Importing set-theoretic tools into quantitative research: the case of necessary and sufficient conditions

In this article, we import set-theoretic methods from the qualitative research tradition into the quantitative research tradition. We focus specifically on set-theoretic methods designed to analyze the extent to which a condition is necessary and is sufficient for an outcome of interest. We use these methods to reanalyze four major studies from the quantitative tradition. We find that set-theoretic methods call attention to asymmetrical patterns in the data that otherwise go unnoticed and unanalyzed. We develop a general set-theoretic framework for the study of necessity and sufficiency. We conclude that the use of this framework can enrich existing and future quantitative research in the social sciences.