Definition:Student's t-Test
Definition
Student's $t$-test is a test to see whether a sample of $n$ observations with mean $\overline x$ comes from a normal distribution with mean $\mu_0$.
Under the null hypothesis, the statistic:
- $t = \dfrac {\overline x - \mu_0} {s / \sqrt n}$
where:
- $s^2 = \dfrac 1 {n - 1} \ds \sum_i \paren {x_i - \overline x}$
has the Student's $t$-distribution with $n - 1$ degrees of freedom.
Also known as
Student's $t$-test is also known just as the $t$-test.
However, there are other tests with similar names, for example Hotelling's $T$-test, so $\mathsf{Pr} \infty \mathsf{fWiki}$ prefers to retain the distinction.
Also see
- Results about Student's $t$-test can be found here.
Source of Name
This entry was named for William Sealy Gosset.
Historical Note
Student's $t$-test was devised by William Sealy Gosset in $1908$.
Note on Gosset's Pen Name
William Sealy Gosset's employer, Guinness, had previously had trade secrets disclosed within academic papers. Because of this, they disallowed entirely their employees from publishing academic papers, irrespective of their content.
However, after much convincing that his results regarding the $t$-distribution and $t$-test were of high mathematical importance, and that they were of no direct commercial use to rival breweries, he was allowed to publish.
To avoid the attention of other employees, Guinness allowed Gosset to publish under his pen name Student.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Student's $t$-test
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): $t$-test (W.S. Gosset, 1908)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Student's $t$-test
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): $t$-test (W.S. Gosset, 1908)