Inferences about population correlations

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An important, scientific meaning of the term, "relationship," is the extent to which the presence or absence of one attribute provides useful information about the presence or absence of another. For example, if there is a relationship between a symptom and a disease, then the presence of the symptom suggests the presence of the disease. Another example would be the relationship between a people's employment test scores and their subsequent performance on the job. Using two different but related lines of research, we plan to investigate how people form and maintain beliefs about relationships. In one series of studies, we will employ both computer simulations and experiments with human beings to investigate the counterintuitive proposition that, under some mathematical conditions, people can detect relationships more accurately in small than in large data sets. Recent research in Israel and Sweden has produced contradictory evidence on this topic. However, our pilot research explains the disagreement, and demonstrates that the mathematical structure of our environment does indeed favor small rather than large samples, under certain conditions. We plan to conduct additional research to determine whether human beings can exploit this feature of the environment when they form beliefs about relationships.The second series of studies will investigate the conditions under which people form and maintain false beliefs, which are assertions that a relationship exists when in fact there is no relationship. This phenomenon, known as illusory correlation, has been studied extensively with regard to prejudice and to the validity of personality tests. We plan to examine how the mathematical environment described above, together with current psychological theory, influences illusory correlation.The results of our investigations will be relevant to what has become a central issue in our understanding of the nature of human thought--that is, the question of whether and to what degree people's limited ability to process information can be adaptive in different environments.