Editing Ronald Fisher (section)

===Rothamsted Experimental Station, 1919–1933===
In 1919, he began working at the [[Rothamsted Research|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>{{ cite journal | title=) Studies in Crop Variation. I. An Examination of the Yield of Dressed Grain from Broadbalk | first1=Ronald A. | last1=Fisher | journal=Journal of Agricultural Science | volume=11 | pages=107–135| year=1921 | issue=2 | doi=10.1017/S0021859600003750 | hdl=2440/15170 | s2cid=86029217 | hdl-access=free }}</ref> ''Studies in Crop Variation II'' written with his first assistant, [[Winifred Mackenzie]], became the model for later ANOVA work.<ref>{{ cite journal | title=) Studies in Crop Variation. II. The Manurial Response of Different Potato Varieties | first1=Ronald A. | last1=Fisher | journal=Journal of Agricultural Science | volume=13 | pages=311–320| year=1923 | issue=3 | doi=10.1017/S0021859600003592 | hdl=2440/15179 | s2cid=85985907 | hdl-access=free }}</ref> Later assistants who mastered and propagated Fisher's methods were [[Joseph Oscar Irwin]], [[John Wishart (statistician)|John Wishart]] and [[Frank Yates]]. Between 1912 and 1922 Fisher recommended, analysed (with heuristic [[mathematical proof|proofs]]) and vastly popularized the [[maximum likelihood estimation]] method.<ref>{{cite book | title=Parametric statistical theory | last1=Pfanzagl | first1=Johann | first2=R. | last2=Hamböker | year=1994 | publisher=Walter de Gruyter | location=Berlin | isbn=978-3-11-013863-4 | pages=207–208}}</ref>

[[File:Ronald Fisher 1912 graduation Cambridge.JPG|thumb|upright|On graduating from Cambridge University, 1912]]
[[File:Peacock Flying.jpg|thumb|The peacock tail in flight, the classic example of a Fisherian runaway]]
[[File:Rothamstead_Research_Centre_-_geograph.org.uk_-_1724254.jpg|thumb|Rothamsted Research]]

Fisher's 1924 article ''On a distribution yielding the error functions of several well known statistics'' presented [[Pearson's chi-squared test]] and [[William Sealy Gosset|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|''F''-distribution]]. He pioneered the principles of the [[design of experiments]] and the statistics of small samples and the analysis of real data.<ref name=":2">{{Cite journal |last=Krishnan |first=T. |date=1997-09-01 |title=Fisher's contributions to statistics |url=https://doi.org/10.1007/BF02834579 |journal=Resonance |language=en |volume=2 |issue=9 |pages=32–37 |doi=10.1007/BF02834579 |issn=0973-712X}}</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>{{cite journal |last1=Conniffe |first1=Denis |title=R.A. Fisher and the development of statistics - a view in his centerary year |journal=Journal of the Statistical and Social Inquiry Society of Ireland |volume=26 |issue=3 |date=1991 |pages=55–108 |id={{ProQuest|911976618}} |hdl=2262/2764 |hdl-access=free }}</ref> [[Fisher's method]]<ref>{{cite book | last=Fisher | first=R.A. | year=1925 | title=Statistical Methods for Research Workers | publisher=Oliver and Boyd (Edinburgh) | url=https://archive.org/details/statisticalmethoe7fish | isbn=978-0-05-002170-5 }}</ref><ref>{{cite journal| doi=10.2307/2681650| last=Fisher | first=R.A.| author2=Fisher, R. A | title=Questions and answers #14 | journal=The American Statistician | year=1948 | volume=2| pages=30–31 | issue=5 | jstor=2681650}}</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>{{ cite book | url=https://www.jerrydallal.com/LHSP/LHSP.htm | title=The Little Handbook of Statistical Practice | last1=Dallal | first1=Gerard E. | year=2012 }}</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.
<blockquote>
"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>
{{cite book | first=Ronald | last=Fisher | author-link=Ronald Fisher | title=Statistical Methods for Research Workers | year=1925 | isbn=978-0-05-002170-5 | page=[https://archive.org/details/statisticalmethoe7fish/page/46 46] | publisher=Oliver and Boyd | location=Edinburgh | url=https://archive.org/details/statisticalmethoe7fish/page/46 }}</ref>
</blockquote>
In Table 1 of the work, he gave the more precise value 1.959964.<ref>
{{cite book | first=Ronald | last=Fisher |author-link=Ronald Fisher |title=Statistical Methods for Research Workers |year=1925 |isbn=978-0-05-002170-5| publisher=Oliver and Boyd| location=Edinburgh| title-link=Statistical Methods for Research Workers }}, [https://psychclassics.yorku.ca/Fisher/Methods/tabI-II.gif Table 1]</ref>

In 1928, Fisher was the first to use [[diffusion equation]]s to attempt to calculate the distribution of [[allele]] frequencies and the estimation of [[genetic linkage]] by maximum likelihood methods among populations.<ref>{{cite journal | first1=R. A. | last1=Fisher | last2=Balmukand | first2=B. | year=1928 | title =The estimation of linkage from the offspring of selfed heterozygotes | journal= [[Journal of Genetics]] | volume=20 | pages=79–92 | doi = 10.1007/bf02983317 | s2cid=27688031 }}</ref>

In 1930, ''[[The Genetical Theory of Natural Selection]]'' was first published by [[Oxford University Press|Clarendon Press]] and is dedicated to [[Leonard Darwin]]. A core work of the neo-Darwinian [[Modern synthesis (20th century)|modern evolutionary synthesis]],<ref>{{cite book|title= Richard Dawkins: How A Scientist Changed the Way We Think|last= Grafen|first= Alan|author-link= Alan Grafen|author2= Ridley, Mark|year= 2006|publisher= Oxford University Press|location= New York|isbn= 978-0-19-929116-8|page= [https://archive.org/details/richarddawkinsho00alan/page/69 69]|url= https://archive.org/details/richarddawkinsho00alan/page/69}}</ref> 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]].<ref>[https://bio.research.ucsc.edu/~barrylab/classes/evolution/SEXUAL.HTM Sexual Selection and Summary of Population Genetics] Accessed from uscs.edu 2 August 2015</ref>

One of Fisher's favourite aphorisms was "Natural selection is a mechanism for generating an exceedingly high degree of improbability."<ref>[https://www.genetics.org/content/154/4/1419.full ''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.{{citation needed|date=July 2017}}