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

Area of Science:

• Multilevel modeling
• Statistical power analysis
• Interactionism theories

Background:

• Cross-level interactions are central to multilevel contingency and interactionism theories.
• Evaluating statistical power for detecting cross-level interactions has been a significant challenge.
• Previous research lacked methods for assessing the power of tests for cross-level interactions.

Purpose of the Study:

• To develop a method for evaluating the statistical power of tests for cross-level interactions.
• To identify key factors influencing the power to detect cross-level interactions.
• To provide a tool for researchers to design more efficient multilevel studies.

Main Methods:

• Development of a statistical power evaluation method for cross-level interactions.
• Conducting a large-scale simulation study to verify the method's accuracy.
• Analyzing the relative importance of factors affecting statistical power.

Main Results:

• Statistical power is primarily determined by the magnitude of the cross-level interaction.
• The standard deviation of lower-level slopes significantly impacts power.
• Both lower and upper-level sample sizes are crucial determinants of statistical power.

Conclusions:

• A Monte Carlo tool is provided to aid a priori study design for multilevel research.
• The tool helps researchers interpret nonsignificant findings more effectively.
• Recommendations are offered for designing future multilevel studies to improve inferences about cross-level interactions.