Case Studies and Theory Development in the Social Sciences - Alexander L. George [129]
The trade-offs involved in adding variables to a typology are different from those involved in adding an independent variable to a statistical research design. Statistical methods require positive degrees of freedom for a meaningful result. In such methods, each additional independent variable requires a corresponding increase in the number of cases to be included in order to estimate the likelihood of a nonrandom relationship. This creates considerable pressure to keep the number of independent variables low unless data is extremely abundant, particularly if interaction effects (which also require a larger sample size to estimate) are to be taken into account.
This reasoning is appropriate to statistical methods, but it can be misleading on the issue of whether additional variables or types should be included in a typological theory that is to be explored through case studies. For the case study researcher, the exclusion of potentially relevant variables can be a greater threat to valid inferences than the inclusion of additional variables that may or may not be spurious. The exclusion of a relevant variable interferes with both within-case analyses and cross-case comparisons. Inclusion of an additional variable, on the other hand, is rather unlikely to lead to spurious inferences as long as sufficient process-tracing evidence is available to test whether the variable plays a causal role.
Adding variables increases the complexity of the research design, and each new variable requires additional observations if it is to be tested, but new variables do not raise an inherent problem of indeterminacy as long as they generate additional independent observable implications on causal processes and outcomes. This is true whether these independent observable implications are in the same case or in a separate case. The number of independent observations, not the number of cases, sets the upper limit on the number of independent variables that can be tested. Thus, the investigator should start with a broad range of variables that are potentially relevant to the phenomenon under study.
The more general trade-off for the case study researcher is whether the problem at hand requires added theoretical complexity, whether process-tracing evidence is available to deal with this complexity, and whether the problem is important enough to merit a complex theory—political scientists will create many subtypes of war, while the Inuit differentiate among many types of snow. Parsimony and simplicity are always preferable, but they should be sacrificed when complexity is necessary for adequate explanatory theory.489
As in the inductive development of typological theories, researchers should give as much thought to differentiation of the dependent variable in deductive theories as they do to that of the independent variables. Far too many research designs provide detailed attention to the independent variables while lumping the dependent variable into a few vaguely defined categories. As emphasized in Chapter 4 on research design, the careful characterization of the dependent variable and its variance is often one of the most important and lasting contributions to research.
Once the specification of variables is complete, it defines the property space—the relevant universe of all possible combinations of variables, or types.490 This is the point at which Ph.D. students often veer toward a nervous breakdown. Having specified their independent and dependent variables, and explored the theoretical literature on the causal mechanisms associated with each variable when it acts alone, thesis students are often dismayed to find, for example, that when five independent variables are assembled together with one dependent variable, there are sixty-four possible types. Moreover, with only a preliminary knowledge of the values that the variables assume in different cases, the researcher can only tentatively