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be more approximate and general. The partitions between typological categories should be placed so that the underlying theories predict the greatest difference between the probabilities of the specified outcomes on either side of the partition. This may be difficult to do in practice, and the researcher must be alert to whether the underlying theories or their expected interactions produce “threshold effects,” or discontinuous jumps in the relationship between the magnitudes of the independent and dependent variables, and/or “inflection points,” values at which the relationship between independent and dependent variables may reverse in direction, from a direct relationship to an inverse relationship, or vice versa.

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Intervening variables—or variables temporally or spatially between independent and dependent variables that do not have any independent causal effects of their own—should not be included in constructing a typological theory. Intervening variables are often important sources of data for process-tracing, as they can indicate whether a specified process took place, but as they lack causal weight, they are not part of the theory.

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Gary King, Robert O. Keohane, and Sidney Verba, Designing Social Inquiry: Scientific Inference in Qualitative Research (Princeton, N.J.: Princeton University Press, 1994).

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A well-specified type provides an answer to the important question, “What is this a case of?” Howard Becker and Charles C. Ragin, eds., What is a Case? Exploring the Foundations of Social Inquiry (Cambridge: Cambridge University Press, 1992), p. 6.

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Two points are worth noting here from our experience in urging students and colleagues to construct typological theories. First, the process of visually arraying variables into types shifts theorizing from univariate thinking on causal mechanisms and a focus on the explanatory weight of individual variables and “alternative hypotheses,” to typological thinking and a focus on combinations of variables and their effects. Second, when graduate students construct a typological theory for the first time, they often discuss variables in their text that do not appear in their typological table, or include variables in the table that they do not discuss in their text. This suggests that by fostering more systematic thinking about theories and the contexts in which they apply, typological theorizing can quickly reveal inconsistencies in a theorist’s views.

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This discussion assumes that cases may be selected on the basis of preliminary knowledge of the values of their variables. Of course, the values of the variables may turn out to be different once the researcher undertakes the actual case study, and finding that a case has commonly been misclassified is an important contribution. This is one reason that the selection of cases based on preliminary knowledge of the values of the variables is not necessarily vulnerable to confirmation bias.

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Daniel Little, “Causal Explanation in the Social Sciences.”

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In some circumstances, statistical tests may be misleading if particular combinations of variables are impossible but the researcher is not aware of this. For example, a 2x2 table in which one square is not possible gives misleading results when a chi-squared test is applied. We thank Bear Braumoeller for providing this insight in private correspondence.

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It is useful to distinguish between cases that are not logically possible and those that are not socially possible or at least highly unlikely in the social world. A logically impossible case would be a case of deterrence “success” when either no deterrent threat was issued or no action was contemplated by the state that was supposedly challenging the status quo. By definition, such cases do not constitute successful deterrence. A case that is socially impossible, or at least highly unlikely, is one in which all of the relevant variables, both singly and conjunctively, point in the same direction in overdetermining an outcome, yet that outcome does not occur. Except for measurement error or the