Estimating Causal Power between Binary Cause and Continuous Outcome

Previous studies of causal learning heavily focused on binary outcomes; little is known about causal learning with continuous outcomes. The present paper proposes a qualitative extension of the causal power theory to the situation where a binary cause influences a continuous effect, and induces causal power under various ceiling situations with the continuous outcomes. To test the predictions, we systematically manipulated the type of outcome (continuous vs. percentage vs. binary) and the contingency information. The experiment shows that people estimate causal strength based on the linear-sum rule for continuous outcomes and the noisy-OR rule for binary outcomes. In the partial ceiling situation where causal power is partially inferred but not precisely estimated, the distribution of participants’ judgments was bimodal with one mode at the minimum value and the other at the maximum value, suggesting some participants made conservative estimates while others made optimistic estimates. These results are generally consistent with the predictions of the causal power theory. Theoretical implications and future directions are discussed.