Estimating confidence intervals for eigenvalues in exploratory factor analysis

Exploratory factor analysis (EFA) has become a common procedure in educational and psychological research. In the course of performing an EFA, researchers often base the decision of how many factors to retain on the eigenvalues for the factors. However, many researchers do not realize that eigenvalues, like all sample statistics, are subject to sampling error, which means that confidence intervals (CIs) can be estimated for each eigenvalue. In the present article, we demonstrate two methods of estimating CIs for eigenvalues: one based on the mathematical properties of the central limit theorem, and the other based on bootstrapping. References to appropriate SAS and SPSS syntax are included. Supplemental materials for this article may be downloaded from http://brm.psychonomic-journals.org/content/supplemental.