Ronald Fisher

Sir Ronald Fisher
Born (1890-02-17)17 February 1890
East Finchley, London, England
Died 29 July 1962(1962-07-29) (aged 72)
Adelaide, South Australia
Residence England and Australia
Nationality British
Fields Statistics, Genetics, and Evolutionary biology
Institutions Rothamsted Research, University College London, Cambridge University, University of Adelaide, Commonwealth Scientific and Industrial Research Organisation
Alma mater Gonville and Caius College, Cambridge
Academic advisors James Hopwood Jeans and F. J. M. Stratton
Doctoral students C. R. Rao, D. J. Finney, and Walter Bodmer [1]
Influenced

Sir Ronald Aylmer Fisher FRS[2] (17 February 1890 – 29 July 1962), who published as R. A. Fisher, was an English statistician and biologist who used mathematics to combine Mendelian genetics and natural selection. This helped to create the new Darwinist synthesis of evolution known as the modern evolutionary synthesis. He was also a prominent eugenicist in the early part of his life.

He worked at Rothamsted Research for 14 years[3] from 1919, where he developed the analysis of variance (ANOVA) to analyse its immense data from crop experiments since the 1840s, and established his reputation there in the following years as a biostatistician. He is known as one of the three principal founders of population genetics. He outlined Fisher's principle as well as the Fisherian runaway and sexy son hypothesis theories of sexual selection. He also made important contributions to statistics, including the maximum likelihood, fiducial inference, the derivation of various sampling distributions among many others.

Anders Hald called him "a genius who almost single-handedly created the foundations for modern statistical science",[4] 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."[5] and Geoffrey Miller said of him "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."[6]

Personal life

Ronald Fisher as a child
Inverforth House North End Way NW3. Fisher lived here from 1896 to 1904.
Ronald Fisher

Fisher was born in East Finchley in London, England, one of twins with the other being still-born[7] and grew up the youngest with three sisters and one brother.[8] From 1896 until 1904 they lived at Inverforth House in London, where English Heritage installed a blue plaque in 2002, before moving to Streatham.[9] His mother, Kate, died from acute peritonitis when he was 14, and his father, George, then lost his business as a successful partner in Robinson & Fisher,[10] auctioneers and fine art dealers, 18 months later.

Lifelong poor eyesight caused his rejection by the British Army for World War I,[11] but also developed his ability to visualize problems in geometrical terms, but not in writing mathematical solutions, or proofs. He entered Harrow School age 14 and won the school's Neeld Medal in mathematics. In 1909, he won a scholarship to Gonville and Caius College at the Cambridge University.

Fisher worked for six years as a statistician in the City of London and taught physics and maths at a sequence of public schools, and at the Thames Nautical Training College, and Bradfield College where he settled with his new bride, Eileen Guinness, with whom he had two sons and six daughters.[12] In 1919 he began working at Rothamsted Research.

His 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 before returning again in 1936. 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, being the guest of honour at its 25th anniversary in 1957 when it had 2000 employees.[13]

Memorial plaque over remains of Ronald Aylmer Fisher, lectern-side aisle of St Peter's Cathedral, Adelaide

His marriage disintegrated during World War II and his oldest son George, an aviator, was killed in combat.[14] His daughter and one of his biographers, Joan, married the noted statistician George E. P. Box.[15] In 1957, a retired Fisher emigrated to Australia where he spent time as a senior research fellow at the Australian Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Adelaide, where he died in 1962, with his remains interred within St Peter's Cathedral.[16]

Academic career

Ronald Fisher in his graduation ceremony at Cambridge University
Ronald Fisher in 1913
The peacock tail in flight, the classic example of a Fisherian runaway

Fisher gained a scholarship to study Mathematics at the University of Cambridge in 1909, gaining a First in Astronomy in 1912.[17] In 1915 he published a paper The evolution of sexual preference[18] on sexual selection and mate choice. He published The Correlation Between Relatives on the Supposition of Mendelian Inheritance in 1918, in which he introduced the term variance and proposed its formal analysis.[19] He put forward a genetics conceptual model showing that continuous variation amongst phenotypic traits measured by the 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 the establishment of population genetics and quantitative genetics, which demonstrated that natural selection could change allele frequencies in a population, resulting in reconciling its discontinuous nature with gradual evolution.[20] Joan Box, Fisher's biographer and daughter says that Fisher had resolved this problem in 1911.[21]

