Aggregation Bias and Ambivalent Cases: A New Parameter of Consistency to Understand the Significance of Set-theoretic Sufficiency in fsQCA

The Boolean minimization, used in fuzzy-set qualitative comparative analysis (fsQCA) to establish sufficient relationships between conditions and outcome, automatically produces false positive subset relationships in the presence of random data. However, because this type of aggregation bias mainly produces ambivalent subset relationships between the condition(s) and the outcome, such false positives do not pose a problem for the fsQCA results per se. The aggregation bias has a negative impact on fsQCA analysis only because the consistency score is not able to detect set-theoretic subset relationships. Indeed, the existent parameter of consistency does not distinguish whether the subset relationship between conditions and outcome is the result of the mere Boolean minimization or whether it has set-theoretic significance. This article proposes a new consistency formula that provides information about subset relationships between conditions and outcome and detects the difference between randomly-generated subsets and meaningful subset relationships. The new parameter of consistency proposed here can be considered as an additional tool to test the significance of a meaningful sufficient relationship without being subject to the aggregation bias.