Case study analysis focuses on a small number of cases that are expected to provide insight into a causal relationship across a larger population of cases. This presents the researcher with a formidable problem of case selection. Which cases should be chosen?

In large-sample research, case selection is usually handled by some version of randomization. If a sample consists of a large enough number of independent random draws, the selected cases are likely to be fairly representative of the overall population on any given variable. Furthermore, if cases in the population are distributed homogeneously across the ranges of the key variables, then it is probable that some cases will be included from each important segment of those ranges, thus providing sufficient leverage for causal analysis. (For situations in which cases with theoretically relevant values of the variables are rare, a stratified sample that oversamples some subset of the population may be employed.)

A demonstration of the fact that random sampling is likely to produce a representative sample is shown in Figure 5.1, a histogram of the mean values of 500 random samples, each consisting of 1,000 cases. For each case, one variable has been measured: a continuous variable that falls somewhere between zero and one. In the population, the mean value of this variable is 0.5. How representative are the random samples? One good way of judging this is to compare the means of each of the 500 random samples to the population mean.