If you are a bit tired of all the calculations that are usually involved with statistics, learning about the **Student’s T distribution** will be right up your alley. We will begin our journey of understanding it by telling a story about its origin.

**The Story about William Gosset**

William Gosset was an English statistician who worked for the Guinness Brewery.

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. Therefore, he was trying to develop a way to extract small samples but still come up with meaningful predictions.

**The Origin of the Student’s T Distribution**

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**.

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

**The Student’s T Distribution**

The **Student’s T distribution** is one of the biggest breakthroughs in statistics, as 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.

Visually, the **Student’s T distribution** looks much like a **Normal distribution **but generally has fatter tails. Fatter tails, as you may know, allow for a higher dispersion of variables, as there is more uncertainty.

**The z-statistic**

In the same way that the **z-statistic** is related to the **standard Normal distribution**, the **t-statistic** is related to the **Student’s T distribution**. The formula that allows us to calculate it is: t with *n-1* **degrees of freedom** and a **significance level** of *alpha* equals the **sample mean** minus the **population mean**, divided by the **standard error** of the sample.

As you may realize, it is very similar to the **z-statistic**. After all, this is an approximation of the **Normal distribution**.

**Degrees of Freedom**

The last characteristic of the **Student’s T-statistic** is that there are **degrees of freedom**. Usually, for a sample of *n*, we have *n-1* degrees of freedom. So, for a sample of 20 observations, the **degrees of freedom** are 19.

Much like the standard **Normal distribution** table, we also have a **Student’s T** table. You can see it in the picture below. The rows indicate different **degrees of freedom**, abbreviated as *d.f*., while the columns – common alphas.

Please note that after the 30^{th} row, the numbers don’t vary that much. Actually, after 30 degrees of freedom, the **t-statistic** table becomes almost the same as the **z-statistic**.

As the **degrees of freedom** depend on the sample, in essence, the bigger the sample, the closer we get to the actual numbers. A common rule of thumb is that for a sample containing more than 50 observations, we use the z-table instead of the t-table.

**New Concept**

Now, you know how the **Student’s T distribution** works. Combined with all the knowledge from our other tutorials on statistics, you are ready to take on a greater challenge. We are talking about one of the fundamental tasks in statistics – **hypothesis** testing.

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**Next Tutorial: **Hypothesis Testing: Null Hypothesis and Alternative Hypothesis