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IES Grant

Title: A General Framework for Statistical Power Analysis with Non-normal and Missing Data through Monte Carlo Simulation
Center: NCER Year: 2014
Principal Investigator: Zhang, Zhiyong Awardee: University of Notre Dame
Program: Statistical and Research Methodology in Education      [Program Details]
Award Period: 3 years (7/1/146/30/17) Award Amount: $573,097
Type: Methodological Innovation Award Number: R305D140037

Co-Principal Investigator: Ke-Hai Yuan (Notre Dame)

The increasing complexity of education research poses great challenges on existing techniques used to estimate statistical power. For example, education research often involves longitudinal and multilevel designs as well as advanced techniques such as structural equation and multilevel models. Furthermore, practical data in education are often not normally distributed and are incomplete. Without careful consideration of the complexity of study designs and the impact of non-normal data and missing data on power estimation, the validity of education research can be weakened.

In this project, researchers will develop a general method to enable the specification of models including structural equation models and multilevel models as well missing data mechanisms and non-normality of data through drawing path diagrams. The researchers will then develop methods for simulating data based on those models and methods for calculating statistical power based on repeated simulations, with the resulting methods being robust to non-normal data and missing data. Researchers will also develop software called MCpower to conduct power analysis via the proposed framework. MCpower will run as a web application and can be used locally on a personal computer or remotely on a Web server within a web browser. The project is expected to offer the community of education researchers an easy-to-use and general-purpose tool to conduct sophisticated statistical power analysis for structural equation and multilevel models with non-normal and missing data.


Journal article, monograph, or newsletter

Cain, M.K., Zhang, Z., and Yuan, K.H. (2017). Univariate and Multivariate Skewness and Kurtosis for Measuring Nonnormality: Prevalence, Influence and Estimation. Behavior Research Methods, 49(5), 1716–1735.

Liu, H., and Zhang, Z. (2017). Logistic Regression With Misclassification in Binary Outcome Variables: A Method and Software. Behaviormetrika, 44(2), 447–476.

Mai, Y., and Zhang, Z. (2018). Software Packages for Bayesian Multilevel Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 1–9.

Mai, Y., Zhang, Z., and Wen, Z. (2018). Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression With Latent Variables. Structural Equation Modeling: A Multidisciplinary Journal, 1–13.

Yuan, K.H., Zhang, Z., and Zhao, Y. (2017). Reliable and More Powerful Methods for Power Analysis in Structural Equation Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 24(3), 315–330.

Zhang, Z. (2016). Modeling Error Distributions of Growth Curve Models Through Bayesian Methods. Behavior Research Methods, 48(2), 427–444.

Zhang, Z., and Yuan, K. (2016). Robust Coefficients Alpha and Omega and Confidence Intervals with Outlying Observations and Missing Data: Methods and Software. Educational and Psychological Measurement, 76(3): 387–411.


Mai, Y., and Zhang, Z. (2016, July). Statistical Power Analysis for Comparing Means with Binary or Count Data Based on Analogous ANOVA. In The Annual Meeting of the Psychometric Society (pp. 381–393). Springer, Cham.