3 distribution of the sample mean deviated noticeably from the normal distribution. This finding prompted his quest for a new distribution that would resemble the normal distribution but suitable for small sample observations. Despite achieving a first in the mathematical moderations examination during his time at Oxford, Gosset was clearly not a professional mathematician. The creation of the Student’s t-distribution was closely tied to his extensive correspondence with many of the leading statisticians of his time. Karl Pearson (footnote 1) was one of the key influences on Gosset’s career. Pearson introduced Gosset to nearly all the statistical methods known at the time and invited Gosset to visit his department at University College London from 1906 to 1907. During this period, Gosset worked on his small-sample problem and published the landmark paper “The Probable Error of a Mean” in the journal Biometrika [4], where Pearson served as editor, in 1908. Some curious readers may have noticed that the author of the paper is credited as “Student” rather than William Sealy Gosset. This was due to a policy at the Guinness brewery that prohibited staff from publishing under their own names or using any company data. To comply with this policy, Gosset adopted the pen name “Student,” which is believed to have been inspired by the cover of a notebook he was using at the time – The Student’s Science Notebook [5]. Yet Gosset himself did not coin the term “t-distribution.” In his 1908 paper, he still used the symbol z in his derivation of the sampling distribution of the sample mean for sample sizes ranging from 4 to 10. The symbol t was later introduced by Ronald Fisher (footnote 2), a legendary statistician and close friend of Gosset, in a 1925 paper [6]. In this work, Fisher fully derived the values of the Student’s t-distribution and demonstrated that it is a transformed normal distribution. The shape of the t-distribution changes depending on the sample size n, which is represented Figure 1 Normal distribution (pink) and t-distribution when the degree of freedom is 1 (blue). The t-distribution is flatter at the peak and has “thicker” tails compared to the normal distribution.
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