Editing William Sealy Gosset

{{Short description|British statistician}}
{{EngvarB|date=August 2014}}
{{Use dmy dates|date=August 2014}}
{{Infobox scientist
| name              = William Sealy Gosset
| other_names       = Student
| image             = William Sealy Gosset.jpg
| image_size        = 240px
| caption           = William Sealy Gosset (aka ''Student'') in 1908 (age 32)
| birth_date        = {{Birth date|df=yes|1876|06|13}}
| birth_place       = [[Canterbury]], Kent, England
| death_date        = {{death date and age|df=yes|1937|10|16|1876|06|13}}
| death_place       = [[Beaconsfield]], Buckinghamshire, England
| residence         =
| citizenship       = 
| field             = 
| work_institutions = [[Guinness Brewery]]
| alma_mater        = [[Winchester College]], [[New College, Oxford]]
| known_for         = [[Student's t-distribution]], [[statistical significance]], [[design of experiments]], [[Monte Carlo method]], [[quality control]], [[Modern synthesis]], [[agricultural economics]], [[econometrics]]
| prizes            = 
| children          = 5, including [[Isaac Henry Gosset]] 
}}
'''William Sealy Gosset''' (13 June 1876 – 16 October 1937) was an English statistician, chemist and brewer who worked for [[Guinness]]. In statistics, he pioneered small sample experimental design. Gosset published under the [[pen name]] '''Student''' and developed [[Student's t-distribution]] – originally called Student's "z" – and "Student's test of [[statistical significance]]".<ref name="Ziliak2008" />

== Life and career ==
Born in [[Canterbury, England|Canterbury]], England the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset, R.E. [[Royal Engineers]], Gosset attended [[Winchester College]] before matriculating as Winchester Scholar in [[natural sciences]] and mathematics at [[New College, Oxford]]. Upon graduating in 1899, he joined the brewery of [[Arthur Guinness]] & Son in [[Dublin]], Ireland; he spent the rest of his 38-year career at Guinness.<ref name="Ziliak2008" /><ref name=Biog>{{cite web|url=http://www.swlearning.com/quant/kohler/stat/biographical_sketches/bio12.1.html|title=BIOGRAPHY 12.1 William S. Gosset (1876–1937)|access-date=11 January 2015}} The site cites ''Dictionary of Scientific Biography'' (New York: Scribner's, 1972), pp. 476–477; ''International Encyclopedia of Statistics'', vol. I (New York: Free Press, 1978), pp. 409–413.</ref>

Gosset had three children with [[Marjory Gosset]] (née Phillpotts). [[Isaac Henry Gosset|Harry Gosset]] (1907–1965) was a consultant paediatrician; Bertha Marian Gosset (1909–2004) was a geographer and nurse; the youngest, Ruth Gosset (1911–1953) married the Oxford mathematician Douglas Roaf and had five children.

In his job as Head Experimental Brewer at [[Guinness]], Gosset developed new statistical methods – both in the brewery and on the farm – now central to the design of experiments, to proper use of significance testing on repeated trials, and to analysis of [[economic significance]] (an early instance of [[decision theory]] interpretation of statistics) and more, such as his small-sample, stratified, and repeated balanced experiments on [[barley]] for proving the best [[crop yield|yielding]] varieties.<ref name="cultsignificance2008">{{cite book|author1=Ziliak, S. |author2=[[Deirdre McCloskey|D. McCloskey]] |year=2008|url= https://www.press.umich.edu/186351/cult_of_statistical_significance |title=The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives| publisher = University of Michigan Press|isbn=978-0-472-07007-7|doi=10.3998/mpub.186351}}</ref> Gosset acquired that knowledge by study, by trial and error, by cooperating with others, and by spending two terms in 1906–1907 in the Biometrics laboratory of [[Karl Pearson]].<ref name="Ziliak2019" /> Gosset and Pearson had a good relationship.<ref name="Ziliak2019">{{cite journal|author=[[Stephen T. Ziliak]] |title=How Large Are Your G-Values? Try Gosset's Guinnessometrics when a Little "p" is Not Enough|journal=The American Statistician|year=2019|volume=73|pages=281–290|doi=10.1080/00031305.2018.1514325|s2cid=127347145|doi-access=free}}</ref> Pearson helped Gosset with the mathematics of his papers, including the 1908 papers, but had little appreciation of their importance. The papers addressed the brewer's concern with small samples; biometricians like Pearson, on the other hand, typically had hundreds of observations and saw no urgency in developing small-sample methods.<ref name=Biog />

