Statistics

== History ==
{{main|History of statistics|Founders of statistics}}
[[File:Jakob Bernoulli.jpg|thumb|Bernoulli's ''[[Ars Conjectandi]]'' was the first work that dealt with [[probability theory]] as currently understood.]]
Formal discussions on inference date back to [[Mathematics in medieval Islam|Arab mathematicians]] and [[cryptographers]], during the [[Islamic Golden Age]] between the 8th and 13th centuries. [[Al-Khalil ibn Ahmad al-Farahidi|Al-Khalil]] (717–786) wrote the ''Book of Cryptographic Messages'', which contains one of the first uses of [[permutation]]s and [[combination]]s, to list all possible [[Arabic language|Arabic]] words with and without vowels.<ref name="LB">{{cite journal|last=Broemeling|first=Lyle D.|title=An Account of Early Statistical Inference in Arab Cryptology|journal=The American Statistician|date=1 November 2011|volume=65|issue=4|pages=255–257|doi=10.1198/tas.2011.10191|s2cid=123537702}}</ref> [[Al-Kindi|Al-Kindi's]] ''Manuscript on Deciphering Cryptographic Messages'' gave a detailed description of how to use [[frequency analysis]] to decipher [[encrypted]] messages, providing an early example of [[statistical inference]] for [[Code|decoding]]. [[Ibn Adlan]] (1187–1268) later made an important contribution on the use of [[sample size]] in frequency analysis.<ref name="LB"/>

Although the term 'statistic' was introduced by the Italian scholar [[Girolamo Ghilini]] in 1589 with reference to a collection of facts and information about a state, it was the German [[Gottfried Achenwall]] in 1749 who started using the term as a collection of quantitative information, in the modern use for this science.<ref>{{cite journal |last=Ostasiewicz |first=Walenty |year=2014 |title=The emergence of statistical science |journal=Śląski Przegląd Statystyczny |volume=12 |issue=18 |doi=10.15611/sps.2014.12.04 |pages=76–77|doi-access=free }}</ref><ref>{{cite book |last=Bruneau |first=Quentin |url=https://books.google.com/books?id=63RnEAAAQBAJ&pg=PT64 |title=States and the Masters of Capital: Sovereign Lending, Old and New |publisher=[[Columbia University Press]] |year=2022 |isbn=978-0231555647}}</ref> The earliest writing containing statistics in Europe dates back to 1663, with the publication of ''[[Natural and Political Observations upon the Bills of Mortality]]'' by [[John Graunt]].<ref>Willcox, Walter (1938) "The Founder of Statistics". ''Review of the [[International Statistical Institute]]'' 5(4): 321–328. {{JSTOR|1400906}}</ref> Early applications of statistical thinking revolved around the needs of states to base policy on demographic and economic data, hence its [[History of statistics#Etymology|''stat-'' etymology]]. The scope of the discipline of statistics broadened in the early 19th century to include the collection and analysis of data in general. Today, statistics is widely employed in government, business, and natural and social sciences.

[[File:Carl Friedrich Gauss 1840 by Jensen.jpg|thumb|left|[[Carl Friedrich Gauss]] made major contributions to probabilistic methods leading to statistics.]]
The mathematical foundations of statistics developed from discussions concerning [[Game of chance|games of chance]] among mathematicians such as [[Gerolamo Cardano]], [[Blaise Pascal]], [[Pierre de Fermat]], and [[Christiaan Huygens]]. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of [[Juan Caramuel]]), [[probability theory]] as a mathematical discipline only took shape at the very end of the 17th century, particularly in [[Jacob Bernoulli|Jacob Bernoulli's]] posthumous work ''[[Ars Conjectandi]]''.<ref>J. Franklin, The Science of Conjecture: Evidence and Probability before Pascal, Johns Hopkins Univ Pr 2002</ref> This was the first book where the realm of games of chance and the realm of the probable (which concerned opinion, evidence, and argument) were combined and submitted to mathematical analysis.<ref>Schneider, I. (2005). Jakob Bernoulli, ''Ars Conjectandi'' (1713). In I. Grattan-Guinness (Ed.), ''Landmark writings in Western Mathematics, 1640-1940'' (pp. 88-103). </ref><ref>{{Cite book |last1=Sylla |first1=E. D. |url=https://books.google.com/books?id=-xgwSAjTh34C |title=The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis (trans.) |last2=Bernoulli |first2=Jacob |publisher=JHU Press |year=2006 |isbn=978-0-8018-8235-7 |language=en}}</ref> The [[method of least squares]] was first described by [[Adrien-Marie Legendre]] in 1805, though [[Carl Friedrich Gauss]] presumably made use of it a decade earlier in 1795.<ref>{{Cite web |last=Lim |first=M. |date=2021 |title=Gauss, Least Squares, and the Missing Planet |url=https://www.actuaries.digital/2021/03/31/gauss-least-squares-and-the-missing-planet/ |access-date=2022-11-01 |website=Actuaries Digital}}</ref>