Between 1912 and 1922 Fisher recommended, analyzed (with flawed attempts at proofs) and vastly popularized Maximum likelihood.[22]

Rothamsted Research

In 1919 he was offered a position at the Galton Laboratory in University College London led by Karl Pearson, but instead accepted a temporary job at Rothamsted Research in Harpenden to investigate the possibility of analysing the vast amount of data accumulated since 1842 from the "Classical Field Experiments" where he analysed the data recorded over many years and published Studies in Crop Variation in 1921. In 1928 Joseph Oscar Irwin began a three-year stint at Rothamsted and became one of the first people to master Fisher's innovations.

His first application of the analysis of variance was published in 1921.[23]

Fisher's article On a distribution yielding the error functions of several well known statistics (1924) presented Pearson's chi-squared test and William Gosset's Student's t-distribution in the same framework as the Gaussian distribution and 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.[24] Fisher's method[25][26] is a technique for data fusion or "meta-analysis" (analysis of analyses). This book also popularized the p-value, and it 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), thus yielding the rule of two standard deviations (on a normal distribution) for statistical significance.[27] The 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 = .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."[28]

In Table 1 of the work, he gave the more precise value 1.959964.[29]

The Genetical Theory of Natural Selection was first published in 1930 by Clarendon Press and is dedicated to Leonard Darwin. A core work of the neo-Darwinian modern evolutionary synthesis,[30] it helped define population genetics, which Fisher founded alongside Sewall Wright and J. B. S. Haldane, and revived the idea of sexual selection,[31] neglected since Darwin's death. Commonly cited in biology books, it outlines many important concepts, such as:

In 1933 he became Professor of Eugenics at University College London until 1939 when the department was dissolved.

Teapot, creamer and teacup full of tea with milk, the ingredients required for the Lady tasting tea

In 1935, he published by 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 his treatise".[24][41] 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.[42][43]

The same year he also published a paper on fiducial inference[44][45] 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.[46]

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.[47] Out of this also came the Fisher–Kolmogorov equation.[48]

In 1938 the Fisher–Yates shuffle was described by Fisher and Frank Yates in their book Statistical tables for biological, agricultural and medical research.[49] Their description of the algorithm used pencil and paper; a table of random numbers provided the randomness.

Although a prominent opponent of Bayesian statistics, Fisher was the first to use the term "Bayesian".[50]

He 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.[51]

In 1943, along with A.S. Corbett and C.B. Williams he published a paper on Relative species abundance where he developed the logseries to fit two different abundance data sets[52] 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 1947, Fisher used a Pearson's chi-squared test to analyze Mendel's data and concluded that Mendel's results with the predicted ratios were far too perfect, suggesting that adjustments (intentional or unconscious) had been made to the data to make the observations fit the hypothesis.[53] Later authors have claimed Fisher's analysis was flawed, proposing various statistical and botanical explanations for Mendel's numbers.[54] In the same year, Fisher cofounded 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"[55] on the wave of advance of advantageous genes and on clines of gene frequency, being notable as the first application of a computer, the EDSAC, to biology. He developed computational algorithms for analyzing data from his balanced experimental designs,[56] with various editions and translations, becoming a standard reference work for scientists in many disciplines. In ecological genetics he and E. B. Ford showed how 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.[57]

Tobacco light flake

Fisher publicly spoke out against the 1950 study showing that smoking tobacco causes lung cancer, arguing that correlation does not imply causation.[58] 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."[2]

He gave the 1953 Croonian lecture on population genetics.[59]

Debabrata Basu, the Indian statistician, met Fisher in the winter of 1954–1955; he 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.[60] My efforts to understand this Fisher compromise led me to the likelihood principle".[61]

He is also known for the following theories:

Eugenicist

Fisher as a steward at the First International Eugenics Conference in 1912

In 1910 he joined the Eugenics Society at Cambridge, whose members included John Maynard Keynes, R. C. Punnett, and Horace Darwin. He saw eugenics as addressing pressing social and scientific issues that encompassed both genetics and statistics. During World War I Fisher started writing book reviews for the Eugenic 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 focussed 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, 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. He served in several official committees to promote Eugenics. In 1934, he resigned from the Eugenics Society over a dispute about increasing the power of scientists within the movement.

