Statistical Modeling and Inference for Social Science

In hypothesis testing, we make conjectures about the data-generating process (DGP) and assess the weight of evidence that the sample offers in support of them. The conjectures about the DGP that are subject to testing should have some theoretically interesting foundation, but they are made before any evaluation or analysis of the observed sample data. Hypothesis testing does not address where the conjectures come from; they are taken as given, supplied by theory, and are tested against data.

Statistical estimation, by contrast, does not take as given conjectures to be evaluated. Instead it uses the observed data to make conjectures about the unobserved DGP that are in some sense good or reasonable. There are two general types of estimation, interval estimation and point estimation. These types of estimation are treated in this chapter.

Interval estimates specify a range of values that are all “reasonable” guesses about an unknown parameter of a DGP. Typically the interval estimate contains the parameter of a DGP in a user-specified probability of random samples. Interval estimates are useful because they combine a sense of the “best guess” of a parameter's value and some uncertainty about that best guess into one statement. Another name for an interval estimate in classical statistics is a confidence interval. Although a hypothesis test asks whether a particular conjecture about the DGP is reasonable in light of the data, a confidence interval can be thought of as a range of reasonable conjectures about the DGP.