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. In 1918 he published "
The Correlation between Relatives on the Supposition of Mendelian Inheritance", in which he introduced the term
variance and proposed its formal analysis. He put forward a
genetics conceptual model showing that
continuous variation amongst
phenotypic traits measured by biostatisticians could be produced by the combined action of many discrete genes and thus be the result of
Mendelian inheritance. This was the first step towards establishing
population genetics and
quantitative genetics, which demonstrated that
natural selection could change
allele frequencies in a population, reconciling its discontinuous nature with gradual
evolution. Joan Box, Fisher's biographer and daughter, says that Fisher had resolved this problem already in 1911. Today, Fisher's additive model is still regularly used in
genome-wide association studies.
Rothamsted Experimental Station, 1919–1933 In 1919, he began working at the
Rothamsted Experimental Station in Hertfordshire, where he would remain for 14 years.
Studies in Crop Variation II written with his first assistant,
Winifred Mackenzie, became the model for later ANOVA work. 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. Fisher's 1924 article
On a distribution yielding the error functions of several well known statistics presented
Pearson's chi-squared test and
William Gosset's
Student's t-distribution in the same framework as the
Gaussian distribution, and is where he developed
Fisher's z-distribution, a new statistical method commonly used decades later as the
F-distribution. He pioneered the principles of the
design of experiments and the statistics of small samples and the analysis of real data. In 1925 he published
Statistical Methods for Research Workers, one of the 20th century's most influential books on statistical methods.
Fisher's method 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. 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." In Table 1 of the work, he gave the more precise value 1.959964. In 1928, Fisher was the first to use
diffusion equations to attempt to calculate the distribution of
allele frequencies and the estimation of
genetic linkage by maximum likelihood methods among populations. In 1930,
The Genetical Theory of Natural Selection was first published by
Clarendon Press and is dedicated to
Leonard Darwin. A core work of the neo-Darwinian
modern evolutionary synthesis, it helped define
population genetics, which Fisher founded alongside
Sewall Wright and
J. B. S. Haldane, and revived Darwin's neglected idea of
sexual selection. One of Fisher's favourite aphorisms was "Natural selection is a mechanism for generating an exceedingly high degree of improbability." 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. In 1934, he become editor of the
Annals of Eugenics (now called
Annals of Human Genetics). 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". 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. The same year he published a paper on
fiducial inference and applied it to the
Behrens–Fisher problem, the solution to which, proposed first by
Walter Behrens and a few years later by Fisher, is the
Behrens–Fisher distribution. In 1936, he introduced the
Iris flower data set as an example of
discriminant analysis. 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. Out of this also came the
Fisher–Kolmogorov equation. 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 2,000 employees. In 1938, Fisher and
Frank Yates described the
Fisher–Yates shuffle in their book
Statistical tables for biological, agricultural and medical research. Their description of the algorithm used pencil and paper; a table of random numbers provided the randomness.
University of Cambridge, 1943–1956 In 1943, along with
A. S. Corbet and
C. B. Williams, he published a paper on
relative species abundance where he developed the
log series distribution (sometimes called the logarithmic distribution) to fit two different abundance data sets. In the same year he took the
Balfour Chair of Genetics where the Italian researcher
Luigi Luca Cavalli-Sforza was recruited in 1948, establishing a one-man unit of bacterial genetics. 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. Later authors have claimed Fisher's analysis was flawed, proposing various statistical and botanical explanations for Mendel's numbers. 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". He developed computational
algorithms for analyzing data from his balanced experimental designs, 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. Fisher publicly spoke out against the 1950 study showing that smoking
tobacco causes
lung cancer, arguing that
correlation does not imply causation. 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." Others have suggested that his analysis was biased by professional conflicts and his own love of smoking; he was a heavy pipe smoker. 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. My efforts to understand this Fisher compromise led me to the
likelihood principle".
Adelaide, 1957–1962 In 1957, a retired Fisher immigrated to Australia, where he spent time as a senior research fellow at the Australian
Commonwealth Scientific and Industrial Research Organisation (CSIRO) in
Adelaide, South Australia. His remains are interred in
St Peter's Cathedral, Adelaide. ==Legacy==