Exploring the determinants of dual goal facilitation in a rule discovery task

Abstract

Wason's standard 2-4-6 task requires discovery of a single rule and leads to around 20% solutions, whereas the dual goal (DG) version requires discovery of two rules and elevates solutions to over 60%. We report an experiment that aimed to discriminate between competing accounts of DG facilitation by manipulating the degree of complementarity between the to-be-discovered rules. Results indicated that perfect rule complementarity is not essential for task success, thereby undermining a key tenet of the goal complementarity account of DG facilitation. The triple heterogeneity account received a good degree of support since more varied triple exploration was associated with facilitatory DG conditions, in line with this account's prediction that task success is associated with the creative search of the problem space. The contrast class account (an extension of Oaksford & Chater's, 1994, iterative counterfactual model) was also corroborated in that the generation of descending triples was demonstrated to be the dominant predictor of DG success. We focus our discussion on conceptual ideas relating to the way in which iterative counterfactual testing and contrast class identification may work together to provide a powerful basis for effective hypothesis testing.

Contrast class cues and performance facilitation in a hypothesis-testing task: evidence for an iterative counterfactual model

“…It is not clear, however, why DG instructions should necessarily lead to a greatly enhanced breadth of triple testing. It is also not the case that such breadth is consistently observed with DG instructions (Gale & Ball, 2009) Previous research by Gale and Ball (e.g., 2003;2009) has suggested an alternative mechanism by which DG instructions might facilitate task performance. This mechanism is based on the "contrast class cues" that are afforded by MED feedback, with these cues enabling participants to clarify the scope of the DAX rule as relating to "ascending" sequences.…”

“…In support of their theory, Wharton et al reported a study in which DG instructions failed to elicit facilitated performance when the complementary nature of the rules was left implicit. However, a recent experiment by Gale and Ball (2009) directly manipulated the relationship between the experimenter's two rules such that triples could be DAX, MED or "neither DAX nor MED" (i.e., the DAX and MED rules were no longer logically complementary), yet the level of facilitated performance was equivalent to that observed with the usual DG instructions. Gale and Ball's (2009) findings therefore confirm that rule complementarity is not the causal factor underpinning the DG facilitation effect (see also Vallée-Tourangeau et al, 1995, for a study similar to that of Gale & Ball, 2009, which likewise produced evidence opposing the goal complementarity hypothesis).…”

“…Furthermore, Oaksford and Stenning (1992) proposed that the process of computing the most relevant contrast class in hypothesis testing will exploit all available sources of information, including phonetic, syntactic, semantic, and pragmatic cues. Gale and Ball's (e.g., 2006;2009) contrast class account of hypothesis testing in the 2-4-6 paradigm stems directly from these notions, with the idea being that the seemingly oppositional nature of DAX and MED provides participants with cues (via triple generation) that soon facilitate insight into the ascending nature of the DAX rule. In particular, receiving MED feedback for a descending triple such as 6-4-2 in the DG task is argued to alert reasoners to the realization that MED and DAX triples may fall at opposite poles of the dimension "descending versus ascending."…”

“…In our previous research (Gale & Ball, 2006, 2009, we noted that successful solvers are those who uncover at least one descending triple during their hypothesis testing, and that DG instructions promote the production of at least one descending triple. With these findings in mind, we examined the present data set for any effect of the presence versus absence of the participants' production of a descending triple on their task success.…”

“…As one final index of triple heterogeneity, we also computed the overall number of different types of triples generated by each participant, whether positive or negative. This index, which ranged from 1 to 10, is referred to as a participant's "triptype score" and is a more accurate measure of the full breadth of triples that a participant has generated (see Gale & Ball, 2009). Table 4 summarizes participants' triple-generation profiles across solvers and nonsolvers for the indices described.…”