Editing Student's t-test (section)

==History==
[[File:William Sealy Gosset.jpg|thumb|upright|[[William Sealy Gosset]], who developed the "''t''-statistic" and published it under the [[pseudonym]] of "Student"]]

The term "''t''-statistic" is abbreviated from "hypothesis test statistic".<ref>{{Cite book |url=https://books.google.com/books?id=kiToDwAAQBAJ&pg=PA397 |title=The Microbiome in Health and Disease |date=2020-05-29 |publisher=Academic Press |isbn=978-0-12-820001-8 |pages=397 }}</ref> In statistics, the ''t''-distribution was first derived as a [[Posterior probability|posterior distribution]] in 1876 by [[Friedrich Robert Helmert|Helmert]]<ref>{{cite book |last=Szabó |first=István |chapter=Systeme aus einer endlichen Anzahl starrer Körper |date=2003 |title=Einführung in die Technische Mechanik |language=de |pages=196–199 |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-642-61925-0_16 |doi-broken-date=1 November 2024 |isbn=978-3-540-13293-6}}</ref><ref>{{Cite journal |last=Schlyvitch |first=B. |date=October 1937 |title=Untersuchungen über den anastomotischen Kanal zwischen der Arteria coeliaca und mesenterica superior und damit in Zusammenhang stehende Fragen |language=de |journal=Zeitschrift für Anatomie und Entwicklungsgeschichte |volume=107 |issue=6 |pages=709–737 |doi=10.1007/bf02118337 |s2cid=27311567 |issn=0340-2061}}</ref><ref>{{Cite journal |last=Helmert |date=1876 |title=Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Beobachtungsfehlers directer Beobachtungen gleicher Genauigkeit |journal=Astronomische Nachrichten |language=de |volume=88 |issue=8–9 |pages=113–131 |doi=10.1002/asna.18760880802 |bibcode=1876AN.....88..113H |url=https://zenodo.org/record/1424695}}</ref> and [[Jacob Lüroth|Lüroth]].<ref>{{Cite journal |last=Lüroth |first=J. |date=1876 |title=Vergleichung von zwei Werthen des wahrscheinlichen Fehlers|journal=Astronomische Nachrichten |language=de |volume=87 |issue=14 |pages=209–220 |doi=10.1002/asna.18760871402 |bibcode=1876AN.....87..209L |url=https://zenodo.org/record/1424693}}</ref><ref>{{cite journal |doi=10.1093/biomet/83.4.891 |mr=1766040 |title=Studies in the history of probability and statistics XLIV. A forerunner of the ''t''-distribution |year=1996 |last1=Pfanzagl |first1=J. |journal=Biometrika |volume=83 |issue=4 |pages=891–898 }}</ref><ref>{{Cite journal |last=Sheynin |first=Oscar |s2cid=121241599 |date=1995 |title=Helmert's work in the theory of errors |journal=Archive for History of Exact Sciences |volume=49 |issue=1 |pages=73–104 |doi=10.1007/BF00374700 |issn=0003-9519}}</ref> The ''t''-distribution also appeared in a more general form as Pearson type&nbsp;[[Pearson distribution|IV]] distribution in [[Karl Pearson]]'s 1895 paper.<ref>{{cite journal | doi=10.1098/rsta.1895.0010 | title=X. Contributions to the mathematical theory of evolution.—II. Skew variation in homogeneous material | journal=Philosophical Transactions of the Royal Society of London A | year=1895 | volume=186 | pages=343–414 | bibcode=1895RSPTA.186..343P | last1=Pearson | first1=Karl | doi-access=free }}</ref> However, the ''t''-distribution, also known as [[Student's t-distribution|Student's ''t''-distribution]], gets its name from [[William Sealy Gosset]], who first published it in English in 1908 in the scientific journal [[Biometrika]] using the pseudonym "Student"<ref name="The Probable Error of a Mean"/><ref>{{Cite web |url=https://www.tdistributiontable.com |title=T Table}}</ref> because his employer preferred staff to use [[pen name]]s when publishing scientific papers.<ref>{{cite journal | doi=10.1126/science.351.6280.1406 | title=Pseudonymous fame | year=2016 | last1=Wendl | first1=Michael C. | journal=Science | volume=351 | issue=6280 | page=1406 | pmid=27013722 }}</ref> Gosset worked at the [[Guinness Brewery]] in [[Dublin]], [[Ireland]], and was interested in the problems of small samples{{snd}} for example, the chemical properties of barley with small sample sizes. Hence a second version of the etymology of the term Student is that Guinness did not want their competitors to know that they were using the ''t''-test to determine the quality of raw material. Although it was William Gosset after whom the term "Student" is penned, it was actually through the work of [[Ronald Fisher]] that the distribution became well known as "Student's distribution"<ref>{{Cite book |last=Walpole, Ronald E. |title=Probability & statistics for engineers & scientists |date=2006 |publisher=Pearson |others=Myers, H. Raymond |isbn=81-7758-404-9 |edition= 7th |location=New Delhi |oclc=818811849}}</ref> and "Student's ''t''-test".

Gosset devised the ''t''-test as an economical way to monitor the quality of [[stout]]. The ''t''-test work was submitted to and accepted in the journal ''[[Biometrika]]'' and published in 1908.<ref name="The Probable Error of a Mean">{{cite journal |author=Student |title=The Probable Error of a Mean |journal=[[Biometrika]] |date=1908 |volume=6 |issue=1 |pages=1–25 |url=http://seismo.berkeley.edu/~kirchner/eps_120/Odds_n_ends/Students_original_paper.pdf |access-date=24 July 2016 |doi=10.1093/biomet/6.1.1 |hdl=10338.dmlcz/143545}}</ref>

Guinness had a policy of allowing technical staff leave for study (so-called "study leave"), which Gosset used during the first two terms of the 1906–1907 academic year in Professor [[Karl Pearson]]'s Biometric Laboratory at [[University College London]].<ref>{{cite journal |last=Raju |first=T. N. |s2cid=32745754 |title=William Sealy Gosset and William A. Silverman: Two 'Students' of Science |journal=[[Pediatrics (journal)|Pediatrics]] |volume=116 |issue=3 |pages=732–735 |year=2005 |pmid=16140715 |doi=10.1542/peds.2005-1134}}</ref> Gosset's identity was then known to fellow statisticians and to editor-in-chief Karl Pearson.<ref name="Dodge2008">{{cite book |first=Yadolah |last=Dodge |author-link=Yadolah Dodge |title=The Concise Encyclopedia of Statistics |url=https://books.google.com/books?id=k2zklGOBRDwC&pg=PA234 |year=2008 |publisher=Springer Science & Business Media |isbn=978-0-387-31742-7 |pages=234–235}}</ref>
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==Properties of the ''t''-statistic== -->