Statistical Modeling and Inference for Social Science

Positive theories in social science assert relationships among concepts. An example is that the number of police officers on the beat leads to a drop in crime or that monolingual education in linguistically diverse schools leads to stronger attachments of group members to their own ethnic identity. Postulating a statistical model – (some aspects of) a data-generating process (DGP) for the data and (some aspects of) a link from its parameters to covariates – is how we translate theories into statements about stochastic DGPs. Often, as we have seen (Chapter 6), these translations relate to the conditional mean of Y given some explanatory factors. For instance, a (very simple) theory might assert that the mean of the DGP (generating crime levels conditional on beat cops) is higher when there are “few” beat cops than when there are “many.” This can also be stated in terms of the slope coefficients in a regression model; for example, in a linear model for the conditional mean of turnout levels given voters’ information, saying the former is positively related to the latter is the same as saying the slope term on information levels is positive.

Sampling distributions of the sort covered in Chapter 7 provide a basis for evaluating theoretical claims about the DGP based on evidence from a collection of draws from that DGP (i.e., a sample). This is the subject of hypothesis testing, which provides a set of statistical techniques for evaluating the strength of sample evidence supporting specific conjectures about the DGP.