Analysing necessity and sufficiency with Qualitative Comparative Analysis: how do results vary as case weights change?

Ragin’s Qualitative Comparative Analysis (QCA) and related set theoretic methods are increasingly popular. This is a welcome development, since it encourages systematic configurational analyses of social phenomena. One downside of this growth in popularity is a tendency for more researchers to use the approach in a formulaic manner—something made possible, and more likely, by the availability of free software. We wish to see QCA employed, as Ragin intended, in a self-critical manner. For this to happen, researchers need to understand more of what is going on behind the results generated by the available software packages. One important aspect of set theoretic analyses of sufficiency and necessity is the effect that the distribution of cases in a dataset can have on results. We explore this issue in a number of ways. We begin by exploring how both deterministic and nondeterministic data-generating processes are reflected in the analyses of populations differing in only the weights of types of cases. We show how and why weights matter in causal analyses that focus on necessity and also, where models are not fully specified, sufficiency. We then draw on this discussion to show that a recent textbook discussion of hidden necessary conditions is weakened as a result of its neglect of weighting issues. Finally, having shown that case weights raise a number of difficulties for set theoretic analyses, we offer suggestions, drawing on two imagined population datasets concerning health outcomes, for mitigating their effect.