Two-sample test for ambivalent subset relationship in fuzzy set qualitative comparative analysis

In fuzzy set qualitative comparative analysis (fsQCA), ambivalent subset relationships (ASR), occur when solution term X is in subset relation with the outcome Y and its absence ~ Y, leading to false-positive results. While ASR can be empirically detected in small-N and medium-N cases through in-depth case knowledge, it is challenging to identify them in large-N case designs. QCA parameters such as proportion reduction inconsistency (PRI) and consistency are commonly used to identify simultaneous subset relationships (SSR), but they are not specifically designed to detect ASR. To address this issue, this article introduces the DTS test, a new test based on two-sample statistics. The DTS test identifies distributional convergence between a solution term’s empirical cumulative distribution function (eCDF) and an eCDF of solution formulas with asymptotic ASR characteristics. By comparing empirical solutions’ patterns with spurious artificially built solutions' patterns, the DTS test reduces the risk of causal fallacies in interpreting the empirical results. Overall, the DTS test provides a valuable tool for identifying and addressing potential ASR bias in fsQCA, particularly in large-N case designs.