# Estimating Causal Power between Binary Cause and Continuous Outcome

- Motoyuki Saito,
*University of California, Los Angeles*
- Patricia Cheng,
*University of California, Los Angeles*

## Abstract

Previous studies of causal learning heavily focused on binary
outcomes; little is known about causal learning with continuous outcomes. The
present paper proposes 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. We
systematically manipulated the type of outcome and the contingency information
and found 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 are discussed.

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