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study, if a correlation is the result not of the hypotheses under consideration but of learning or diffusion from one case to the others, then the additional cases do not provide substantially new information and there are fewer degrees of freedom than the researcher thought (this is sometimes referred to as “Galton’s Problem”).72 In case studies, as in large-N research, there is a danger that the researcher will fail to identify a lack of independence between cases and will consequently reach false conclusions. This danger does not manifest itself as a “degrees of freedom” problem, however, and it is not necessarily amplified by the intentional selection of cases based on a preliminary knowledge of their variables (indeed, intentional selection can address the issue of the lack of independence of cases).

The question of whether the independence of cases is a relevant consideration depends on the research objectives of a particular study, what theory or hypothesis is being developed or tested, and how the comparison of cases is structured.73 Process-tracing can inductively uncover linkages between cases and may thereby reduce the danger of any unanticipated lack of independence of cases. When learning or diffusion processes are anticipated or uncovered and taken into account, they need not undercut the value of studying partially dependent cases. Indeed, only perfectly dependent cases are capable of providing additional information. 74 Moreover, process-tracing can be particularly effective at examining the kinds of detailed sequences in learning and diffusion processes that can create relationships between cases, allowing researchers to gauge more accurately how much of the variance in outcomes is explained by learning or diffusion and how much is explained by other variables.75

A lack of independence of cases is useful in research that aims to test whether the lessons of an earlier case played a causal role in a later one. Hugh Heclo made use of this in studying the process of “political learning.” Stephen Stedman’s study of four sequential efforts at international mediation in Rhodesia’s civil war also used the lack of case independence to identify possible learning from earlier cases. And, more generally, Jack Levy has suggested that intensive case studies that make use of process-tracing may be better suited than large-N quantitative studies for exploring the possibility of learning.76

Opportunities for Multi-Method Collaborative Research

The increasingly evident complementarity of case studies, statistical methods, and formal models is likely to lead toward more collaborative work by scholars using these various methods. The recent interest among rational choice theorists in using historical case studies to test their theories, for example, is an important step in this direction.77 More generally, there are a variety of ways in which the three methods can be used together, either in a single study or sequentially.78 Statistical analysis can help identify outliers or deviant cases, and case studies can then investigate why these cases are deviant, perhaps leading to the identification of omitted variables. Case studies can also explore the possible causal mechanisms behind the correlations or patterns observed in statistical studies, providing a check on whether correlations are spurious or potentially causal and adding details on how hypothesized causal mechanisms operate. Alternatively, when case studies lead to the specification of new variables or the refinement of concepts, statistical studies can explore whether these new variables and concepts are relevant to larger populations of cases. Formal models can be tested in case studies to see if their hypothesized causal mechanisms were in fact in operation, and the variables and concepts developed through case studies can be formalized in models.

Because case studies, statistical methods, and formal modeling are all increasingly sophisticated, however, it is becoming less likely that a single researcher can be adept at more than one set of methods while