Do children misbehave during a full moon? Are Asians “pushy”? Are the members of minority group X particularly prone to alcoholism?

People often fall prey to developing such associations even though they are entirely illusory—that is, the actual statistics of the environment warrant no such beliefs. In the laboratory, those illusory correlations are readily evoked in participants by manipulations of frequency. In a classic study by Hamilton and Gifford nearly 40 years ago, participants were presented with instances of behaviors by two groups of (hypothetical) people; Group A and Group B. As shown in the table below, each group was twice as likely to engage in desirable behaviors than undesirable behaviors, but there were twice as many “A” people overall than there were “B’s.”

Do “B’s” behave more badly than “A’s”?

No. If you encounter an “A” there is a 30% chance (8/(8+18)) that they might misbehave, and the same is true for a “B” (4/(9+4)). Notwithstanding, when participants are asked to judge the prevalence of desirable behaviors after being exposed to the above fictitious people one-by-one, they believe that desirable behaviors are far more common for Group A whereas undesirable behaviors are seen as being more representative of Group B.

This illusory perception that undesirable behaviors are more common among members of a minority group is easy to induce, and it is notably enhanced by a person’s political views. A common explanation of the phenomenon appeals to the fact that badly behaving members of a minority “stick out more”, because they are observed less frequently. In the above table, the most frequent event is an “A” person behaving in a desirable manner. The least frequent event is a “B” person engaging in an undesirable behavior—thereby “sticking out”. And one governing principle of memory is that distinctive events, things that “stick out”, are remembered better. Presto, children are thought to misbehave during a full moon or Asians are “pushy.”

Does this mean people are necessarily prejudiced? Does our cognitive apparatus prevent us from learning the true structure of our environment? No, far from it. Even the strong and pervasive illusory correlations just described disappear with additional training, as recent research has shown.

Indeed, people can be very good at discerning causal relationships. The above table of hypothetical behaviors is very similar to the type of stimulus contingencies that are studied in causal learning experiments. In a recent article in Learning and Behavior, a journal of the Psychonomic Society, researchers Liu and Luhmann investigated the trial-by-trial learning processes in experiments that somewhat resemble those known to give rise to illusory correlations. It is crucial to understand those trial-by-trial events because they may differentiate between different explanations and theories of causal learning.

Liu and Luhmann presented participants with a causal learning task in which the stimuli were hypothetical patients who either did or did not have a fictitious disease and who either did or did not take a particular medication. Aside from the change in cover story and the use of different contingencies, this task was nearly identical to the illusory-correlation paradigm from above. One crucial difference was that participants additionally had to perform an unrelated tone-discrimination task. For this task people had to decide which of three tones was presented via headphones. The only purpose of the tone-discrimination task was to provide a “secondary-task” measure of how much participants had to focus on the primary, causal-learning task. We all know that when we drive a car through heavy traffic, the conversation with our passengers slows down compared to when we are cruising on a deserted country road. In the same way, the speed of responding to a secondary task tells us how much people are occupied by the primary learning task.

Liu and Luhmann found that secondary-task responses were slower during the “minority” trials (equivalent to Group B misbehaving) than during the “majority” trials (Group A engaging in desirable behaviors), suggesting that the former trials required more cognitive processing resources. It appeared as though the violation of expectancy, by an unusual trial, triggered more intensive processing.

In a follow-up experiment, Liu and Luhmann changed the statistical structure of the task halfway through training, such that an expectancy that was built up initially was violated during the second half. As expected, people’s secondary-task performance suffered when the statistical structure of the task changed, although it quickly sped up again as the new structure became expected.

In a final experiment, Liu and Luhmann showed that the secondary-task effects were driven by people’s beliefs about what they had learned: The more they thought they had learned about the relationship between the medication and the disease, the greater the disruption of secondary-task performance on “minority” trials.

Taken together, the three studies suggest that people generate expectations during causal learning. When those expectations are violated, additional processing is required, and that additional processing can be detected with a secondary task.

An intriguing implication of this result is that when we associate the moon to our children’s bad behavior, this illusory correlation arises because we don’t expect the rare events that we then strongly associate.