Understanding the T-Distribution: Estimation based on small sample to quantify the uncertainty 👀

A version of Normal distribution with Heavier tails where population variance is unknown.

When you step into the world of statistics, you’ll encounter various distributions, each with its own unique characteristics and applications.

One such distribution is the T-distribution, which plays a crucial role in statistical inference, particularly when dealing with small sample sizes.

Why T - Distribution is named so ?

An interesting fact about the t-distribution is that it is sometimes referred to as the “Student’s t-distribution.”

This is because William Gosset who discovered T-Distribution was an English statistician who worked for the brewery of Guinness in 1908.

He developed different methods for the selection of the best yielding varieties of barley — an important ingredient when making beer. Gosset found big samples tedious, so he was trying to develop a way to extract small samples but still come up with meaningful predictions.

He was a curious and productive researcher and published a number of papers that are still relevant today. However, due to the Guinness company policy, he was not allowed to sign the papers with his own name. Therefore, all of his work was under the pen name: Student.

This is because the inventor of the distribution, William Sealy Gosset, an English statistician, published it using his pseudonym “Student” to keep his identity anonymous, thus leading to the name “Student’s t-distribution.”

Later on, a friend of his and a famous statistician, Ronald Fisher, stepping on the findings of Gosset, introduced the t-statistic, and the name that stuck with the corresponding distribution even today is Student’s t.

The Student’s t distribution is one of the biggest breakthroughs in statistics. It allowed inference through small samples with an unknown population variance. This setting can be applied to a big part of the statistical problems we face today and is an important part of this course.

The “T” symbolized the test statistic associated with the distribution, and the…