RE: st: multiple regression power analysis using powerreg

[Cameron McIntosh <cnm100@hotmail.com>]

Nancie,
Without knowing anything about your study, survey methodology or population of interest, I think I can still say that in part you're talking about sample size determination using a finite population correction factor (FPC), at least for finite population parameters (i.e., means, totals).  However, with regression coefficients you also get into superpopulation parameter territory (i.e., parameters representing stochastic data-generating mechanisms, rather than just direct functions of the observations in the sample). I also imagine you had some idea about meaningful effect sizes. I suggest you do some more reading:
Naing, L., Winn, T., & Rusli, B.N. (2006). Practical Issues in Calculating the Sample Size for Prevalence Studies. Archives of Orofacial Sciences, 1, 9-14.http://www.kck.usm.my/ppsg/aos/Vol_1/09_14_Ayub.pdf

Sarndal, C.E., Swensson, B., & Wretman, J.H. (1989). The Weighted Residual Technique for Estimating the Variance of the General Regression Estimator of the Finite Population Total. Biometrika, 76, 527-537.

Graubard, B.I., & Korn, E.L. (2002). Inference for Superpopulation Parameters Using Sample Surveys. Statistical Science, 17(1), 73-96. 

Fuller, W.A., & Wu, Y.Y. (2006). Estimation of Regression Parameters with Survey Data. Proceedings of Statistics Canada Symposium 2006, Methodological Issues in Measuring Population Health. http://www.statcan.gc.ca/pub/11-522-x/2006001/article/10417-eng.pdf

Fuller, W. A. (2002). Regression estimation for survey samples. Survey Methodology, 28, 5-23. http://www.statcan.gc.ca/ads-annonces/12-001-x/6408-eng.pdf

Pfeffermann, D., & Sverchkov, M. (1999). Parametric and semi-parametric estimation of regression models fitted to survey data. Sankhyā, Series B, 61(Pt. 1), 166-186. http://sankhya.isical.ac.in/search/61b1/61b1dan.pdf

and also:

Murphy, K.R., Myors, B., & Wolach, A. (2009). Statistical Power Analysis: A Simple and General Model for Traditional and Modern Hypothesis Tests (3rd Ed.). Mahwah, NJ: Erlbaum.

Hoenig, J.M., & Heisey, D.M. (2001). The Abuse of Power: The Pervasive Fallacy of Power Calculations for Data Analysis. The American Statistician, 55(1), 19-24. http://druginfo.creighton.edu/EBMCertificate/The%20abuse%20of%20power.pdf
Baguley, T. (2004). Understanding statistical power in the context of applied research. Applied Ergonomics, 35(2), 73-80.http://nottinghamtrent.academia.edu/ThomBaguley/Papers/212458/Understanding_Statistical_Power_In_the_Context_of_Applied_Research

Qian, J., Ou, C.-Q., Wang, T., & Chen, P.-Y. (2009).  The Study on Reasonability of Retrospective Power. In: Proceedings of the Second International Conference on Information and Computing Science, May 21-22, 2009, vol 4., pp. 323-326. 
Lenth, R.V. (2001). Some Practical Guidelines for Effective Sample Size Determination. The American Statistician, 55(3), 187-193.

Maxwell, S.E., Kelley, K., & Rausch, J.R. (2008). Sample Size Planning for Statistical Power and Accuracy in Parameter Estimation. Annual Review of Psychology, 59, 537-563.http://nd.edu/~kkelley/publications/articles/Maxwell_Kelley_Rausch_2008.pdf ;

O'Keefe, D.J. (2007). Brief Report: Post Hoc Power, Observed Power, A Priori Power, Retrospective Power, Prospective Power, Achieved Power: Sorting Out Appropriate Uses of Statistical Power Analyses. Communication Methods and Measures, 1(4), 291-299.http://www.dokeefe.net/pub/OKeefe07CMM-posthoc.pdf
Kelley, K., Maxwell, S.E., & Rausch, J.R. (2003). Obtaining power or obtaining precision: Delineating methods of sample-size planning. Evaluation and the Health Professions, 26(3), 258-287.http://nd.edu/~kkelley/publications/articles/Kelley_Maxwell_Rausch_2003.pdf

Ultimately, a fully-specified simulation study might be the best way to go.
Cam

Date: Mon, 2 Jan 2012 15:26:57 -0500
From: nancie.celini@thinkcab.com
Subject: st: multiple regression power analysis using powerreg
To: statalist@hsphsun2.harvard.edu


I hope someone can help me. I did a survey (validated) to collect data from a fixed population of 600 as a convenience sample for an academic study. My response rate was  14% or 83 responses. I am being asked to conduct a power analysis retrospectively. Has anyone used powerreg in Stata for this purpose on a survey/convenience sample in this manner? What advice can you provide - I understand this a rather subjective number so need to know the inputs required in this type of analysis to yield the best result. Thank you. Nancie
 		 	   		  
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