Do modals identify better models? A comparison of signal detection and probabilistic models of inductive reasoning

The nature of the relationship between deductive and inductive reasoning is a hotly debated topic. A key question is whether there is a single dimension of evidence underlying both deductive and inductive judgments. Following Rips (2001), Rotello and Heit (2009) and Heit and Rotello (2010) implemented one- and two-dimensional models grounded in signal detection theory to assess predictions for receiver operating characteristic data (ROCs), and concluded in favor of the two-dimensional model. Recently, Lassiter and Goodman (2015) proposed a different type of one-dimensional model, the Probability Threshold Model (PTM), that they concluded offered a good account of data collected over a range of decision modals (e.g., How likely, possible, or necessary is the argument conclusion?). Here, we apply the PTM and the signal detection models to ROCs from 3 large experiments in which participants made judgments about arguments varying in terms of modals introduced by Lassiter and Goodman (2015). Two independent variables that are theoretically important for the study of inductive reasoning, namely premise-conclusion similarity (as utilized in Heit & Rotello, 2010) and number of premises (as utilized in Rotello & Heit, 2009), are also varied in Experiments 1 and 2, respectively. In all cases, the PTM provides the poorest fit both quantitatively and qualitatively; the two-dimensional signal detection model is preferred.