Number of Cases

Conceptual Overview and Discussion

Determining the number of cases depends on two major criteria: the research goal—whether to describe a phenomenon, to explain an outcome, or to test or to build a theory—and the features of the cases to be studied. Other considerations include techniques of analysis and epistemological perspectives.

Single-case designs can result from a constructivist epistemological perspective that considers any case as being idiosyncratic. In other perspectives, single-case designs are usually used because the chosen case displays intrinsic features that make it valuable to study. Robert Yin presents three such situations. The first one is uniqueness or rareness that makes the case intrinsically interesting to describe and analyze, such as the Challenger and Columbia space shuttle accidents. The second situation is the revelatory case that provides knowledge about phenomena previously inaccessible to the scientific community, such as William Foote Whyte's landmark research on the social structure of an Italian slum. The third situation is the representative or typical case, such as Robert S. Lynd and Helen M. Lynd's study of “Middletown,” the archetypal American city. Provided the typicality of the case is demonstrated, findings can be extended to all cases that the case studied is representative of or typical for. In addition to the intrinsic value of a case, single-case designs are appropriate to disconfirm a theory or test alternative theories when a case is critical, that is, when it meets the conditions under which formulated propositions should be true.

Multiple-case designs can serve various purposes: exploration, testing, building theories, or explanations. Although each additional case can extend theory and increase the validity of claims, multiple case studies rarely go far beyond a dozen cases. The relative features of cases in terms of similarity and dissimilarity are more important than their intrinsic features because cases are instrumental in serving theoretical purposes. Two major criteria guide the selection of cases and their number: internal validity and generalization of findings. Internal validity is best favored by selecting contrasted cases because they allow for rejecting alternative explanations. Contrasted cases can be selected either on the outcome (e.g., success vs. failure) or on the studied causes (e.g., present vs. absent or high vs. low) since contrast in the studied causes is expected to lead to contrast in the outcome. A contrasted case, similar in any aspect to the first one except for cause X, creates a condition of invariant law that is enough for the internal validity of a causal claim of X on outcome Y. However, contrasted cases available for study are not always similar enough to the first one to reject all relevant alternative explanations. Generalization is obtained through replication of findings. Each case chosen for replication that includes dissimilarity on one dimension allows extending findings to this dimension, provided analyses confirm expected findings. In addition, it makes evidence more compelling and increases internal validity by showing consistency. Although each additional replication, including dissimilarity, increases generalization, a single case differing on several dimensions can be enough because the number of dissimilarities matters more than the number of cases. For instance, one replication in a context that differs according to four dimensions such as organization, governance, industry, and country provides roughly as much external validity as four cases differing on a single dimension. As a result, careful selection of cases allows reducing the number of cases required for desired internal and external validity down to three for a single claim: one contrasted case similar in all relevant features except for cause X, and one [Page 615]replication dissimilar in all relevant features except for X. Following the same rationale, additional claims require additional cases. Consequently, research aiming at building explanations for an outcome usually requires more cases than research aiming at theory building or testing. Finally, a complex relationship also requires more cases. For instance, a claim about a contingency instead of a simple effect requires having contrasts both on the contingency and on the main determinant, which leads to four contrasted cases instead of two for internal validity.

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