Case Study: Logic

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Case Study: Methods and Analysis reviewing the development of case study and comparative methods, argued that these methods have advantages in defining and measuring qualitative variables in conceptually valid ways and forestalling the problem of conceptual stretching (Collier 1993). Charles Ragin argued that qualitative methods were also better than statistical methods at accounting for equifinality and complex interaction effects. Although statistical methods can model several kinds of interaction effects, Ragin noted, they can do so only at the cost of requiring a larger sample size, and models of nonlinear interactions rapidly become complex and difficulttointerpret.Raginalsointroducedthe method of Qualitative Comparative Analysis, which uses Boolean algebra to reduce a series of comparisons of cases to the minimum number of logical statements or hypotheses that entail the results of all the cases compared (Ragin 1987). This method, he argues, makes comparisons among cases in ways that treat them inherently as configurations of variables, and that thus allow for the possibility of equifinality and complex interactions (see Configurational Analysis). Both Collier and Ragin also noted the limitations of case study methods, including the potential for indeterminacy when attempting to sort out rival explanations in a small number of cases, the difficulty of attaining a detailed understanding of more than a few cases, and the inability to make broad generalizations on the basis of small numbers of cases. 3. New Deelopments in Case Study Methods The thousands of applications of case study methods in the last two decades have provided fertile ground for further methodological refinements. Three key recent developments include the strengthening of linkages between case study methods and the philosophy of science, the elaboration of the concept of typological theories, and the emergence of elements of consensus on the comparative advantages and limitations of case study methods. 3.1 Case Studies and the Philosophy of Science With regard to the philosophy of science, the ‘scientific realist’ school of thought has emphasized that causal mechanisms, or independent stable factors that under certain conditions link causes to effects, are important to causal explanation (Little 1998). This has resonated with case study researchers’ use of process tracing to uncover evidence of causal mechanisms at work. It has also provided a philosophical counterpoint to attempts by researchers from the statistical tradition to place ‘causal effects,’ or the expected difference in outcomes brought about by the change in a single independent variable, at the center of causal explanation (King et al. 1994). Case study researchers have argued that both causal mechanisms, which are more easily addressed by case studies, and causal effects, which are best assessed through statistical means, are essential to the development of causal theories and causal explanations (George and Bennett 2001). Another relevant development in the philosophy of science has been the resurgence of interest in Bayesian logic, or the logic of using new data to update prior confidence levels assigned to hypotheses. Bayesian logic differs from that of most statistics, which eschew reliance on prior probabilities. Eckstein’s crucial, most likely, and least likely case study designs implicitly use a Bayesian logic, assigning prior probabilities to the likelihood of particular outcomes (McKeown 1999). One new development here is the refinement of Eckstein’s approach, taking into consideration the likelihood of an outcome not just in view of one theory, but in the presence of alternative hypotheses. If a case is ‘most likely’ for a theory, and if the alternative hypotheses make the same prediction, then the theory will be strongly impugned if the prediction does not prove true. The failure of the theory cannot be blamed on the influence of the variables highlighted by the alternative hypotheses. Conversely, if a theory makes only a weak prediction in a ‘least likely’ case, the alternative hypotheses make a different prediction, but if the first theory’s prediction proves true, this is the strongest possible evidence in favor of the theory (Van Evera 1997). This helps address the central problemofaBayesianapproach—thatofassigningand justifying prior probabilities—even if it does not fully resolve it. The continuing development of the logic of hypothesis testing has also been relevant to case study methods (see Hypothesis Testing: Methodology and Limitations). On this topic, Imre Lakatos argued that a theory can be considered progressive only if it predicts and later corroborates ‘new facts,’ or novel empirical content not anticipated by other theories (Lakatos 1976). This criterion helps provide a standard for judging whether process tracing, the designation of new subtypes, and the proposal of new theories from heuristic case studies are being done in a progressive or regressive way. It also provides a philosophical basis for arguing that a hypothesis can be derived from one set of observations within a case and then to some extent tested against the ‘new facts’ or previously unexamined or unexpected data that it predicts within that same case, although independent corroboration in other cases is usually advisable as well (Collier 1993). 3.2 Typological Theories and ‘Fuzzy Logic’ A second recent development in case study methods has been the elaboration of the concept of typological theory. Typological theories occupy a middle ground between covering laws, or highly general abstract propositions, and causal mechanisms. Typological 1516
