This paper identifies an important vulnerability in Qualitative Comparative Analysis (QCA): relying on the consistency value alone can produce false-negative conclusions that remove true causal configurations from the analysis.

🔍 Why consistency alone misleads

Consistency scores are commonly used to judge whether a term is consistent with a set-relational claim. Prior work (Braumoeller 2015) showed that the consistency value is not a proper test on its own because its sampling distribution under the null is unknown. Permutation testing was introduced to estimate a p value for a consistency score and protect against false positives.

🧪 What is introduced here and why it matters

This paper extends the permutation-testing logic to estimate statistical power for QCA as a guard against false negatives. Low power can cause:

• The false exclusion of truth table rows from the minimization procedure
• The generation and interpretation of invalid solutions that omit real causal patterns

Permutation-based power estimation provides a way to quantify that risk for a given hypothesis and sample size.

📊 What simulations and reanalysis reveal

Simulations across many constellations of alternative versus null hypotheses and varying numbers of cases show:

• Power estimates can range continuously from 1 to 0 depending on the scenario and sample size
• Even under the most favorable parameter constellations, ex post power analysis of 63 published truth table analyses finds that about half are low-powered

These results demonstrate that low power is a realistic and common problem in practical QCA applications.

⚠️ Practical takeaway for researchers

Estimating permutation-based power and calculating the required number of cases before performing truth table analysis is recommended to avoid false-negative exclusions and invalid solutions. Incorporating power checks complements permutation p values and strengthens the inferential credibility of QCA findings.