Gosset's first publication came in 1907, "On the Error of Counting with a [[Haemocytometer]]," in which – unbeknownst to Gosset aka "Student" – he rediscovered the [[Poisson distribution]].<ref name="cultsignificance2008" /> Another researcher at Guinness had previously published a paper containing trade secrets of the Guinness brewery. The economic historian Stephen Ziliak discovered in the Guinness Archives that to prevent further disclosure of confidential information, the Guinness Board of Directors allowed its scientists to publish research on condition that they do not mention "1) beer, 2) Guinness, or 3) their own surname".<ref name="Ziliak2019" /> To Ziliak, Gosset seems to have acquired his pen name "Student" from his 1906–1907 notebook on counting yeast cells with a haemocytometer, "The Student's Science Notebook"<ref name="Ziliak2008" /><ref>{{cite journal |journal=[[Journal of the American Statistical Association]] |year=1930 |volume=25 |pages=186–190 |title=British Statistics and Statisticians Today |author=[[Harold Hotelling|Hotelling, H.]] |issue=170 |jstor=2277631 |doi=10.1080/01621459.1930.10503118 |url=https://www.gwern.net/docs/statistics/1930-hotelling.pdf}}</ref> Thus his most noteworthy achievement is now called Student's, rather than Gosset's, [[Student's t-distribution|t-distribution]] and test of [[statistical significance]].<ref name=Biog />

[[File:William Gosset plaque in Guinness storehouse tour, Ireland.jpg|left|thumb|Plaque in the Guinness storehouse commemorating Gosset]]

Gosset published most of his 21 academic papers, including ''The probable error of a mean,'' in Pearson's journal ''[[Biometrika]]'' under the pseudonym ''Student''.<ref>{{cite journal|author=[[Michael Christopher Wendl|M Wendl]] |title=Pseudonymous fame|doi=10.1126/science.351.6280.1406|doi-access=|journal= [[Science (journal)|Science]]|year=2016|volume=351|issue=6280|page=1406|pmid=27013722|bibcode=2016Sci...351.1406W}}</ref> It was, however, not Pearson but [[Ronald A. Fisher]] who appreciated the understudied importance of Gosset's small-sample work. Fisher wrote to Gosset in 1912 explaining that Student's z-distribution should be divided by [[Degrees of freedom (statistics)|degrees of freedom]] not total [[sample size]]. From 1912 to 1934 Gosset and Fisher would exchange more than 150 letters. In 1924, Gosset wrote in a letter to Fisher, "I am sending you a copy of Student's Tables as you are the only man that's ever likely to use them!" Fisher believed that Gosset had effected a "logical revolution".<ref name="cultsignificance2008" /> In a special issue of ''Metron'' in 1925 Student published the corrected tables, now called [[Student's t]] <math display=inline>z=\frac{t}{\sqrt{n-1}}</math>. In the same volume Fisher contributed applications of Student's ''t''-distribution to [[regression analysis]].<ref name="cultsignificance2008" />

Although introduced by others, [[Studentized residual]]s are named in Student's honour because, like the problem that led to Student's t-distribution, the idea of adjusting for estimated standard deviations is central to that concept.<ref>{{cite journal|url=https://cpb-us-e1.wpmucdn.com/blogs.roosevelt.edu/dist/b/153/files/2012/02/William-S-Gosset-and-Experimental-Statistics-Ziliak-JWE-2011.pdf |doi=10.1017/S1931436100001632|title=W.S. Gosset and Some Neglected Concepts in Experimental Statistics: Guinnessometrics II|year=2011|last1=Ziliak|first1=Stephen T.|journal=Journal of Wine Economics|volume=6|issue=2|pages=252–277|s2cid=12175939}}</ref>

