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By Philip J. Boland, contributor to the Dictionary of Irish Biography, a Royal Irish Academy project. William Sealy Gosset is the biographical subject. Originally published October 2009; last revised October 2009.

Online biography: www.dib.ie/biography/gosset-william-sealy-student-a3543

DOI: doi.org/10.3318/dib.003543.v1

Inspected locators: opening profession and employment paragraphs; pseudonym discussion; final biographical paragraph; Publishing information.

William Sealy Gosset worked at Guinness as a chemist and brewer and developed methods of statistical inference for small samples. He published under the pseudonym "Student". His employment as a chemist is independently recorded by MacTutor; the Dictionary of Irish Biography identifies him as an applied statistician and brewer and explains the pseudonym policy. ^{[ref] [ref]}

The 1908 paper The Probable Error of a Mean appeared in Biometrika 6(1), pages 1–25, with the byline "Student". Its introduction identifies the uncertainty introduced by estimating a standard deviation from few observations and explicitly assumes a normal distribution. Sections II and III develop the relation between sample spread and the standardized sample mean. Its notation uses a sample spread with divisor $n$ and calls the ratio $z$; with that convention, the modern $T$ equals $\sqrt{n-1}z$. The modern exact independence argument is given under studentized normal sample mean. ^[ref]

Section VI describes a physical sampling check: 3,000 cards carrying existing paired measurements were shuffled, then divided into 750 groups of four. He compared observed frequencies of sample spread and standardized sample mean with theoretical frequencies. This was a check using finite, grouped, approximately normal distribution data; it did not prove exact calibration for arbitrary populations. ^[ref]

Philip J. Boland works on statistical and probabilistic aspects of reliability and the history of statistics. UCD's 2005–06 institutional record lists research interests in reliability theory, life testing, actuarial probability and mathematical statistics. These are historical affiliations and interests in that record, rather than a claim about his present appointment.^[ref]

reliability theory connects distributions of component lifetimes to the behavior of a whole system. Statistical inference then estimates those lifetime distributions or compares designs from observed failures and surviving units. Boland also wrote the Dictionary of Irish Biography entry on William Sealy Gosset, connecting the mathematical development of small-sample inference with its industrial setting.^[ref]

Institutional biographical record: www.ucd.ie/students/t4media/2005-6%20science_pg.pdf

By William Sealy Gosset, published under the pseudonym Student. Biometrika 6(1), 1–25, March 1908. Wikisource hosts the inspected transcription of the original paper; its editing dates are not journal publication dates.

Inspected text: en.wikisource.org/wiki/The_Probable_Error_of_a_Mean

DOI: doi.org/10.1093/biomet/6.1.1

Inspected locators: original title and Student byline; Introduction; Sections II, III and VI. Historical notation differs from the modern convention.

William Sealy Gosset published statistical research under the name Student while working as a brewer for Guinness. His practical problems involved variation in ingredients and brewing conditions, where obtaining a large sample was often difficult. This motivated methods that account for uncertainty in estimating variability from a small sample.^[ref]

The Student's t-distribution describes the standardized mean of an independent normal sample when its unknown standard deviation is replaced by the sample standard deviation. Its heavier tails, compared with a Standard normal distribution, reflect that extra uncertainty. Gosset's work helped turn the limitations of a small experiment into an explicit part of inference rather than treating a variance estimate as known.

Biography: www.dib.ie/biography/gosset-william-sealy-student-a3543

By John Joseph O'Connor and Edmund Frederick Robertson, credited as J J O’Connor and E F Robertson, in the University of St Andrews MacTutor History of Mathematics archive. Last Update: October 2003; this is an online revision date. William Sealy Gosset is the subject, not the author.

Online biography: mathshistory.st-andrews.ac.uk/Biographies/Gosset/

Inspected locators: Quick Info; opening employment paragraph; discussion of the Student pseudonym; Written by and Last Update footer.