Statistical Modeling and Inference for Social Science

Chapter 2 dealt with the summary and analysis of data that is actually observed. It is possible that a researcher or analyst has no interest in the variables or concepts being analyzed beyond the particular set of observations available to him or her. If a university wants to know whether its admissions decisions last year were less favorable to members of underrepresented groups than to others, taking as given other aspects of each application file (grade point average, entrance exam scores, etc.), it need only analyze last year's admissions data. A linear regression, purely descriptive of this data, would shed light on the question.

However, the remainder of this book covers elements of probability theory and statistical inference and modeling, which itself rests heavily on probability theory. Before launching into that treatment, it is necessary to consider why (or conditions under which) we need it.

When a theory relating two or more variables is part of the consideration, it is unusual that a researcher's interest in the variables ends with the data that happens to have been observed. Such a theory deals with the process or behaviors that give rise to the data that was observed, not just that data itself. That data helps to inform whether the theory has any drawing power in reality, but that data is not the sum total of possible observations of the social process in question.