[[File:Karl Pearson, 1910.jpg|thumb|right|upright=1.05|[[Karl Pearson]], a founder of mathematical statistics]]

The modern field of statistics emerged in the late 19th and early 20th century in three stages.<ref>{{cite book|url=https://books.google.com/books?id=jYFRAAAAMAAJ|title=Studies in the history of statistical method|author=Helen Mary Walker|author-link=Helen M. Walker|year=1975|publisher=Arno Press|isbn=978-0405066283|access-date=2015-06-27|archive-date=2020-07-27|archive-url=https://web.archive.org/web/20200727141905/https://books.google.com/books?id=jYFRAAAAMAAJ|url-status=live}}</ref> The first wave, at the turn of the century, was led by the work of [[Francis Galton]] and [[Karl Pearson]], who transformed statistics into a rigorous mathematical discipline used for analysis, not just in science, but in industry and politics as well. Galton's contributions included introducing the concepts of [[standard deviation]], [[correlation]], [[regression analysis]] and the application of these methods to the study of the variety of human characteristics—height, weight and eyelash length among others.<ref name=Galton1877>{{cite journal | last1 = Galton | first1 = F | year = 1877 | title = Typical laws of heredity | journal = Nature | volume = 15 | issue = 388| pages = 492–553 | doi=10.1038/015492a0| bibcode = 1877Natur..15..492. | doi-access = free }}</ref> Pearson developed the [[Pearson product-moment correlation coefficient]], defined as a product-moment,<ref>{{Cite journal | doi = 10.1214/ss/1177012580 | last1 = Stigler | first1 = S.M. | year = 1989 | title = Francis Galton's Account of the Invention of Correlation | journal = Statistical Science | volume = 4 | issue = 2| pages = 73–79 | doi-access = free }}</ref> the [[Method of moments (statistics)|method of moments]] for the fitting of distributions to samples and the [[Pearson distribution]], among many other things.<ref name="Pearson, On the criterion">{{Cite journal|last1=Pearson|first1=K.|year=1900|title=On the Criterion that a given System of Deviations from the Probable in the Case of a Correlated System of Variables is such that it can be reasonably supposed to have arisen from Random Sampling|url=https://zenodo.org/record/1430618|journal=Philosophical Magazine|series=Series 5|volume=50|issue=302|pages=157–175|doi=10.1080/14786440009463897|access-date=2019-06-27|archive-date=2020-08-18|archive-url=https://web.archive.org/web/20200818110818/https://zenodo.org/record/1430618|url-status=live}}</ref> Galton and Pearson founded ''[[Biometrika]]'' as the first journal of mathematical statistics and [[biostatistics]] (then called biometry), and the latter founded the world's first university statistics department at [[University College London]].<ref>{{cite web|title=Karl Pearson (1857–1936)|publisher=Department of Statistical Science&nbsp;– [[University College London]]|url=http://www.ucl.ac.uk/stats/department/pearson.html|url-status=dead|archive-url=https://web.archive.org/web/20080925065418/http://www.ucl.ac.uk/stats/department/pearson.html|archive-date=2008-09-25}}</ref>

