The belief-bias effect is one of the most-studied biases in reasoning. A recent study of the phenomenon using the signal detection theory (SDT) model called into question all theoretical accounts of belief-bias by demonstrating that belief-based differences in the ability to discriminate between valid and invalid syllogisms may be an artifact stemming from the use of inappropriate linear measurement models such as analysis of variance (Dube, Rotello, & Heit, 2010). The discrepancy between Dube et al.'s (2010) results and the previous three decades of work, together with former's methodological criticisms suggests the need to revisit earlier results, this time collecting confidence-rating responses. Using a hierarchical-Bayesian meta-analysis, we reanalyzed a corpus of twenty-two confidence-rating studies (N = 993). The results indicated that extensive replications using confidence-rating data are unnecessary as the observed Receiver Operating Characteristic functions are not systematically asymmetric. These results were subsequently corroborated with a novel experimental design based on SDT's generalized area theorem. Although the meta-analysis confirms that believability does not influence discriminability unconditionally, it also confirmed previous results that factors such as individual differences mediate the effect. The main point is that data from previous and future studies can be safely analyzed using appropriate hierarchical methods which do not require confidence-ratings. More generally, our results set a new standard for analyzing data and evaluating theories in reasoning. Important methodological and theoretical considerations for future work on belief bias and related domains are discussed.
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