OVERVIEW

Researchers aspire to draw conclusions about the entire population of cases that are relevant to a particular research question. However, in most cases, they must rely on data from only a sample of those cases to do so. In this chapter, we lay the foundation for how researchers make inferences about a population of cases while only observing a sample of data. This foundation rests on probability theory, which we introduce here with extensive references to examples. We conclude the chapter with an example familiar to political science students – namely, the “plus-or-minus” error figures in presidential approval polls, showing where such figures come from and how they illustrate the principles of building bridges from samples we know about with certainty to the underlying population of interest.

POPULATIONS AND SAMPLES

In Chapter 5, we learned how to measure our key concepts of interest, and how to use descriptive statistics to summarize large amounts of information about a single variable. In particular, you discovered how to characterize a distribution by computing measures of central tendency (like the mean or median) and measures of dispersion (like the standard deviation or IQR). For example, you can implement these formulae to characterize the distribution of income in the United States, or, for that matter, the scores of a midterm examination your professor may have just handed back.