Gosset's interest in the cultivation of barley led him to speculate that the [[design of experiments]] should aim not only at improving the average yield but also at breeding varieties whose yield was insensitive to variation in soil and climate (that is, "robust"). Gosset called his innovation "balanced layout", because treatments and controls are allocated in a balanced fashion to stratified growing conditions, such as differential soil fertility.<ref>{{cite journal|url=https://cpb-us-e1.wpmucdn.com/blogs.roosevelt.edu/dist/b/153/files/2014/01/Final-Balanced-vs-Randomized-Field-Experiments-_-Ziliak-Rev-Behavioral-Economics-2014.pdf |doi=10.1561/105.00000008|title=Balanced versus Randomized Field Experiments in Economics: Why W. S. Gosset aka "Student" Matters|year=2014|last1=Ziliak|first1=Stephen T.|journal=Review of Behavioral Economics|volume=1|issue=1–2|pages=167–208}}</ref> Gosset's balanced principle was challenged by Ronald Fisher, who preferred randomized designs. The Bayesian Harold Jeffreys, and Gosset's close associates Jerzy Neyman and Egon S. Pearson sided with Gosset's balanced designs of experiments; however, as Ziliak (2014) has shown, Gosset and Fisher would strongly disagree for the rest of their lives about the meaning and interpretation of balanced versus randomized experiments, as they had earlier clashed on the role of bright-line rules of statistical significance.<ref name="Ziliak2019" />

In 1935, at the age of 59, Gosset left [[Dublin]] to take up the position of Head Brewer at a new (and second) [[Guinness]] brewery at [[Park Royal]] in northwestern London. In September 1937 Gosset was promoted to Head Brewer of all Guinness. He died one month later, aged 61, in [[Beaconsfield]], England, of a heart attack.<ref name="Ziliak2008">{{cite journal|doi=10.1257/jep.22.4.199|doi-access=free|title=Retrospectives: Guinnessometrics: The Economic Foundation of "Student's" T|year=2008|last1=Ziliak|first1=Stephen T.|journal=Journal of Economic Perspectives|volume=22|issue=4|pages=199–216}}</ref>

Gosset was a friend of both [[Karl Pearson|Pearson]] and [[Ronald Fisher|Fisher]], a noteworthy achievement, for each had a massive ego and a loathing for the other. He was a modest man who once cut short an admirer with this comment: "Fisher would have discovered it all anyway."<ref>{{cite book | last = Salsburg | first = David | title = The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century | publisher = Holt Paperbacks | date = 2002 | isbn = 0-8050-7134-2}}</ref>

