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to such populations except in contingent ways.64 Statistical methods require a large sample of cases that is representative of and allows inferences about a larger population of cases from which the sample is drawn. Statistical researchers thus devote much effort to trying to make the sample as representative as possible. While useful and necessary in statistical studies, these practices are inappropriate and sometimes counterproductive when extended to case study methods or used to judge these methods, as some methodologists have urged.65

Case study methods involve a trade-off among the goals of attaining theoretical parsimony, establishing explanatory richness, and keeping the number the cases to be studied manageable. Parsimonious theories rarely offer rich explanations of particular cases, and such theories must be stated in highly general terms to be applicable across different types of cases.66 Greater explanatory richness within a type of case usually leads to less explanatory power across other types of cases. In order to explain in rich detail different types of cases, it is usually necessary to give up theoretical parsimony and to study many cases. Case studies may uncover or refine a theory about a particular causal mechanism—such as collective action dynamics—that is applicable to vast populations of cases, but usually the effects of such mechanisms differ from one case or context to another.

In view of these trade-offs, case study researchers generally sacrifice the parsimony and broad applicability of their theories to develop cumulatively contingent generalizations that apply to well-defined types or subtypes of cases with a high degree of explanatory richness.67 Case study researchers are more interested in finding the conditions under which specified outcomes occur, and the mechanisms through which they occur, rather than uncovering the frequency with which those conditions and their outcomes arise. Researchers often select cases with the

In any of these research designs, the cases are necessarily unrepresentative of wider populations. Of course, in such research designs researchers must be careful to point out that they seek only contingent generalizations that apply to the subclass of cases that are similar to those under study, or that they seek to uncover causal mechanisms that may be in operation in a less extreme form in cases that have less extreme values on the pertinent variables. To the extent that there is a representativeness problem or a selection bias problem in a particular case study, it is often better described as the problem of “overgeneralizing” findings to types or subclasses of cases unlike those actually studied.68

SINGLE-CASE RESEARCH DESIGNS

Several of the above critiques of case study methods have converged into skepticism of the value of single-case studies. For example, DSI discourages research designs in which there is no variance on the dependent variable, and it also criticizes “single-observation” research designs.69 As DSI argues, studies involving only a single observation are at great risk of indeterminacy in the face of more than one possible explanation, and they can lead to incorrect inferences if there is measurement error. This same text notes that a single case study can involve many observations, however, and in our view this greatly reduces these two problems.70 Thus, in our view, several kinds of no-variance research designs can be quite useful in theory development and testing using multiple observations from a single case. These include the deviant, crucial, most-likely, and least-likely research designs, as well as single-case study tests of claims of necessity and sufficiency. Several influential works in comparative politics have used such single-case research designs to good effect.71

POTENTIAL LACK OF INDEPENDENCE OF CASES

One research design issue concerns whether cases are “independent” of one another. Here again, the statistical version of this problem does not apply to case studies, but a more fundamental concern does. In a statistical