Is the Weighting of Contingency Data Contingent on the Hypothesis Assessed

Is The Weighting of Contingency Data Contingent on the Hypothesis Assessed? * David R. Mandel 1 (mandel@psych.utoronto.ca) and Oshin Vartanian 2 (oshin.vartanian@drdc-rddc.gc.ca) University of Toronto 1 and Defence Research and Development Canada (DRDC) 1,2 DRDC, 1133 Sheppard Ave. West, P.O. Box 2000, Toronto, ON M3M 3B9, Canada Causal Induction Causal reasoning exerts a significant influence on how people explain the past and predict outcomes in the future. An important question concerns the ways in which people integrate frequency data about the co-occurrence of events, or contingency information, as they learn causal relations. If contingency information is presented in the form of the presence or absence of a cause (c) and an effect (e), the problem appears as follows: Effect (e.g., illness Y) e ~e c Cause A = ∑ (c ∩ e) B = ∑ (c ∩ ~e) (e.g., virus X) ~c C = ∑ (~c ∩ e) D = ∑ (~c ∩ ~e) conforms to the hypothesis tested; Klayman & Ha, 1987), which invariably involves cells A and B. This experiment tested these competing hypotheses. Method Among 40 undergraduate subjects, 20 judged the strength of a generative cause (whether a particular virus causes an illness), and the other 20 judged the strength of an inhibitory cause (whether a particular antivirus prevents an illness). Judgments were made on a 0 (not at all causal/preventative) to 4 (strongly causal/preventative) scale. Contingency data were presented trial by trial. The 24 stimuli used corresponded to the 10- and 20-set size conditions from Mandel and Lehman (1998, Exp. 1). Cell means and variances were constant across the 24 stimuli. Results and Conclusion The delta rule, ∆P = P(e|c) – P(e|~c), is a normative model of information integration for causal learning that assigns equal weight to cells A to D. However, several studies (e.g., Kao & Wasserman, 1993; Mandel & Lehman, 1998) have shown that people tend to give the greatest weight to the cells as follows: A > B > C > D. Mandel and Lehman (1998) accounted for this cell weight inequality (CWI) in terms of a combination of two biases: A positive-event bias, according to which a greater weight is given to information about event presence than event absence, and a sufficiency bias, according to which greater weight is given to assessments of sufficiency than necessity. The table below shows the mean Fisher correlations between subjects’ ratings and the cell frequencies by condition. Cell Hypothesized cause A B C D Generative Inhibitory A Critical Test of the PSB and PCB Accounts A two-way (Cell × Condition) ANOVA revealed a main effect for Cell, such that A and B were weighted more heavily than C and D, F(3, 228) = 74.8, p B = C > D. The PSB account also proposes that B > C due to a sufficiency bias because B is uniquely indicative of sufficiency violations, whereas C is uniquely indicative of necessity violations when testing hypotheses about generative causes. A critical test of the PSB account yet to be conducted consists of asking subjects to test hypotheses about generative and inhibitory causes, respectively. If the PSB account is correct, we should observe a stronger weighting of cell A in the inhibitory condition than in the generative condition because cell A is the “sufficiency” cell in the former case, whereas cell B is the sufficiency cell in the latter case. Conducting this critical test, we pit the PSB account against an alternative positive-test-confirmation-biases (PCB) account. The PCB account posits that the CWI is attributable to a tendency to overweight confirmatory information within a positive-test strategy (i.e., a test that References Kao, S.-F., & Wasserman, E. A. (1993). Assessment of an information integration account of contingency judgment with examination of subjective cell importance and method of information presentation. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19, 1363-1386. Klayman, J., & Ha, Y. -W. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94, Mandel, D. R. , & Lehman, D. R. (1998). Integration of contingency information in judgments of cause, covariation, and probability. Journal of Experimental Psychology: General, 127, 269-285. This research was funded by Discovery Grant #249537-02 from the Natural Sciences and Engineering Research Council of Canada.