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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. As a consequence, much of the research on belief-bias conducted in the last four decades was put into question, implying that extensive replications featuring confidence-ratings are necessary. The present meta-analysis in combination with a novel study demonstrates that the latter conclusion is invalid and driven by the common practice of relying on data aggregated across participants and stimuli. Using a hierarchical-Bayesian meta-analysis we reanalyzed a corpus of twenty-two studies (N = 993). The results indicated that extensive replications using confidence-rating data are unnecessary as the observed ROCs are not asymmetric. These results were 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.