ThatsMaths

This week, That’s Maths in The Irish Times ( TM044 ) is about the originator of Students t-distribution.

In October 2012 a plaque was unveiled at St Patrick’s National School, Blackrock, to commemorate William Sealy Gosset, who had lived nearby for 22 years. Sir Ronald Fisher, a giant among statisticians, called Gosset “The Faraday of Statistics”, recognising his ability to grasp general principles and apply them to problems of practical significance.

Gosset’s name may not be familiar, but his work is known to anyone who has taken an introductory course in statistics. Using the pseudonym Student, he published a paper in 1908 that has been of importance ever since.

Gosset was born in Canterbury in 1876 into an old Huguenot family. He studied chemistry and mathematics in Oxford, graduating in 1899, with First Class Honours in both subjects. He then joined Arthur Guinness Son & Company in Dublin as a chemist, and worked at the brewery in St. James’s Gate for 36 years, before becoming head brewer at a new Guinness brewery at Park Royal in London.

 Guinness was interested in agricultural experimentation and hired scientists who could apply their expertise to the business. Gosset was one or these, and he used statistics to solve a range of problems connected with brewing — ranging from barley production to yeast fermentation — that affected the quality of the product. One problem involved the selection of varieties of barley having maximum yields for given soil types and allowing for the vagaries of climate.

To extend his knowledge, Gosset spent a year at the biometric laboratory of the leading statistician Karl Pearson at University College London. Reliable statistics require adequate sample size. Gosset soon realised that Pearson’s large-sample theory required refinement if it was to be useful for the small-sample problems arising in brewing. His fame today rests on a statistical test called Student’s t-test.

But why Student? Gosset’s main paper, The Probable Error of a Mean, was published in 1908. But, to protect trade secrets, Guinness would not allow employees to publish the results of their research. They wished to keep secret from competitors the advantages gained from employing statisticians. Gosset persuaded his bosses that there was nothing in his work that would benefit competitors, and they allowed him to publish, but under an assumed name. Hence, anyone studying statistics encounters the name Student rather than that of the true author of the method.

Gosset’s work has proven fundamental to statistical inference as practiced today. His great discovery was to derive the correct distribution for the sample mean. Student’s t-test arises when we estimate the average value of a randomly varying quantity from a small sample. It plays a crucial role in statistical analysis: for example, it is used to evaluate the effect of medical treatment, when we compare patients taking a new drug with a control group taking a placebo. It was also central to the development of quality control, which is vital in modern industry.

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Sources

Boland, Philip J., 2011: William Sealy Gosset – An Inspiring ‘Student’. Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin. PDF

Prof Adrian Raftery, currently visiting UCD, will present the inaugural Gosset Lecture in the Royal Irish Academy at 6:30pm on 29 May. To reserve a place, visit www.ria.ie.

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