Power Analysis on Repeated Measures Designs

  • Taylor King North Dakota State University
  • Curt Doetkott
  • Rhonda Magel North Dakota State University
Keywords: Variance Components, Compound Symmetry, First-Order Autoregressive, Toeplitz, Unstructured


A simulation study comparing powers of the multivariate analysis (PROC GLM) with using a mixed model (PROC MIXED) using a variety of covariance structures for various treatment, time, and interaction affect sizes in a repeated measures design is conducted.  Type 1 errors are estimated.  Powers are estimated for a variety of covariance structures when the actual covariance structure is AR(1).  It was found that the estimated powers for treatment effect were all very similar with PROC MIXED with the correct covariance structure having the largest estimated powers. When testing for time and interaction effect, it was found when in doubt that it was better to use a simpler covariance structure.  The powers were generally higher in this case than with a more complex covariance structure.

Author Biography

Rhonda Magel, North Dakota State University

Department of Statistics

North Dakota State University

Fargo, ND  58108


[1] Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., & Schabenberger, O. (2006). Appendix 1: Linear Mixed Model Theory. SAS® for Mixed Models, Second Edition (pp. 734-756). Cary, NC: SAS Institute.
[2] SAS Institute Inc. (2017). SAS/STAT® 14.3 User’s Guide. Cary, NC: SAS Institute Inc. Retrieved from http://support.sas.com/documentation/onlinedoc/stat/143/statug.pdf
[3] Littell, R. C. (2011). The Evolution of Linear Models in SAS: A Personal Perspective. SAS Global Forum 2011. Retrieved from http://support.sas.com/resources/papers/proceedings11/325-2011.pdf
[4] Littell, R.C., Henry, P.R., & Ammerman, C.J. (1998). Statistical Analysis of Repeated Measures Data Using SAS Procedures. J. Animal Science, 76. Retrieved from http://www.stat.ncsu.edu/people/arellano/courses/ST524/Fall08/Homeworks/Homework7/articles/Littell_mixed_JAS.pdf
[5] Guerin, L. & Stroup, W. W. (2000). A Simulation Study to Evaluate PROC MIXED Analysis of Repeated Measures Data. Annual Conference on Applied Statistics in Agriculture. Retrieved from http://newprairiepress.org/agstatconference/2000/proceedings/15
[6] Kincaid, C. (2005). Guidelines for Selecting the Covariance Structure in Mixed Model Analysis. SUGI 30 Proceedings. Retrieved from http://www2.sas.com/proceedings/sugi30/198-30.pdf
[7] Kowalchuk, R. K., Keselman, H. J., Algina, J., & Wolfinger, R. D. (2004). The Analysis of Repeated Measurements with Mixed-Model Adjusted F Tests. Educational and Psychological Measurement, 64. Retrieved from http://journals.sagepub.com/doi/abs/10.1177/0013164403260196
[8] Wolfinger, R. D. (1996). Heterogeneous Variance: Covariance Structures for Repeated Measures. Journal of Agricultural, Biological, and Environmental Statistics, 1(2). Retrieved from https://www.researchgate.net/profile/Russ_Wolfinger2/publication/272579574_Heterogeneous_Variance_Covariance_Structures_for_Repeated_Measures/links/5756da6808ae5c654903f3fe/Heterogeneous-Variance-Covariance-Structures-for-Repeated-Measures.pdf
[9] Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., & Schabenberger, O. (2006a). Chapter 5: Analysis of Repeated Measures Data. SAS® for Mixed Models, Second Edition (pp. 160-186). Cary, NC: SAS Institute.
[10] Field, A. (2010). A Bluffer’s Guide to ... Sphericity. BPS-MSC Newsletter 6 (1). Retrieved from http://www.discoveringstatistics.com/docs/sphericity.pdf
