Case Study: Logic

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
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