Understanding and estimating the power to detect cross-level interaction effects in multilevel modeling

Correction Notice: An Erratum for this article was reported in Vol 97(5) of Journal of Applied Psychology (see record 2012-18665-001). The article contained production-related errors in a number of the statistical symbols presented in Table 1, the Power in Multilevel Designs section, the Simulation Study section, and the Appendix.] 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. (PsycINFO Database Record (c) 2012 APA, all rights reserved).