The Race Question

He opposed UNESCO's The Race Question, believing 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 exist". The revised statement titled "The Race Concept: Results of an Inquiry" (1951) was accompanied by Fisher's dissenting commentary.[71]

Personal beliefs

Stained glass window in the dining hall of Caius College, in Cambridge, commemorating Ronald Fisher and representing a Latin square, discussed by him in The Design of Experiments

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."[2] 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".[72] In a 1955 broadcast on Science and Christianity,[2] 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. ”

Recognition and legacy

Fisher was elected to the Royal Society in 1929. He was made a Knight Bachelor by Queen Elizabeth II in 1952 and awarded the Linnean Society of London Darwin–Wallace Medal in 1958.

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.[73] 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 Fisher kernel was named after Fisher in 1998.[74]

The R. A. Fisher Lectureship is a prize of a lecture given yearly in North America that was established in 1963. On April 28, 1998 a minor planet, 21451 Fisher, was named after him.[75]

Quotations

Bibliography

References

  1. ↑ Ronald Fisher at the Mathematics Genealogy Project
  2. 1 2 3 4 Yates, F.; Mather, K. (1963). "Ronald Aylmer Fisher 1890-1962". Biographical Memoirs of Fellows of the Royal Society. 9: 91–129. doi:10.1098/rsbm.1963.0006.
  3. ↑ E. John Russell. Letter to The Times of London
  4. ↑ Hald, Anders (1998). A History of Mathematical Statistics. New York: Wiley. ISBN 0-471-17912-4.
  5. ↑ Dawkins, R. (2010). WHO IS THE GREATEST BIOLOGIST SINCE DARWIN? WHY? Edge "Who is the greatest biologist since Darwin? That's far less obvious, and no doubt many good candidates will be put forward. My own nominee would be Ronald Fisher. 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."
  6. ↑ Miller, Geoffrey (2000). The mating mind: how sexual choice shaped the evolution of human nature, London, Heineman, ISBN 0-434-00741-2 (also Doubleday, ISBN 0-385-49516-1) p.54
  7. ↑ Fisher biography
  8. ↑ Box, R. A. Fisher, pp 8–16
  9. ↑ Aldrich, John. "A Blue Plaque for Ronald Fisher's Childhood Home". Economics, Soton University. Soton.ac.uk. Retrieved 9 December 2013.
  10. ↑ >Heritage: The Hampstead years of Sir Ronald Aylmer Fisher - most significant British statistician of the 20th century
  11. ↑ [onlinelibrary.wiley.com/doi/10.1002/0470011815.b2a17045/abstract Fisher, Ronald Aylmer]
  12. ↑ Box, R. A. Fisher, pp 35–50
  13. ↑ Box, R. A. Fisher, p 337
  14. ↑ Box, R. A. Fisher, p 396
  15. ↑ Box, Joan Fisher (1978) R. A. Fisher: The Life of a Scientist Preface, ISBN 0-471-09300-9
  16. ↑ http://samhs.org.au/Virtual%20Museum/Notable-individuals/rafisher/index-rafisher.htm
  17. ↑ Sir Ronald Aylmer Fisher Published by University of Minnesota
  18. ↑ Fisher, R. A. (1915). "The evolution of sexual preference". Eugenic Review. 7 (3): 184–192. PMC 2987134Freely accessible. PMID 21259607.
  19. ↑ Fisher, Ronald A. (1918). "The Correlation Between Relatives on the Supposition of Mendelian Inheritance". Philosophical Transactions of the Royal Society of Edinburgh. 52: 399–433. doi:10.1017/s0080456800012163.
  20. ↑ Box, R. A. Fisher, pp 50–61
  21. ↑ R A Fisher: the life of a scientist Preface
  22. ↑ Pfanzagl, Johann; Hamböker, R. (1994). Parametric statistical theory. Berlin: Walter de Gruyter. pp. 207–208. ISBN 3-11-013863-8.
