The History Column: William Sealy Gosset – ‘Student’

William Sealey Gosset was a statistician, born in 1876 in Canterbury, England. He studied Natural Sciences and Mathematics at New College, Oxford University, then joined the brewery of Arthur Guinness in Dublin, Ireland in 1899, where he held the position of Head Brewer. He spent the rest of his 38-year career at Guinness.

William Sealy Gosset (1876–1937). Public domain.

In his role at the brewery he was responsible for assessing the quality of the raw ingredients of the beer, and of the beer itself, and he turned his mathematical talent to the problem of how to do this with a small number of samples. He developed the fundamental theory behind this problem, and sought to publish the results, in a paper titled ‘The probable error of a mean’. This may easily be downloaded, and it will be seen that it is beautifully and clearly written.

However, the brewery did not want to reveal their identity (and hence the fact that they were using such methods), nor that of the author, so they insisted that he publish under a pseudonym. He chose the name ‘student’, and the statistical distribution derived in the paper, (essentially a generalization of the normal distribution) and the associated test that he derived, are known as the student-t distribution and the student-t test.

Joan Fisher Box describes Gossett as ‘an extraordinarily appealing individual, generous to a fault, humble, enthusiastic in the pursuit of his varied interests, and helpful.’

Gosset met and corresponded with two of the foremost academic statisticians of the early twentieth century: Ronald Fisher of Cambridge University, and Karl Pearson of University College London, and Gossett spent a sabbatical year working in Pearson’s department at University College London. Both Fisher and Pearson worked on the application of advanced statistical techniques to agriculture, and Fisher took up a position at the Rothamsted Research Institute, which exists to this day and undertakes important research in this field. He is now known for the concepts of Maximum Likelihood Estimation, and of Fisher Information, which forms the basis of the Cramér-Rao Lower Bound (CRLB) in statistical estimation. Apparently, Fisher and Pearson were not especially friendly with each other, but Gosset corresponded freely with both. Fisher and Pearson both now attract some criticism for their work and opinions on eugenics.

Ronald Fisher (1890–1962) in 1913. Public domain.

The significance of this is that it shows the origins of some of the statistical methods in (for example) radar clutter distributions and radar detection theory that we now take for granted. It is interesting that, even now, Gosset’s true identity as the source of some of these ideas is not fully appreciated.

Further information may be found in:

• Student, ‘The probable error of a mean’. Biometrika. 6 (1): 1–25. March 1908  https://www.york.ac.uk/depts/maths/histstat/student.pdf
• Joan Fisher Box, ‘Gosset, Fisher, and the t Distribution’, The American Statistician, Vol. 35, No. 2 (May, 1981), pp. 61-66. https://doi.org/10.2307/2683142
• Zabell, S., ‘On Student's 1908 Article "The Probable Error of a Mean”’, Journal of the American Statistical Association, March 2008, https://www.jstor.org/stable/27640017
• Joan Fisher Box was the daughter of Ronald Fisher and the second wife (of three) of George Box – another famous statistician – she is the author of R.A. Fisher, The Life of a Scientist (Wiley, 1978).

Authored by Hugh Griffiths, University College London