= History of Student's t-distribution
<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. <William Sealy Gosset by John Joseph O'Connor and Edmund Frederick Robertson>[Biography, opening paragraphs and discussion of the name Student]{ref} <Gosset, William Sealy (‘Student’) by Philip J. Boland>[Philip J. Boland, Gosset, William Sealy ('Student'), opening paragraphs and pseudonym discussion; published and last revised October 2009]{ref}
The 1908 paper https://en.wikisource.org/wiki/The_Probable_Error_of_a_Mean[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>. <The Probable Error of a Mean by William Sealy Gosset>[1908 original text: byline, Introduction, Section I definition of sample spread, and Sections II–III]{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. <The Probable Error of a Mean by William Sealy Gosset>[Section VI, Practical Test of the foregoing Equations: cards, groups of four and limitations from nonnormality and coarse grouping]{ref}
Back to article page
