The Student’s *t*-distribution is named in honor of William Sealy Gosset (1876-1937), who first
determined it in 1908. Gosset was one of the best Oxford graduates in
chemistry and mathematics in his generation. In 1899, he took up a job
as a brewer at Arthur Guinness Son & Co, Ltd in Dublin,
Ireland. Working for the Guinness brewery, he was interested in quality
control based on small samples in various stages of the production
process. Since Guinness prohibited its employees from publishing any
papers to prevent disclosure of confidential information, Gosset
published his work under the pseudonym “Student”. His identity was not
known for some time after the publication of his most famous
achievements, so the distribution was named Student’s or
*t*-distribution, leaving his name less well known than his
important contributions to statistics (Lovric, 2010).

The *t*-distribution curve is, like the normal distribution
curve, symmetric (bell shaped) about the mean. However, the
*t*-distribution curve is flatter than the standard normal
distribution curve. Consequently, the *t*-distribution curve has
a lower height and a wider spread than the standard normal
distribution.

The *t*-distribution only has one parameter, called the **degrees of freedom** \((df)\). The shape of a particular
*t*-distribution curve depends on the number of degrees of
freedom \((df)\). The number of degrees
of freedom for a *t*-distribution is equal to the sample size
minus one, that is:

\[df = n - 1\]

As the sample size, \(n\), and thus
\(df\) increases, the
*t*-distribution approaches the standard normal distribution. The
units of a *t*-distribution are denoted by *t*. The mean
of the *t*-distribution is equal to \(0\) and its standard deviation is \(\sqrt{df/(df-2)}\) (Mann, 2012).

- The total area under a
*t*-curve equals 1. - A
*t*-curve extends indefinitely in both directions, approaching, but never touching, the horizontal axis as it does so. - A
*t*-curve is symmetric about 0. - As the number of degrees of freedom becomes larger,
*t*-curves look increasingly like the standard normal curve.

**Citation**

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: *Hartmann,
K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis
using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.*