Assessing the belief bias effect with ROCs: reply to Dube, Rotello, and Heit (2010).
Dube, Rotello, and Heit (2010) argued (a) that the so-called receiver operating characteristic is nonlinear for data on belief bias in syllogistic reasoning; (b) that their data are inconsistent with Klauer, Musch, and Naumer's (see record 2000-02818-008) model of belief bias; (c) that their data are inconsistent with any of the existing accounts of belief bias and only consistent with a theory provided by signal detection theory; and (d) that in fact, belief bias is a response bias effect. In this reply, we present reanalyses of Dube et al.'s data and of old data suggesting (a) that the receiver operating characteristic is linear for binary "valid" versus "invalid" responses, as employed by the bulk of research in this field; (b) that Klauer et al.'s model describes the old data significantly better than does Dube et al.'s model and that it describes Dube et al.'s data somewhat better than does Dube et al.'s model; (c) that Dube et al.'s data are consistent with the account of belief bias by misinterpreted necessity, whereas Dube et al.'s signal detection model does not fit their data; and (d) that belief bias is more than a response bias effect.