The second wave of the 1910s and 20s was initiated by [[William Sealy Gosset]], and reached its culmination in the insights of [[Ronald Fisher]], who wrote the textbooks that were to define the academic discipline in universities around the world. Fisher's most important publications were his 1918 seminal paper ''[[The Correlation between Relatives on the Supposition of Mendelian Inheritance]]'' (which was the first to use the statistical term, [[variance]]), his classic 1925 work ''[[Statistical Methods for Research Workers]]'' and his 1935 ''[[The Design of Experiments]]'',<ref>{{cite journal | author = Box, JF | title = R.A. Fisher and the Design of Experiments, 1922–1926 | jstor = 2682986 | journal = [[The American Statistician]] | volume = 34 | issue = 1 |date=February 1980 | pages = 1–7 | doi = 10.2307/2682986}}</ref><ref>{{cite journal | author = Yates, F | title = Sir Ronald Fisher and the Design of Experiments | jstor = 2528399 | journal = [[Biometrics (journal)|Biometrics]] | volume = 20 | issue = 2 |date=June 1964 | pages = 307–321 | doi = 10.2307/2528399}}</ref><ref>{{cite journal
|title=The Influence of Fisher's "The Design of Experiments" on Educational Research Thirty Years Later
|first1=Julian C. |last1=Stanley
|journal=American Educational Research Journal
|volume=3 |issue=3 |year=1966|pages= 223–229
|jstor=1161806 |doi=10.3102/00028312003003223|s2cid=145725524 }}</ref> where he developed rigorous [[design of experiments]] models. He originated the concepts of [[sufficiency (statistics)|sufficiency]], [[ancillary statistic]]s, [[linear discriminant analysis|Fisher's linear discriminator]] and [[Fisher information]].<ref>{{cite journal|last=Agresti|first=Alan|author2=David B. Hichcock|year=2005|title=Bayesian Inference for Categorical Data Analysis|journal=Statistical Methods & Applications|issue=3|page=298|url=http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf|doi=10.1007/s10260-005-0121-y|volume=14|s2cid=18896230|access-date=2013-12-19|archive-date=2013-12-19|archive-url=https://web.archive.org/web/20131219212926/http://www.stat.ufl.edu/~aa/articles/agresti_hitchcock_2005.pdf|url-status=live}}</ref> He also coined the term [[null hypothesis]] during the [[Lady tasting tea]] experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation".<ref name="oed">OED quote: '''1935''' R.A. Fisher, ''[[The Design of Experiments]]'' ii. 19, "We may speak of this hypothesis as the 'null hypothesis', and the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation."</ref><ref>Fisher|1971|loc=Chapter II. The Principles of Experimentation, Illustrated by a Psycho-physical Experiment, Section 8. The Null Hypothesis</ref> In his 1930 book ''[[The Genetical Theory of Natural Selection]]'', he applied statistics to various [[biology|biological]] concepts such as [[Fisher's principle]]<ref name="Edwards98">{{cite journal|last1=Edwards|first1=A.W.F.|year=1998|title=Natural Selection and the Sex Ratio: Fisher's Sources|journal=American Naturalist|volume=151|issue=6|pages=564–569|doi=10.1086/286141|pmid=18811377|s2cid=40540426}}</ref> (which [[A. W. F. Edwards]] called "probably the most celebrated argument in [[evolutionary biology]]") and [[Fisherian runaway]],<ref name="fisher15">Fisher, R.A. (1915) The evolution of sexual preference. Eugenics Review (7) 184:192</ref><ref name="fisher30">Fisher, R.A. (1930) [[The Genetical Theory of Natural Selection]]. {{isbn|0-19-850440-3}}</ref><ref name="pers00">Edwards, A.W.F. (2000) Perspectives: Anecdotal, Historical and Critical Commentaries on Genetics. The Genetics Society of America (154) 1419:1426</ref><ref name="ander94">{{cite book|last = Andersson|first = Malte|date = 1994|title = Sexual Selection|isbn = 0-691-00057-3|publisher = Princeton University Press|url = https://books.google.com/books?id=lNnHdvzBlTYC|access-date = 2019-09-19|archive-date = 2019-12-25|archive-url = https://web.archive.org/web/20191225202726/https://books.google.com/books?id=lNnHdvzBlTYC|url-status = live}}</ref><ref name="ander06">Andersson, M. and Simmons, L.W. (2006) Sexual selection and mate choice. Trends, Ecology and Evolution (21) 296:302</ref><ref name="gayon10">Gayon, J. (2010) Sexual selection: Another Darwinian process. Comptes Rendus Biologies (333) 134:144</ref> a concept in [[sexual selection]] about a positive feedback runaway effect found in [[evolution]].

The final wave, which mainly saw the refinement and expansion of earlier developments, emerged from the collaborative work between [[Egon Pearson]] and [[Jerzy Neyman]] in the 1930s. They introduced the concepts of "[[Type I and type II errors|Type II]]" error, [[power of a test]] and [[confidence interval]]s. Jerzy Neyman in 1934 showed that stratified random sampling was in general a better method of estimation than purposive (quota) sampling.<ref>{{cite journal | last1 = Neyman | first1 = J | year = 1934 | title = On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection | journal = [[Journal of the Royal Statistical Society]] | volume = 97 | issue = 4| pages = 557–625 | jstor=2342192| doi = 10.2307/2342192 }}</ref>

Today, statistical methods are applied in all fields that involve decision making, for making accurate inferences from a collated body of data and for making decisions in the face of uncertainty based on statistical methodology. The use of modern [[computer]]s has expedited large-scale statistical computations and has also made possible new methods that are impractical to perform manually. Statistics continues to be an area of active research, for example on the problem of how to analyze [[big data]].<ref>{{cite web|url=http://www.santafe.edu/news/item/sfnm-wood-big-data/|title=Science in a Complex World – Big Data: Opportunity or Threat?|work=Santa Fe Institute|date=2 December 2013 |access-date=2014-10-13|archive-date=2016-05-30|archive-url=https://web.archive.org/web/20160530001750/http://www.santafe.edu/news/item/sfnm-wood-big-data/|url-status=live}}</ref>