Examining the representation of causal knowledge

Abstract

Three experiments investigated reasoners' beliefs about causal powers; that is, their beliefs about the capacity of a putative cause to produce a given effect. Covariation-based theories (e.g., Cheng, 1997; Kelley, 1973; Novick & Cheng, 2004) posit that beliefs in causal power are represented in terms of the degree of covariation between the cause and its effect; covariation is defined in terms of the degree to which the effect occurs in the presence of the cause, and fails tooccur in the absence of the cause. To test the degree to which beliefs incausal power are reflected in beliefs about covariation information, participants in three experiments rated their beliefs that putative causes have the capacity to produce a given effect (i.e., possess the causal power to produce an effect) as well as their beliefs regarding the degree to which the putative cause and effectcovary. A strong positive correlation was discovered between participants' beliefs in causal power and their beliefs that the effect occurs in the presence of the cause. However, no direct relationship was found between participants' beliefs in causal power and their belief that the effect will fail tooccur in the absence of the cause. These findings were replicated using bothwithin- (Experiments 1 and 3) and between-subject designs (Experiment 2). In Experiment 3, we extended these analyses to measures of familiarity, imageability, and detailedness of the representation. We found that participants' beliefs in causal power were strongly associated with familiarity, and imageability, but not the perceived detailedness of the cause and effect relationship. These data provide support for a multidimensional account of causal knowledge whereby people's representations of causation include, but are not limited to, the covariation, familiarity, and imageability of cause and effect relationships.

Notes

We would like to thank Ron Borowsky, Marc Buehner, Jamie Campbell, David Green, David Lagnado, David Over, and Courtney Stein for comments and helpful suggestions on a previous version of this manuscript. This research was supported by a postgraduate scholarship from the Natural Sciences and Engineering Research Council of Canada (NSERC) awarded to Jonathan Fugelsang, an NSERC discovery grant awarded to Valerie Thompson, and a Dartmouth College research grant awarded to Kevin Dunbar.

The analyses for this experiment and subsequent experiments consist of zero order correlations between the ratings obtained for each of the stimuli. Therefore, the correlational analyses in Experiment 1 and 2 have 38 degrees of freedom (40 items) and Experiment 3 has 18 degrees of freedom (20 items). Note that the stability of these correlations is greatly increased due to the large number of subjects contributing to each data point (60 in Experiment 1, 91 in Experiment 2, and 40 in Experiment 3).

When both P(e/c) and P(e/-c) are regressed on beliefs in a causal power, the obtained standardized beta coefficients suggest that P(e/c) provides over two times greater predictive influence of beliefs in causal powers than P(e/-c) in Experiment 1 [Causal Beliefs = .875_P(e/c) −  .319_P(e/-c)], Experiment 2 [Causal Beliefs = .685_P(e/c) − .327_P(e/-c)], and Experiment 3 [Causal Beliefs = .789_P(e/c) − .388_P(e/-c)].

The overall pattern of data for the omnibus ANOVA between BELIEF and COVARIATION as a function of the three judgment types was replicated in Experiments 2 and 3. In order to maintain parsimony in the dissemination of the remainder of the findings, these analyses will not be presented. However, the mean pattern of these data can be extrapolated from the raw scores in Appendix D and E.

All participants in Experiments 1, 2, and 3 made the judgements regarding P(e/c) before they made the judgements regarding P(e/-c). However, in order to ensure that the order of the stimulus presentation for P(e/c) and P(e/-c) did not influence participants' judgements, we ran an additional group of 20 participants with the reverse presentation order [i.e., they made judgements regarding P(e/-c) before P(e/c)]. In addition, we counterbalanced the order of the remaining judgements (familiarity, imageability and belief in causal powers). This new order did not influence the data in any significant way. Specifically, participants' beliefs in causal powers were significantly correlated with their judgements regarding P(e/c), imageability, and familiarity [r(18)'s = .68, .98, and .74 respectively], and were not significantly correlated with their judgements regarding P(e/-c) [r(18) = − .22].