Statistics is about using data to learn about unknown things.

This is rather different from probability theory. In probability, we usually begin with a known random variable or probability distribution, and investigate what we expect to happen.

In statistics, we instead begin with realised data, and try to work backwards to learn about the unknown distribution that produced them.

For example, we may not know the average income of a population, but we can collect a sample of incomes and use these data to estimate it. Probability theory then helps us work out whether our method is likely to give a good answer.

This basic process underlies much of statistics: we develop methods for estimating unknown quantities, and then use probability to investigate how well those methods work.

We can also use data to assess claims about a population. This brings us to the major subject of hypothesis testing, which is central in econometrics.

In this subject, we build these ideas up from the basics, before looking at properties of estimation methods, the central limit theorem, maximum likelihood estimation, confidence intervals, and hypothesis testing.

Material is also provided on some topics which for econometricians are rather niche, including the Bayesian approach and simulation methods.