Characterizing Belief Bias in Syllogistic Reasoning: A Hierarchical-Bayesian Meta-Analysis of ROC Data

Abstract

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 beliefbased 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 et al., Psychological Review, 117 (3), 2010). The discrepancy between Dube et al. 's, Psychological Review, 117(3), 831-863 (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 22 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 by a novel experimental design based on SDT's generalized area theorem. Although the metaanalysis 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 that 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.

Rethinking the link between cognitive sophistication and politically motivated reasoning

“…The conclusion either does (valid) or does not (invalid) deductively follow from the premises, and either contradicts or aligns with people's prior beliefs. Results from studies using this paradigm suggest that, while cognitively sophisticated individuals perform better overall-correctly discriminating valid from invalid conclusions-their performance is also more sensitive to whether the conclusion coheres with their prior beliefs (Trippas et al, 2015(Trippas et al, , 2018.…”

Who detects and why: How individual differences in cognitive characteristics underpin different types of responses on reasoning tasks?

“…Thus, in the case of belief bias syllogisms, the false intuitive response is the product of believability of the conclusion, while strong conformity with logical principles are needed to come up with the right, logically valid response. This tendency to evaluate conclusions based on believability instead of validity is called belief bias, and, similarly as the tendency of giving the wrong intuitive answers on the CRT problems, is a well documented phenomenon (Evans, Barston, & Pollard, 1983;Newman, Gibb, & Thompson, 2017;Trippas et al, 2018). BBS and CRT have also been found to be closely related in number of research and the magnitudes of these correlations were quite high (e.g.…”

“…What makes both CRT and belief bias syllogisms attractive and very appropriate for studying the reasoning processes is that they both have clear and appropriate normative standards for evaluating the answers and that they have been shown to be predictive of normative responding across many other tasks of judgment and choice (Stupple et al, 2017;Trippas et al, 2018). Previous studies have found that the reasoning tasks tap into a range of different abilities and dispositions.…”

Testing the foundations of signal detection theory in recognition memory.

“…The popularity of SDT can be attributed to two factors: Its empirical success and its theoretical inclusiveness. First, SDT has been shown to characterize judgments across a wide variety of psychological domains beyond memory, such as perception and reasoning (e.g., Green & Swets, 1966;Macmillan & Creelman, 2005;Rotello, 2018;Trippas et al, 2018). Second, its core assumption that judgments are based on an evaluation of latent-strength values sampled from continuous distributions plays well with popular theoretical accounts of learning, forgetting, and generalization, among others (Lockhart & Murdock, 1970).…”