# William Sealy Gosset

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**William Sealy Gosset** (13 June 1876 – 16 October 1937) was Head Brewer of Guinness, Head Experimental Brewer of Guinness, and a pioneer of modern statistics. He pioneered small sample experimental design and analysis with an economic approach to the logic of uncertainty. Gosset published under the pen name **Student** and developed most famously Student's t-distribution - originally called Student's "z" - and "Student's test of statistical significance".^{[1]}

William Sealy Gosset | |
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William Sealy Gosset (aka Student) in 1908 (age 32). | |

Born | Canterbury, Kent, England | 13 June 1876

Died | 16 October 1937 Beaconsfield, Buckinghamshire, England | (aged 61)

Other names | Student |

Alma mater | New College, Oxford, Winchester College |

Known for | Student's t-distribution, statistical significance, design of experiments, Monte Carlo method, quality control, Modern synthesis, agricultural economics, econometrics |

Scientific career | |

Institutions | Guinness Brewery |

Influences | William Archibald Spooner, Karl Pearson |

Influenced | Ronald A. Fisher, Harold Jeffreys, Egon Pearson, Jerzy Neyman, John Wishart, W. Edwards Deming, Edwin S. Beaven, Herbert Hunter |

## Contents

## Life and careerEdit

Born in 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, where he would spend the rest of his short but brilliant 38 year career^{[1]}^{[2]}

In his job as Head Experimental Brewer at Guinness, the self-trained 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 yielding varieties^{[3]} 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.^{[4]} Gosset and Pearson had a good relationship.^{[5]} 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.^{[2]}

Gosset's first publication came in 1907, "On the Error of Counting with a Haemacytometer," in which - unbeknownst to Gosset aka "Student" - he rediscovered the Poisson distribution.^{[3]} 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".^{[5]} to Ziliak, Gosset seems to have gotten his pen name "Student" from his 1906-1907 notebook on counting yeast cells with a haemacytometer, "The Student's Science Notebook"^{[1]}^{[6]} Thus his most noteworthy achievement is now called Student's, rather than Gosset's, t-distribution and test of statistical significance.^{[2]}

Gosset published most of his 21 academic papers, including *The probable error of a mean,* in Pearson's journal *Biometrika* under the pseudonym *Student*.^{[7]} 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 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".^{[3]} In a special issue of *Metron* in 1925 Student published the corrected tables, now called Student's t . In the same volume Fisher contributed applications of Student's *t*-distribution to regression analysis.^{[3]}

Although introduced by others, Studentized residuals 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.^{[8]}

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.^{[9]} 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.^{[5]}

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 two years later, aged 61, in Beaconsfield, England, of a heart attack.^{[1]}

Gosset was a friend of both Pearson and 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."^{[10]}

## BibliographyEdit

Gosset:

- "The application of the 'law of error' to the work of the Brewery" (1904,
*Guinness*internal report) - "On the error of counting with hæmacytometer".
*Biometrika*.**5**(3): 351–360. February 1907. doi:10.1093/biomet/5.3.351. - "The probable error of a mean" (PDF).
*Biometrika*.**6**(1): 1–25. March 1908. doi:10.1093/biomet/6.1.1. - "Probable error of a correlation coefficient".
*Biometrika*.**6**(2/3): 302–310. September 1908. doi:10.1093/biomet/6.2-3.302. - "The distribution of the means of samples which are not drawn at random".
*Biometrika*.**7**(1/2): 210–214. July – October 1909. doi:10.1093/biomet/7.1-2.210. - "An experimental determination of the probable error of Dr Spearman's correlation coefficients".
*Biometrika*.**13**(2/3): 263–282. July 1921. doi:10.1093/biomet/13.2-3.263. - "Review of Statistical Methods for Research Workers (R. A. Fisher)".
*Eugenics Review*.**18**: 148–150. 1926. - Zabell, S. L (March 2008). "On Student's 1908 Article "The Probable Error of a Mean" (S.L. Zabell)" (PDF).
*Journal of the American Statistical Association*.**103**(481): 1–7. doi:10.1198/016214508000000030. - "Evolution By Selection: The Implications of Winter's Selection Experiment", 1933,
*Eugenics Review*, 24, pg293 *'Student's' Collected Papers*(edited by E.S. Pearson and John Wishart, with a foreword by Launce McMullen), London: Biometrika Office. (1942)

## ReferencesEdit

- ^
^{a}^{b}^{c}^{d}Ziliak, S. (2008), "Guinnessometrics: The Economic Foundation of Student's*t*",*Journal of Economic Perspectives*(Fall, 22 [4]) - ^
^{a}^{b}^{c}"BIOGRAPHY 12.1 William S. Gosset (1876–1937)". Retrieved 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. - ^
^{a}^{b}^{c}^{d}Ziliak, S. and D. McCloskey (2008),*The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives*(University of Michigan Press) **^**h- ^
^{a}^{b}^{c}Stephen T. Ziliak (2019), "How large are your*G*-values? Try Gosset's Guinnessometrics when a little '*p*' is not enough",*The American Statistician*73 **^**Hotelling, H.. British Statistics and Statisticians Today.*Journal of the American Statistical Association*. 1930;25:186–190. doi:10.1080/01621459.1930.10503118.**^**M Wendl (2016) "Pseudonymous fame", Science, 351(6280), 1406.**^**Ziliak 2011, "W.S. Gosset and Some Neglected Concepts in Experimental Statistics: Guinnessometrics II"**^**Ziliak, S. (2014) "Balanced versus Randomized Field Experiments in Economics: Why W. S. Gosset aka "Student" Matters",*Review of Behavioral Economics*: Vol. 1: No. 1–2, pp 167-208.**^**Salsburg, David (2002).*The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century*. Holt Paperbacks. ISBN 0805071342.

## Further readingEdit

- Biographies

- E. S. Pearson (1990) '
*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. - Pearson, E. S. (1939). "'Student' as Statistician" (PDF).
*Biometrika*.**30**(3/4): 210–250. doi:10.1093/biomet/30.3-4.210. - Beaven 1947,
*Barley: Fifty Years of Observation and Experiment*

## External linksEdit

- Biography by Heinz Kohler
- Student's T Distribution
- 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*. - O'Connor, John J.; Robertson, Edmund F., "William Sealy Gosset",
*MacTutor History of Mathematics archive*, University of St Andrews.