Moving from a mass of data to an informative description of patterns within that data is a basic point of quantitative techniques social science, an area of quantitative analysis called descriptive statistics. It is not the fanciest math, nor does it comprise the most subtle concepts, but it requires serious attention in any quantitative work. Descriptive statistics is an important part of constructing an argument using data and includes making apparent the tendencies, patterns, and relationships in that data. Equally important is that descriptive statistics helps a researcher get a feel for the behavior of the variables in a dataset and for conjectures about relationships that are worth further analysis, both statistically and theoretically.

Before meaningful analysis can proceed, it is necessary to understand how we observe and measure the concepts of interest in any research. Thus this chapter begins with a brief overview of empirical measurement of variables. It then discusses common graphical and statistical summaries and descriptions of aggregate data, first for one variable at a time (univariate distributions) and then for relationships (bivariate or multivariate distributions). It also covers some important theoretical properties of these descriptive tools.

Some basic concepts are important. To fix ideas, imagine a dataset with a set of observations of one or more characteristics of some collection of units. For instance, on the “democratic peace” (see Chapter 1), the units might be pairs of nation-states.