Statistics Basics

We begin our study of statistics by looking at using data to learn about unknown features of a population.

First, we clarify the difference between probability and statistics, before carefully reviewing how data are obtained by sampling from a population. This leads to the important idea of a random sample.

We then introduce one of the central concepts in statistics: an estimator. Once the data have been observed, an estimator produces a particular numerical estimate. But before we collect our data, an estimator is itself a random variable; as such, it can be investigated using the probability theory built up earlier. This is the key bridge between the two subjects!

We develop these ideas through some simple examples, including estimating a population mean and variance, and introduce the method of moments as a general approach to estimation.

Finally, we carefully distinguish between estimands, estimators, and estimates. These words sound highly similar, but keeping them separate will make much of the statistics and econometrics that follows considerably easier to understand!