Assessing the belief bias effect with ROCs: it's a response bias effect.

A belief bias effect in syllogistic reasoning (Evans, Barston, & Pollard, 1983) is observed when subjects accept more valid than invalid arguments and more believable than unbelievable conclusions and show greater overall accuracy in judging arguments with unbelievable conclusions. The effect is measured with a contrast of contrasts, comparing the acceptance rates for valid and invalid arguments with believable and unbelievable conclusions. We show that use of this measure entails the assumption of a threshold model, which predicts linear receiver operating characteristics (ROCs). In 3 experiments, subjects made "valid"/"invalid" responses to syllogisms, followed by confidence ratings that allowed the construction of empirical ROCs; ROCs were also constructed from a base-rate manipulation in one experiment. In all cases, the form of the empirical ROCs was curved and therefore inconsistent with the assumptions of Klauer, Musch, and Naumer's (2000) multinomial model of belief bias. We propose a more appropriate, signal detection-based model of belief bias. We then use that model to develop theoretically sound and empirically justified measures of decision accuracy and response bias; those measures demonstrate that the belief bias effect is simply a response bias effect. Thus, our data and analyses challenge existing theories of belief bias because those theories predict an accuracy effect that our data suggest is a Type I error. Our results also provide support for processing theories of deduction that assume responses are driven by a graded argument-strength variable, such as the probability heuristic model proposed by Chater and Oaksford (1999).