by M. Eileen Magnello

© Oxford University Press 2004 All rights reserved

**Gosset, William Sealy** *[pseud.* Student] (1876-1937), chemist and statistician, was born on 13 June 1876 at 6 St Martin's Hill, St Martin, Canterbury, the eldest son of five children of Frederic Gosset, a lieutenant in the Royal Engineers then residing at the infantry barracks in Canterbury, and Agnes Sealy, daughter of Edward Didal. The Gossets were an old Huguenot family who left France at the revocation of the edict of Nantes in 1685.

Gosset was a scholar at Winchester College in 1889-95 and won a scholarship to New College, Oxford. He obtained a first in the mathematical moderations in 1897 and left in 1899 with a first-class degree in chemistry. In October 1899 he became a brewer with Arthur Guinness, Son & Co., Ltd, manufacturers of stout at the St James's Gate Brewery in Dublin. (He was bound by his appointment not to publish in his own name, and this led to his subsequent adoption of the pseudonym Student.) Gosset's appointment at Guinness coincided with its introduction of scientific methods for brewing stout. The firm had large farming interests, especially in growing barley for beer, which led to Gosset's involvement with agricultural experiments and subsequently with laboratory tests. Guinness had by then not only begun to appoint men with first-class science degrees from Oxford and Cambridge, but it had also adopted a policy of sending staff away for specialized study.

Gosset became involved with agricultural experiments some time in 1905 when his advice was sought by the Guinness maltster Edwin S. Beaven, who carried out manurial experiments on eight varieties of barley in twenty small plots of wire cages at a nursery near Warminster in Wiltshire. The aim of these 'chessboard' experiments (so called from the arrangement of the plots) was to increase the yield of the grain, of which Guinness was a very large consumer. His pioneering work with Beaven played a prominent part in the efforts of the Irish department of agriculture and its cereal station at Ballindcurra to improve the Irish barley crop: this work led to Gosset's use of statistical methods to estimate the probable effect of experimental error. Gosset wrote his first statistical paper in 1904, on the application of the 'law of error' to the work in the brewery. The principal tools available to him were Airy's theory of errors of observations, and Merriman's method of least squares, though he found that there were no statistical tests that were suitable for his agricultural plots of barley (for his work at Guinness) because the sample sizes were quite often very small.

The Oxford chemist Vernon Harcourt introduced Gosset to the statistician Karl Pearson, whom Gosset visited at East Ilsey in Berkshire in July 1905. Six months later, on 16 January 1906, Gosset married Marjory Surtees Phillpotts *(b.* 1879/80) at the church of St James in Tunbridge Wells. They had one son and two daughters. The Gossets moved to London in September 1906 so that Gosset could attend Pearson's lectures and tutorials. They stayed in Wimbledon for two terms and left in the spring of 1907. Gosset kept in regular contact with Pearson until 1935. While many of the statistical problems in Pearson's biometric laboratory at University College, London, dealt with large samples, Gosset showed that the results of many agricultural and some chemical experiments produced small samples, and he was therefore concerned that these problems were outside the range of statistical enquiry.

On his return to Dublin, Gosset was put in charge of the experimental barley-growing project, which involved some statistical work. At Guinness he began to investigate the connection between laboratory analysis of various temperatures of malts and the length of time the resulting beer remained potable as measured by acidity. Using the statistical methods he learned in Pearson's biometric school, Gosset was able to deploy the same procedure in various conditions and to test for significant differences between them (as Pearson incorporated probability distributions in his methods). Moreover, he could accomplish all of this by himself without having to engage in the time-consuming procedure of comparing the results obtained by others to establish the degree of error. Gosset's best-known work was his investigation of the probable error of the mean which he published in *Biometrika* in 1908 under the name Student. This called for the distribution of the variance in normal samples (which Gosset found by calculating moments) and used one of Pearson's theoretical curves (from the Pearsonian family of curves) to produce tables from which could be computed the probability that the population mean would lie within certain numbers of standard deviations of the sample mean. This process of making full allowance for a statistical test for uncertainty regarding the standard deviation due to small numbers (by using ratios instead of absolute numbers) has sometimes been termed 'studentizing'. The significance of this paper was that an experimental scientist, who of necessity usually had only small samples from field or laboratory, had been so exercised about the precision of his estimates that he explored the actual distribution of the standard deviation and calculated a function of data that made accurate allowance for the errors of estimation. This became one of the first statistical tests for quality control in industry.

From 1912 to 1913 the Warminster chessboard experiment was extended to barley plots in Cambridge and in Cork. Beaven had been growing the barley for several years without learning much about its performance because he lacked the methods to analyse the results: he wanted to find the statistical difference between the yields of the various plots in the chessboard. Gosset found a single combined estimate of errors from all possible sets of difference between all eight varieties of barley; he devised a statistical method (known as Student's t-test) to test the significance of the differences of the barley in the various plots. He found the probability distribution of his t-test by using Pearson's Type III curve (taken from the family of theoretical curves that Pearson had constructed for data that did not conform with the normal distribution). Gosset's statistical work influenced that of R. A. Fisher, whom he met for the first time at Rothamsted in September 1922. Fisher extended and further developed Student's t-test when he devised his 'analysis of variance' for his classic design of experiments at Rothamsted.

Gosset was rejected by the armed forces when war broke out in 1914 because he was too short-sighted to serve, but he helped Pearson with the calculations involved in estimating the torsional strain in the blades of aeroplane propellers. He published some twenty-two statistical papers which were reissued by *Biometrika* in 1943 as *Student's Collected Papers* (edited by Egon Pearson and John Wishart). Gosset was a Christian but was otherwise reticent about his religious views. He was a keen fruit grower and specialized in pears. He was also a good carpenter and built a number of boats. He enjoyed walking, cycling, fishing, skating, and skiing, and especially enjoyed the operas of Gilbert and Sullivan. In 1935 he left Dublin to take up his appointment as head brewer at the new Guinness brewery at Park Royal in north-west London. Gosset died after a heart attack, on 16 October 1937, at St Joseph's Nursing Home, Beaconsfield, Buckinghamshire. His wife survived him.

M. EILEEN MAGNELLO

**Sources **

E. S. Pearson, *'Student': a statistical biography of William Sealy Gosset,* ed. R. L. Plackett and G. A. Barnard (1990)

L. McMullen and E. S. Pearson, 'William Sealy Gosset, 1876-1937', *Biometrika,* 30 (1939), 205-50

J. F. Box, *R. A. Fisher: the life of a scientist* (1978)

J. F. Box, 'William Sealy Gosset', *American Statistician,* 35 (1981), 61-6

R. A. Fisher, 'William Sealy Gosset', *Annals of Eugenics,* 9 (1939), 1-9

J. F. Box, 'William Sealy Gosset', *Statistical Science,* 2 (1987), 45-52

[W. S. Gosset], *Student's collected papers,* ed. E. S. Pearson and J. Wishart (1943)

E. S. Pearson, 'Mr W. S. Gosset "Student"', *Nature,* 140 (1937), 838

C. Mollan, W. Davis, and B. Finucane, eds., *More people and places in Irish science and technology* (1990)

b. cert.

m. cert.

d. cert.

*CGPLA Eng. & Wales* (1938)

**Archives **

UCL, Pearson MSS

**Likenesses **

portrait, repro. in McMullen and Pearson, 'William Sealy Gossett'

portrait, repro. in Fisher, 'William Sealy Gossett'

**Wealth at death **

£1553 19s. 11d.: probate, 10 June 1938, *CGPLA Eng. & Wales*

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