Calculate the optimal sample allocation that minimizes the variance of treatment effect in multilevel randomized trials under fixed budget and cost structure, perform power analyses with and without accommodating costs and budget. The references for proposed methods are: (1) Shen, Z. (in progress). Using optimal sample allocation to improve statistical precision and design efficiency for multilevel randomized trials. (unpublished doctoral dissertation). University of Cincinnati, Cincinnati, OH. (2) Shen, Z., & Kelcey, B. (revise & resubmit). Optimal sample allocation accounts for the full variation of sampling costs in cluster-randomized trials. Journal of Educational and Behavioral Statistics. (3) Shen, Z., & Kelcey, B. (2018, April). Optimal design of cluster randomized trials under condition- and unit-specific cost structures. Roundtable discussion presented at American Educational Research Association (AERA) annual conference. (4) Champely., S. (2018). pwr: Basic functions for power analysis (Version 1.2-2) [Software]. Available from <https://CRAN.R-project.org/package=pwr>.
