title: Understanding and estimating the power to detect cross-level interaction effects in multilevel modeling.
abstract: Cross-level interaction effects lie at the heart of multilevel contingency and interactionism theories. Researchers have often lamented the difficulty of finding hypothesized cross-level interactions, and to date there has been no means by which the statistical power of such tests can be evaluated. We develop such a method and report results of a large-scale simulation study, verify its accuracy, and provide evidence regarding the relative importance of factors that affect the power to detect cross-level interactions. Our results indicate that the statistical power to detect cross-level interactions is determined primarily by the magnitude of the cross-level interaction, the standard deviation of lower level slopes, and the lower and upper level sample sizes. We provide a Monte Carlo tool that enables researchers to a priori design more efficient multilevel studies and provides a means by which they can better interpret potential explanations for nonsignificant results. We conclude with recommendations for how scholars might design future multilevel studies that will lead to more accurate inferences regarding the presence of cross-level interactions.
authors.affiliation: Department of Management, School of Business, University of Connecticut, CT 06269-1041, USA. John.Mathieu@business.uconn.edu
authors.forename: John E
authors.initials: JE
authors.lastname: Mathieu
authors.forename: Herman
authors.initials: H
authors.lastname: Aguinis
authors.forename: Steven A
authors.initials: SA
authors.lastname: Culpepper
authors.forename: Gilad
authors.initials: G
authors.lastname: Chen
mesh_terms: D006801:Humans; D007398:Interpersonal Relations; D008962:Models, Theoretical; D009010:Monte Carlo Method; D055361:Multilevel Analysis; D011585:Psychology, Applied / Q000379:methods*