Introduction

The goal of statistical inference is to use sample data to estimate a parameter (a statistic about the population) or determine whether to believe a claim that has been made about the population. We never actually observe the parameter we are interested in; instead we use an estimate of the parameter based on data from a sample. The sample estimate is almost always different from the claimed value of the parameter. There are then two possibilities: the difference (between the estimate and the claim) may be real or it may be due to chance. Thus, the fundamental question of statistical inference becomes, Is the difference real or due to chance?

To answer the fundamental question, we require a model for the data generation process, or DGP. The DGP describes how each observation in the data set was produced. It usually contains a description of the chance process at work. Given a DGP and certain parameter values, we can calculate the probability of observing particular ranges of outcomes.

In this chapter, we try to clarify these complicated issues by reviewing basic concepts of inference from introductory statistics. Our approach is somewhat unusual in that we downplay the mathematical formalism and instead emphasize the logic of statistical inference.