Weighting of contingency information in causal judgement: Evidence of hypothesis dependence and use of a positive-test strategy

Abstract

Contingency is an important cue to causation. Research shows that people unequally weight the cells of a 2 × 2 contingency table as follows: cause-present/effect-present (A) > cause-present/effect-absent (B) > cause-absent/effect-present (C) > cause-absent/effect-absent (D). Although some models of causal judgement can accommodate that fact, most of them assume that the weighting of information is invariant as a function of whether one is assessing a hypothesized generative versus preventive relationship. An experiment was conducted that tested the hypothesis-independence assumption against the predictions of a novel weighted-positive-test-strategy account, which predicts hypothesis dependence in cell weighting. Supporting that account, judgements of hypothesized generative causes showed the standard A > B > C > D inequality, but judgements of hypothesized preventive causes showed the predicted B > A > D > C inequality. The findings reveal that cell weighting in causal judgement is both unequal and hypothesis dependent.

Keywords:

• Causation
• Prevention
• Contingency information
• Hypothesis testing
• Positive-test strategy

Acknowledgments

This research was funded by Natural Sciences and Engineering Council of Canada Discovery Grant No. 249537–2002 to the first author. Portions of the present research were presented at the Southern Ontario Behavioral Decision Research Conference in Toronto, Canada, in May 2006 and at the 28th Annual Meeting of the Cognitive Science Society in Vancouver, Canada, in August 2006. We thank Joshua Klayman, Derek Koehler, Robin Murphy, and three anonymous reviewers for their insightful comments on the present research. We also thank Aaron Gregg for programming the experiment and Ahna Kim for her research assistance.

Notes

¹ Indeed, the rule-discovery paradigm does not permit individuals to seek confirmatory information. They can merely decide whether to test an example that either conforms or does not conform to their hypothesis. Then, they will learn whether the evidence revealed confirms or disconfirms their hypothesis, but over that outcome they have no choice.

² This description focuses only on factual causal hypotheses in which the antecedent, x, is affirmed. An extension of this analysis to counterfactual causal hypotheses (e.g., “¬x might have been sufficient to prevent y”) is given in Mandel (2005).

³ In an earlier proceedings report (Mandel & Vartanian, 2006), we presented a slightly different account that focused on the joint influence of positive testing and confirmation bias. That account, however, is less parsimonious than the present account and does not lead to a key prediction: namely, that Cell D will receive greater weight than Cell C in tests of preventive causal relationships.

⁴ Following the judgement task, participants completed another task unrelated to the hypotheses tested in this article.

⁵ Given that we did not have other predictions to test involving format, we aggregate over format in Table 3.

⁶ The transformation is of the form j = sign(support)abs(support) ^k , where k was searched in intervals of .05 to maximize the correlation between support and judgements. For hypothesized generative causation, k = .95 (r = .78); for hypothesized preventive causation, k = 1.0 (r = .88).