The Effect of Nonnormality of Level 1 and Level 2 Errors on Statistical Power: A Comparison Between Monte Carlo Results and Optimal Design Software for Two-Level Hierarchical Linear Modeling

• In Event: Power and Design, Model Misspecification, and Multilevel Modeling

Abstract

A Monte Carlo simulation approach was conducted to study the accuracy level of power provided by Optimal Design (OD) software and to examine to what extent the impact of non-normal distributions, such as Chi-square distribution with df = 4 and df=8, on power estimated by OD. The major findings include 1) the power values estimated by OD are quite reliable. 2) the violation of normality of level-2 errors is more serious when the distribution is more skewed (Chi-square, df=4). And, such violation tends to increase power values in majority of cases. 3) the effect of Chi-square distribution of level-1 errors on power is found to be mixed.

Authors

• Chu-Ting Chung, University of Minnesota

• Robert C. Delmas, University of Minnesota

• Michael R. Harwell, University of Minnesota