[11] Wolfinger, R.. D., & Chang, M. (1995). Comparing the SAS GLM and MIXED Procedures for Repeated Measures. SUGI Proceedings. Retrieved from https://support.sas.com/rnd/app/stat/papers/mixedglm.pdf
[12] Everitt, B.S. (1995). The Analysis of Repeated Measures: A Practical Review with Examples. Journal of the Royal Statistical Society. Series D (The Statistician), 44 (1). Retrieved from http://www.jstor.org/stable/2348622
[13] Gueorguieva, R. & Krystal, J. H. (2004). Move Over ANOVA: Progress in Analyzing Repeated-Measures Data and Its Reflection in Papers Published in the Archives of General Psychiatry. Archives of general psychiatry, 61. Retrieved from https://www.researchgate.net/profile/Ralitza_Gueorguieva/publication/5412094_Move_Over_ANOVA_Progress_in_Analyzing_Repeated-Measures_Data_andIts_Reflection_in_Papers_Published_in_the_Archives_of_General_Psychiatry/links/5617793308ae40a7199a94ca/Move-Over-ANOVA-Progress-in-Analyzing-Repeated-Measures-Data-andIts-Reflection-in-Papers-Published-in-the-Archives-of-General-Psychiatry.pdf
[14] Wang, Z. & Goonewardene, L. A. (2004). The use of MIXED models in the analysis of animal experiments with repeated measures data. Canadian Journal of Animal Science. Retrieved from https://era.library.ualberta.ca/files/crb68xb84k/cjas_84(1)
[15] Stroup, W. W. (1999). On Using PROC MIXED for Longitudinal Data. Annual Conference on Applied Statistics in Agriculture. Retrieved from http://newprairiepress.org/agstatconference/1999/proceedings/5
[16] Kiernan, K., Tao, J., & Gibbs, P. (2012). Tips and Strategies for Mixed Modeling with SAS/STAT® Procedures. SAS Global Forum 2012. Retrieved from http://support.sas.com/resources/papers/proceedings12/332-2012.pdf
[17] Littell, R. C., Pendergast, J., & Natarajan, R. (2000). Modelling covariance structure in the analysis of repeated measures data. Statistics in Medicine, 19(13). Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/1097-0258(20000715)19:13%3C1793::AID-SIM482%3E3.0.CO;2-Q/abstract
[18] Moser, E. B. (2004). Repeated Measures Modeling With PROC MIXED. SUGI 29 Proceedings. Retrieved from http://www2.sas.com/proceedings/sugi29/188-29.pdf
[19] Oberfeld, D. & Franke, T. (2013) Evaluating the robustness of repeated measures analyses: The case of small sample sizes and nonnormal data. Behav Res, 45. Retrieved from https://www.staff.uni-mainz.de/oberfeld/downloads/oberfeld_franke_2013_BRM.pdf
[20] Keselman, H. J., Algina, J., Kowalchuk, R. K. & Wolfinger, R. D. (1999). The Analysis of Repeated Measurements: A Comparison of Mixed-Model Satterthwaite F Tests and a Nonpooled Adjusted Degrees of Freedom Multivariate Test. Communications in Statistics - Theory and Methods, 28(12). Retrieved from http://home.cc.umanitoba.ca/~kesel/cis1999b.pdf
[21] Kenward, M. G. & Roger, J. H. (1997). Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood. Biometrics, 53(3). Retrieved from http://www.public.iastate.edu/~dnett/S511/KR.pdf
[22] Bradley, J. V. (1978). Robustness? British Journal of Mathematical & Statistical Psychology, 31. Retrieved from http://onlinelibrary.wiley.com/doi/10.1111/j.2044-8317.1978.tb00581.x/abstract
[23] Park, T., Park, J., and Davis, C. (2001). Effects of covariance model assumptions on hypothesis tests for repeated measurements: analysis of ovarian hormone data and pituitary-pteryomaxillary distance data. Statistics in Medicine, 20: 2441-2453.
How to Cite
King, T., Doetkott, C., & Magel, R. (2018, February 28). Power Analysis on Repeated Measures Designs. EPH - International Journal of Mathematics and Statistics (ISSN: 2208-2212), 4(2), 28-42. Retrieved from https://ephjournal.com/index.php/ms/article/view/507