Integration of contingency information in judgments of cause, covariation, and probability.

condition claimed to have mapped the abstract events onto other events. Mean causal judgments (shown in Table 1) both across and within stimuli did not differ reliably as a function of any of these three variables, or of gender, smallest p = . 12. 5 Nor did mean causal judgments differ as a function of stimulus set size, p > .15. Thus, subsequent analyses were collapsed across these groupings. The grand mean of participants ' judgments is . 0 1 (SD = 0.42). This statistic indicates that participants, on average, were not biased toward perceiving facilitative relations more readily than inhibitory relations. Rather, the grand mean accurately reflects the fact that the four mean cell frequencies were equal. This finding is consistent with Wasserman and Shaklee (1984) who found no evidence that positive relations were perceived more readily than negative relations when contingency information was presented in summary format (however, these authors did find that positive relations were perceived more readily when contingency informarion was presented along a discrete time-line; see also Erlick & Mills, 1967). The cell weight inequality. To assess the CWI, we correlated each of the four cell frequencies with each participant 's judgments. 6 Next, we Fisher-transformed this 4 × 120 matrix of values from rij to z U, which is our measure of rule viability. The viabilities for B and C were multiplied by 1 so that they would be in the same direction as A and D. We then analyzed the viabilities for the four frequencies using a 3 × 4 (Event Type × Cell) mixed analysis of variance (ANOVA). There were reliable main effects of event type, F(2, 117) = 3 .66,p < .03, MSE = 0.05, and cell, F(3, 351) = 195.47, p < .001, MSE = 0.03. The interaction 5 The ratings in Experiments 1 and 2 were divided by 3 to provide a possible range of 1 to + 1. 6 In this research area, it has been assumed that participants' representations of frequencies reflect the objective values presented to them. In other domains, however, it has been found that people represent numeric magnitude as a nonlinear function of the arithmetic scale (Rule, 1969). This function has been approximated by a logarithmic transformation (Banks & Hill, 1974; Moyer & Landaner, 1967) or by a power transformation with an exponent of about .67 (Banks & Hill, 1974). If participants do transform frequency data as such, then the transformed frequencies should correlate more strongly than the actual frequencies with their ratings. We examined log and power (exponent of .67) transformations of the four cell frequencies and found that the actual frequencies correlated either the same or better than either transformarion. Thus, we used the actual frequencies to calculate rule output. Note also that we used the cell frequencies, not the relative frequencies (i.e., cell frequency divided by total frequency), to calculate rule output. INTEGRATION OF CONTINGENCY INFORMATION 275 Table 2 Mean Viabilities of Cell Frequencies by Event Type in Experiment I