Inferences about population correlations

“关系”一词的一个重要的科学含义是，一种属性的存在或不存在在多大程度上提供了关于另一种属性存在或不存在的有用信息。例如，如果症状和疾病之间存在关系，则症状的存在表明疾病的存在。另一个例子是一个人的就业测试分数和他们随后的工作表现之间的关系。使用两个不同但相关的研究路线，我们计划调查人们如何形成和保持对关系的信念。 在一系列研究中，我们将使用计算机模拟和人类实验来研究一个违反直觉的命题，即在某些数学条件下，人们可以在小数据集中比在大数据集中更准确地发现关系。以色列和瑞典最近的研究在这个问题上产生了相互矛盾的证据。然而，我们的初步研究解释了这种分歧，并表明在某些条件下，我们环境的数学结构确实有利于小样本而不是大样本。我们计划进行更多的研究，以确定人类在形成对关系的信念时是否可以利用环境的这一特征。第二系列研究将调查人们形成和维持错误信念的条件，即在事实上没有关系的情况下断言关系存在。这种现象，被称为虚幻的相关性，已经被广泛研究了偏见和人格测试的有效性。我们计划研究上述的数学环境，以及当前的心理学理论，如何影响虚幻的相关性。我们的研究结果将与我们理解人类思维本质的核心问题有关，即人们处理信息的有限能力是否以及在多大程度上能够适应不同的环境。

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.