Case Study: Methods and Analysis theories identify recurring conjunctions of mechanisms and provide hypotheses on the pathways through which they produce effects. Thus, like QCA, typological theories treat cases as configurations. Unlike QCA, they do not attempt to reduce the number of theoretical statements about the variables, but retain a diverse and admittedly complex set of contingent generalizations, with potentially one generalization per type. Consequently, typological theories are well suited to modeling equifinality. To construct typological theories, researchers first specify the variables and use them to define the typological space, or the set of all mathematically possible combinations of the variables (this is sometimestermedatruthtableinthephilosophyofscience). At first this may seem to produce an unmanageably large number of combinations: a model with five dichotomous variables, for example, would have 32 possible types. However, once the researcher begins to categorize extant cases in a preliminary way into particular types, it often becomes possible to narrow the range of cases of interest for study. Many types may remain empty, with no extant cases. Some types may be overdetermined for the outcome of interest, and hence not worthy of study unless they have an unexpected outcome. From among the cases and types that remain, the researcher can use the preliminary categorization of cases within the typological space to help identify most likely, least likely, most similar, least similar, and crucial cases for study. Cases in the typological space with unexpected outcomes, or deviant cases, can help identify new causal pathways that can be added to the existing theory in a kind of ‘building block’ approach (George and Bennett 2001). A related development concerns the concept of ‘fuzzy logic’ (Ragin 2000). Fuzzy logic treats cases as configurations but rather than using dichotomous or trichotomous variables and categorizations of cases, it allows the use of scaling to give a score on the extent to which a case fits into a certain type. In other respects, the use of fuzzy logic proceeds in ways much like those of typological theories. 3.3 The Emerging Consensus on the Strengths and Limits of Case Study Methods A third development is that while several debates on case study methods continue, others have moved toward synthesis or even closure, and the overall picture is of an emerging consensus on the advantages limitations of case study methods. As noted above, researchers from a variety of methodological traditions have recognized that because case studies can include many observations, they do not suffer from an inherent degrees of freedom problem. At the same time, it is also widely agreed that particular case studies may suffer from indeterminacy, or an inability to exclude all but one explanation on the basis of available process tracing evidence (Njolstad 1990). When this occurs, it may still be possible to narrow the number of plausible explanations, and it is also important to indicate as clearly as possible the extent to which the remaining hypotheses appear to be complementary, competing, and incommensurate in explaining the case. Second, most case study researchers have readily acknowledged the limits of Mill’s methods. Ragin’s alternative of qualitative comparative analysis makes less restrictive assumptions, but its results are highly sensitive to changes in the measurement or coding of a single case (Goldthorpe 1997). There has thus been a movementtowardtypologicaltheoriesandfuzzylogic, which make still less restrictive assumptions than QCA and are not so sensitive to the results of a single case. In addition, there is growing consensus that the use of within-case methods of analysis helps provide a check on the potential spuriousness of cross-case comparisons (Collier 1993, Mahoney 1999, George and Bennett 2001). Case study researchers consequently seldom if ever rely on case comparisons alone. Third, there is growing recognition that the case selection criteria necessary for statistical studies are in some respects inappropriate for case studies. Random selection in a case study research design, for example, can result in worse biases than intentional selection (King et al. 1994). There is also increasing understanding that, consistent with the reliance of some case study designs on a Bayesian logic, case studies are sometimes intentionally selected not to be representative of some wide population but to provide the strongest possible inferences on particular theories (McKeown 1999). There is still disagreement between those who warn against any selection on the dependent variable (King et al. 1994) and those who argue that selection on the dependent variable is appropriate for some research objectives (Collier and Mahoney 1996, Ragin 2000, George and Bennett 2001). Related to this is a continuing disagreement over whether single case studies can make only limited contributions to theory building (King et al. 1994), or whether single case studies have indeed reshaped entire research programs (Rogowski 1995). There is wider agreement, however, that selection bias is potentially more severe in case studies than statistical studies because biased selection of case studies can overstate as well as understate the relationship between the independent and dependent variables (Collier and Mahoney 1996). On the whole discussions of these issues have moved toward an emerging consensus on the comparative advantages and limitations of case study methods. These methods’ advantages include the conceptualization, operationalization, and measurement of qualitative variables (conceptual validity), the avoidance of conceptual stretching, the heuristic identification of new variables and hypotheses (often through study of deviant cases), the assessment of 1517
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