.<ref name="Keane 2022">Template:Cite web</ref>
He won the Copley Medal and the Royal Medal. He was an Invited Speaker of the ICM in 1924 in Toronto and in 1928 in Bologna.<ref>Template:Cite book</ref>
In 1950, Maurice Wilkes and David Wheeler used the Electronic Delay Storage Automatic Calculator to solve a differential equation relating to gene frequencies in a paper by Ronald Fisher.<ref name=":1" /> This represents the first use of a computer for a problem in the field of biology. The Kent distribution (also known as the Fisher–Bingham distribution) was named after him and Christopher Bingham in 1982, while the Fisher kernel was named after Fisher in 1998.<ref>Tommi Jaakkola and David Haussler (1998), Exploiting Generative Models in Discriminative Classifiers. In Advances in Neural Information Processing Systems 11, pages 487–493. MIT Press. Template:IsbnPS, Citeseer</ref>
In 2010, the R.A. Fisher Chair in Statistical Genetics was established in University College London to recognise Fisher's extraordinary contributions to both statistics and genetics.
Anders Hald called Fisher "a genius who almost single-handedly created the foundations for modern statistical science",<ref name="Hald98">Template:Cite book p.738.</ref> while Richard Dawkins named him "the greatest biologist since Darwin":
Not only was he the most original and constructive of the architects of the neo-Darwinian synthesis, Fisher also was the father of modern statistics and experimental design. He therefore could be said to have provided researchers in biology and medicine with their most important research tools, as well as with the modern version of biology's central theorem.<ref>Template:Cite web</ref>
To biologists, he was an architect of the "modern synthesis" that used mathematical models to integrate Mendelian genetics with Darwin's selection theories. To psychologists, Fisher was the inventor of various statistical tests that are still supposed to be used whenever possible in psychology journals. To farmers, Fisher was the founder of experimental agricultural research, saving millions from starvation through rational crop breeding programs.<ref name="Miller00">Miller, Geoffrey (2000). The Mating Mind: how sexual choice shaped the evolution of human nature, London: Heineman, Template:ISBN (also Doubleday, Template:ISBN) p.54.</ref>
Fisher and Sewall Wright both contributed to the development of population genetics, which became part of the modern synthesis. The interpretation of the mathematical theories of population genetics became a bone of contention between Fisher and Wright by the mid-1920s, and the issue became acrimonious. Dispute persisted for the rest of Fisher's life.<ref>Template:Cite book</ref> A 2021 paper, authored by trustees of the "Fisher Memorial Trust", commented that recent criticism of Fisher could mostly be characterised as "reconsideration of the honour given to individuals from preceding times who are felt to have contributed to social injustice in the past, or to have held views that are felt to have promoted social injustice."<ref name="bodmer21"/>
