Inducing a Rule in Wason's 2–4–6 Task: A Test of the Information-Quantity and Goal-Complementarity Hypotheses

Abstract

In the standard 2–4–6 induction task, subjects are instructed to discover the rule generating sequences of three numbers by inventing number triples for which they receive immediate feedback. The rule is “ascending numbers”. Performance is greatly aided with Dual Goal (DG) instructions that ask subjects to discover two rules, one that generates “Dax” triples (equivalent to “yes” instances with Single Goal [SG] instructions) and another that generates “Med” triples (equivalent to “no” instances). The present study eliminates two explanations for this effect suggested by Wharton, Cheng, and Wickens (1993). Experiment 1 tested their Information-Quantity hypothesis that the effect results simply from the DG subjects testing more triples prior to proposing a rule. Our DG subjects were more likely to solve the problem and produced more “negative” triples than SG subjects when both groups generated exactly 15 triples. Two further groups received feedback only after generating all 15 triples, and again DG subjects were more likely to solve the problem and to generate more “negative” triples. Experiment 2 tested Wharton et al.'s Goal-Complementarity hypothesis that success under DG instructions hinges on preserving the complementary representation of the two rules. We compared SG instructions with three types of DG instructions that suggested different types of triples (Dax, Med, both Dax and Med, neither Dax nor Med). DG instructions were more effective in promoting successful rule discovery regardless of differences in rule complementarity. Our analysis of the heterogeneity of the examplars generated with DG instructions in both experiments suggest that success on the 2–4–6 task is as much a consequence of the breadth of hypotheses that subjects entertain as it is a consequence of the testing strategy.

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

“…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).…”

“…The decision to impose a 10-triple limit derived from two previous studies (i.e., Klayman & Ha, 1989;Vallée-Tourangeau et al, 1995) that had used a similar constraint as a method to standardize any influence of triple quantity on rule discovery, while still affording participants an opportunity to examine a variety of triple types should they wish to. Vallée-Tourangeau et al suggested that the production of 10 triples is an especially good cutoff, since many participants are eager to announce their hypotheses just before this point is reached.…”

“…Yet another account of DG facilitation is the tripleheterogeneity theory proposed by Vallée-Tourangeau et al (1995). This theory builds on Wason's (1960) observation that solvers can be differentiated from nonsolvers in terms of the types of triples they produce (i.e., solvers have a higher eliminative/enumerative index).…”

“…Participants are given 2-4-6 as an example of the DAX rule and are then asked to generate triples that are classified as either conforming to the unknown DAX rule (which is "any ascending sequence") or to the unknown MED rule (which is "all other sequences"). Using these amended instructions, success rates on the task for initial rule announcements typically rise to over 60% (e.g., Gale & Ball, 2006;Gorman et al, 1987;Tukey, 1986;Vallée-Tourangeau, Austin & Rankin, 1995;Wharton, Cheng & Wickens, 1993).…”

“…Triples were therefore codified using the system introduced by Vallée-Tourangeau et al (1995), in which positive triples (i.e., ascending sequences) are categorized as either "constant positives" (rising by equal increments) or "variable positives" (rising by nonequal increments), and negative triples (i.e., nonascending sequences) are subdivided into eight discrete "negtype" categories according to the following formulae (where the first number of a triple is a, the second b, and the third c):…”