Sample-Size Adjustments (PMSE) To Accommodate Power-Analysis Parameter Uncertainties: Two Correlated Means Illustrations

• Activity Number: 81
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Social Statistics Section
• Author(s): Alvah C. Bittner*+ and Moataz Eltoukhy
• Companies: Bittner & Associates and University of Miami
• Keywords: Power Analyses ; Parameter Uncertainties ; Propagated Variance ; Sample Size Adjustments ; Practitioner Surveys ; Robustness

Abstract

Power-analyses, for required sample sizes (N), are frequently made with no or arbitrary adjustments for parameter uncertainties, often with substantial ethical and competiveness issues. Reviewed are issues with current informal and formal approaches for determining adequate sample-sizes (esp., kurtosis with variance uncertainties). A generalized adjustment approach is delineated based on a robust analytic function for initially estimating N: U(Parameters, N) = Tau(a,1-Beta) that is solved for initial N with "fixed" parameters and selected Tau. Adjusted Ns are subsequently based on relative increases in U's variance when using uncertain variance estimates "Var(V)" This is assessed via the classic propagation-of-mean-square-error approach (PMSE, Deming, 1966). Two correlated means applications of PMSE are illustrated that minimize kurtosis effects. PMSE - with attendance to sensitive assumptions - is recommended as an ethical and efficient alternative for addressing parameter uncertainties in statistical power analyses.