== Bibliography ==
Gosset:
* "The application of the 'law of error' to the work of the Brewery" (1904, ''Guinness'' internal report)
* {{cite journal
 | title = On the error of counting with hæmacytometer
 | journal = [[Biometrika]]
 | volume  = 5
 | issue = 3
 |date=February 1907
 | pages = 351–360
 | doi=10.1093/biomet/5.3.351
 | url = https://archive.org/details/in.ernet.dli.2015.233812/page/n17
}}
* {{cite journal
 | url = http://www.york.ac.uk/depts/maths/histstat/student.pdf
 | title = The probable error of a mean
 | journal = [[Biometrika]]
 | volume  = 6
 | issue = 1
 |date=March 1908
 | pages = 1–25
 | doi = 10.1093/biomet/6.1.1
| hdl = 10338.dmlcz/143545
 }}
* {{cite journal
 | title = Probable error of a correlation coefficient
 | journal = [[Biometrika]]
 | volume = 6
 | issue = 2/3
 |date=September 1908
 | pages = 302–310
 | doi = 10.1093/biomet/6.2-3.302
 | url = https://archive.org/details/in.ernet.dli.2015.233812/page/n51
}}
* {{cite journal
 | title = The distribution of the means of samples which are not drawn at random
 | journal = [[Biometrika]]
 | volume = 7
 | issue = 1/2
 |date=July–October 1909
 | pages = [https://archive.org/details/in.ernet.dli.2015.233812/page/n228 210]–214
 | doi = 10.1093/biomet/7.1-2.210
 | url = https://archive.org/details/in.ernet.dli.2015.233812
}}
* {{cite journal
 | title = An experimental determination of the probable error of Dr Spearman's correlation coefficients
 | journal = [[Biometrika]]
 | volume = 13
 | issue = 2/3
 |date=July 1921
 | pages = 263–282
 | doi = 10.1093/biomet/13.2-3.263
 | url = https://archive.org/details/in.ernet.dli.2015.233812/page/n86
}}
* {{cite journal
 | url = http://www.economics.soton.ac.uk/staff/aldrich/fisherguide/student.htm
 | title = Review of Statistical Methods for Research Workers (R. A. Fisher)
 | year = 1926
 | journal = [[Eugenics Review]]
 | volume = 18
 | pages = 148–150
}}
* {{cite journal
 | url = http://cda.mrs.umn.edu/~jongmink/Stat2611/s1.pdf
 | title = On Student's 1908 Article "The Probable Error of a Mean" (S.L. Zabell)
 | date = March 2008
 | journal = [[Journal of the American Statistical Association]]
 | volume = 103| issue = 481
 | pages = 1–7
 | doi = 10.1198/016214508000000030
 | last1 = Zabell
 | first1 = S. L
| s2cid = 48322195
 }}
* [https://www.gwern.net/docs/genetics/selection/1933-student.pdf "Evolution By Selection: The Implications of Winter's Selection Experiment"], 1933, ''Eugenics Review'', 24, pg293
* [https://archive.org/details/in.ernet.dli.2015.233812/page/n7 ''{{'}}Student{{'}}s{{'}} Collected Papers''] (edited by E.S. Pearson and John Wishart, with a foreword by Launce McMullen), London: Biometrika Office. (1942)

== References ==
{{Reflist}}

== Further reading ==
;Biographies
* [[E. S. Pearson]] (1990) [https://www.gwern.net/docs/statistics/decision/1990-pearson-studentastatisticalbiographyofwilliamsealygosset.pdf '''Student', A Statistical Biography of William Sealy Gosset,''] Edited and Augmented by [[R. L. Plackett]] with the Assistance of [[G. A. Barnard]], Oxford: University Press. {{ISBN|978-0-19-852227-0}}.
* {{cite journal | last1 = Pearson | first1 = E. S. | year = 1939 | title = 'Student' as Statistician | url = https://www.gwern.net/docs/statistics/decision/1939-pearson.pdf | journal = Biometrika | volume = 30 | issue = 3/4| pages = 210–250 | doi=10.1093/biomet/30.3-4.210}}
* Beaven 1947, [https://archive.org/details/in.ernet.dli.2015.99169/page/n1 ''Barley: Fifty Years of Observation and Experiment'']

== External links ==
* [http://www.swlearning.com/quant/kohler/stat/biographical_sketches/bio12.1.html Biography by Heinz Kohler]
* [http://www-stat.stanford.edu/~naras/jsm/TDensity/TDensity.html Student's T Distribution]
* [http://jeff560.tripod.com/s.html Earliest known uses of some of the words of mathematics: S] under the heading of "Student's ''t''-distribution", describes briefly how Student's ''z'' became ''t''.
* {{MacTutor Biography|id=Gosset}}

{{Authority control}}

{{DEFAULTSORT:Gosset, William Sealey}}
[[Category:1876 births]]
[[Category:1937 deaths]]
[[Category:People from Canterbury]]
[[Category:People educated at Winchester College]]
[[Category:Alumni of New College, Oxford]]
[[Category:English statisticians]]
[[Category:20th-century English mathematicians]]
[[Category:Computational statisticians]]
[[Category:Gosset family|William Sealy]]