  23. ↑ Fisher, Ronald A. (1921). "On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample". Metron. 1: 3–32.
  24. 1 2 Conniffe, Denis (1991). "R.A. Fisher and the development of statistics—a view in his centenary year". Journal of the Statistical and Social Inquiry Society of Ireland. 26 (3): 55–108.
  25. ↑ Fisher, R.A. (1925). Statistical Methods for Research Workers. Oliver and Boyd (Edinburgh). ISBN 0-05-002170-2.
  26. ↑ Fisher, R.A.; Fisher, R. A (1948). "Questions and answers #14". The American Statistician. 2 (5): 30–31. doi:10.2307/2681650. JSTOR 2681650.
  27. ↑ Dallal, Gerard E. (2012). The Little Handbook of Statistical Practice.]
  28. ↑ Fisher, Ronald (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd. p. 47. ISBN 0-05-002170-2.
  29. ↑ Fisher, Ronald (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd. ISBN 0-05-002170-2., Table 1
  30. ↑ Grafen, Alan; Ridley, Mark (2006). Richard Dawkins: How A Scientist Changed the Way We Think. New York, New York: Oxford University Press. p. 69. ISBN 0-19-929116-0.
  31. ↑ Sexual Selection and Summary of Population Genetics Accessed from uscs.edu 2-08-2015
  32. ↑ Clutton-Brock, T.H. (1991). The Evolution of Parental Care. Princeton, NJ: Princeton U. Press. p. 9.
  33. ↑ Trivers, R.L. (1972), "Parental investment and sexual selection", in Campbell, B., Sexual selection and the descent of man 1871-1971, Chicago, IL: Aldine, pp. 136–179, ISBN 0-435-62157-2
  34. ↑ A theory of Fisher's reproductive value Published by PubMed.gov
  35. ↑ The Relation Between Reproductive Value and Genetic Contribution Published by the Genetics journal
  36. ↑ Fisher, R.A. (1930) The Genetical Theory of Natural Selection, Clarendon Press, Oxford
  37. ↑ Orr, Allen (2005). "The genetic theory of adaptation: a brief history". Nature Reviews Genetics. 6 (2): 119–127. doi:10.1038/nrg1523. PMID 15716908.
  38. ↑ "dominance". Oxford Dictionaries Online. Oxford University Press. Retrieved 14 May 2014.
  39. ↑ "express". Oxford Dictionaries Online. Oxford University Press. Retrieved 14 May 2014.
  40. ↑ Fisher R. 1930. The Genetical Theory of Natural Selection.
  41. ↑ Mann, H.B. (1949). Analysis and design of experiments: Analysis of variance and analysis of variance designs. New York, N. Y.: Dover. MR 32177.
  42. ↑ Fisher 1971, Chapter II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment, Section 8. The Null Hypothesis.
  43. ↑ OED quote: 1935 R. A. Fisher, The Design of Experiments ii. 19, "We may speak of this hypothesis as the 'null hypothesis', and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."
  44. ↑ Fisher, R. A. (1935). "The fiducial argument in statistical inference". Annals of Eugenics. 8: 391–398.
  45. ↑ R. A. Fisher's Fiducial Argument and Bayes' Theorem by Teddy Seidenfeld
  46. ↑ R. A. Fisher (1936). "The use of multiple measurements in taxonomic problems" (PDF). Annals of Eugenics. 7 (2): 179–188. doi:10.1111/j.1469-1809.1936.tb02137.x.
  47. ↑ Fisher, R. A. (1937). "The wave of advance of advantageous genes". Annals of Eugenics (7): 353–369.
  48. ↑ Fisher 2
  49. ↑ Fisher, Ronald A.; Yates, Frank (1948) [1938]. Statistical tables for biological, agricultural and medical research (3rd ed.). London: Oliver & Boyd. pp. 26–27. OCLC 14222135. Note: the 6th edition, ISBN 0-02-844720-4, is available on the web, but gives a different shuffling algorithm by C. R. Rao.
  50. ↑ Agresti, Alan; David B. Hichcock (2005). "Bayesian Inference for Categorical Data Analysis" (PDF). Statistical Methods & Applications. 14 (3): 298. doi:10.1007/s10260-005-0121-y.
