What is statistics about?

Well, imagine you obtained some data from a particular collection of *things*. It could be the heights of individuals within a group of people, the weights of cats in a clowder, the number of petals in a bouquet of flowers, and so on.

Such collections are called samples and you can use the obtained data in two ways. The most straightforward thing you can do is give a detailed description of the sample. For example, you can calculate some of its useful properties:

- The average of the sample
- The spread of the sample (how much individual data points differ from each other), also known as its
*variance* - The number or percentage of individuals who score above or below some constant (for example, the number of people whose height is above 180 cm)
- Etc.

You only use these quantities to summarize the sample. And the discipline that deals with such calculations is **descriptive statistics**.

But what if you wanted to learn something more general than just the properties of the sample? What if you wanted to find a pattern that doesn’t just hold for this particular sample, but also for the population from which you took the sample? The branch of statistics that deals with such generalizations is **inferential statistics** and is the main focus of this post.

The two general “philosophies” in inferential statistics are **frequentist inference** and **Bayesian inference**. I’m going to highlight the main differences between them — in the types of questions they formulate, as well as in the way they go about answering them.

But first, let’s start with a brief introduction to inferential statistics.