Bridging the divide between causal illusions in the laboratory and the real world: the effects of outcome density with a variable continuous outcome.

Illusory causation refers to a consistent error in human learning in which the learner develops a false belief that two unrelated events are causally associated. Laboratory studies usually demonstrate illusory causation by presenting two events-a cue (e.g., drug treatment) and a discrete outcome (e.g., patient has recovered from illness)-probabilistically across many trials such that the presence of the cue does not alter the probability of the outcome. Illusory causation in these studies is further augmented when the base rate of the outcome is high, a characteristic known as the outcome density effect. Illusory causation and the outcome density effect provide laboratory models of false beliefs that emerge in everyday life. However, unlike laboratory research, the real-world beliefs to which illusory causation is most applicable (e.g., ineffective health therapies) often involve consequences that are not readily classified in a discrete or binary manner. This study used a causal learning task framed as a medical trial to investigate whether similar outcome density effects emerged when using continuous outcomes. Across two experiments, participants observed outcomes that were either likely to be relatively low (low outcome density) or likely to be relatively high (high outcome density) along a numerical scale from 0 (no health improvement) to 100 (full recovery). In Experiment 1, a bimodal distribution of outcome magnitudes, incorporating variance around a high and low modal value, produced illusory causation and outcome density effects equivalent to a condition with two fixed outcome values. In Experiment 2, the outcome density effect was evident when using unimodal skewed distributions of outcomes that contained more ambiguous values around the midpoint of the scale. Together, these findings provide empirical support for the relevance of the outcome density bias to real-world situations in which outcomes are not binary but occur to differing degrees. This has implications for the way in which we apply our understanding of causal illusions in the laboratory to the development of false beliefs in everyday life.