Power and False Negatives in Qualitative Comparative Analysis: Foundations, Simulation and Estimation for Empirical Studies

In Qualitative Comparative Analysis (QCA), empirical researchers use the consistency value as one, if not sole, criterion to decide whether an association between a term and an outcome is consistent with a set-relational claim. Braumoeller (2015) points out that the consistency value is unsuitable for this purpose. We need to know the probability of obtaining it under the null hypothesis of no systematic relation. He introduces permutation testing for estimating the $p$ value of a consistency score as a safeguard against false positives. In this paper, I introduce permutation-based power estimation as a safeguard against false-negative conclusions. Low power might lead to the false exclusion of truth table rows from the minimization procedure and the generation and interpretation of invalid solutions. For a variety of constellations between an alternative and null hypothesis and numbers of cases, simulations demonstrate that power estimates can range from 1 to 0. Ex post power analysis for 63 truth table analyses shows that even under the most favorable constellation of parameters, about half of them can be considered low-powered. This points to the value of estimating power and calculating the required number of cases before the truth table analysis.