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Membership function sensitivity of descriptive statistics in fuzzy-set relations

Fuzzy-set theory has provided researchers with a new perspective on many social-scientific problems. In particular, the method of fuzzy-set Qualitative Comparative Analysis (fsQCA) has gained in popularity across various disciplines. However, while the methodological development of fsQCA has progressed on a number of fronts, sensitivity diagnostics have only recently been put on the agenda. This article analyses how coverage as an important descriptive statistic in fsQCA is influenced by the interaction between membership function form and crossover threshold choice. Depending on the relative location of the latter, changes in the former influence coverage in either a negative or a positive direction, and to different magnitudes. This influence is not uniform but varies in relation to cases’ distance from unique peak points. Although the orientation of this article is theoretical, its results have implications for empirical research. Most importantly, the influence of membership functions should become part of routine sensitivity checks.