  51. ↑ Fisher, R. A.; Balmukand, B. (1928). "The estimation of linkage from the offspring of selfed heterozygotes". Journal of Genetics (20): 79–92.
  52. ↑ Fisher, R. A.; Corbet, A. S.; Williams, C. B. (1943). "The relation between the number of species and the number of individuals in a random sample of an animal population". Journal of Animal Ecology (12): 42–58.
  53. ↑ Fisher, R. A. (1936). "Has Mendel's work been rediscovered?". Annals of Science. 1 (2): 115–126. doi:10.1080/00033793600200111.
  54. ↑ Sturtevant, A. H. (2001). A History of Genetics. Cold Springs Harbor, New York: Cold Springs Harbor Laboratory Press. pp. 13–16. ISBN 0-87969-607-9.
  55. ↑ Fisher, R. A. (1950). "Gene Frequencies in a Cline Determined by Selection and Diffusion". Biometrics. 6 (4): 353–361. doi:10.2307/3001780. PMID 14791572. JSTOR 3001780
  56. ↑ Box, R. A. Fisher, pp 93–166
  57. ↑ William G. Hill, Trudy F.C. Mackay (1 August 2004). "D. S. Falconer and Introduction to Quantitative Genetics". Genetics. 167 (4): 1529–36. PMC 1471025Freely accessible. PMID 15342495.
  58. ↑ Marston, Jean (8 March 2008). "Smoking gun (letter)". New Scientist (2646): 21.
  59. ↑ Croonian Lecture: Population Genetics by Ronald Fisher, published by The Royal Society Publishing
  60. ↑ 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.
  61. ↑ Page xvii in Ghosh (ed.)
  62. ↑ Fisher, R. A. (1936). "The Use of Multiple Measurements in Taxonomic Problems". Annals of Eugenics. 7 (2): 179–188. doi:10.1111/j.1469-1809.1936.tb02137.x. hdl:2440/15227.
  63. ↑ McLachlan, G. J. (2004). Discriminant Analysis and Statistical Pattern Recognition. Wiley Interscience. ISBN 0-471-69115-1. MR 1190469.
  64. ↑ B. R. Frieden, Science from Fisher Information, Cambridge University Press, Cambridge, England, 2004.
  65. ↑ Fisher, R. A. (1953). "Dispersion on a sphere". Proc. Roy. Soc. London Ser. A. (217): 295–305.
  66. ↑ Fisher, R. A. (1922). "On the Mathematical Foundations of Theoretical Statistics". Philos. Trans. R. Soc. London, Ser. A. 222A: 309–368.
  67. ↑ Fisher, R. A. (1940). "An examination of the different possible solutions of a problem in incomplete blocks". Annals of Eugenics. 10: 52–75. doi:10.1111/j.1469-1809.1940.tb02237.x.
  68. ↑ Fisher, R.A. (1922). "On the mathematical foundations of theoretical statistics". Philosophical Transactions of the Royal Society A. 222: 309–368. doi:10.1098/rsta.1922.0009. JFM 48.1280.02. JSTOR 91208.
  69. ↑ Fisher, R. A. (1925). "Applications of "Student's" distribution" (PDF). Metron. 5: 90–104.
  70. ↑ Walpole, Ronald; Myers, Raymond; Myers, Sharon; Ye, Keying (2002). Probability and Statistics for Engineers and Scientists (7th ed.). Pearson Education. p. 237. ISBN 81-7758-404-9.
  71. ↑ http://unesdoc.unesco.org/images/0007/000733/073351eo.pdf "The Race Concept: Results of an Inquiry", p. 27. UNESCO 1952
  72. ↑ Gould on God: Can religion and science be happily reconciled?
  73. ↑ Gene Frequencies in a Cline Determined by Selection and Diffusion, R. A. Fisher, Biometrics, Vol. 6, No. 4 (Dec., 1950), pp. 353–361
  74. ↑ 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. ISBN 978-0-262-11245-1 PS, Citeseer
  75. ↑ JPL Small-Body Database Browser Source is NASA
  76. ↑ The Genetical Theory of Natural Selection " It was one of his favorite aphorisms, first reported by Julian Huxley in 1936 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.

Sources

Academic offices
Preceded by
Austin Bradford Hill		 Presidents of the Royal Statistical Society
1952—1954 		Succeeded by
William Piercy
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