Design Issues for Experiments in Multilevel Populations

For the design of e,rperiments in multilevel papulations the following questions may arise: What is the optimal level of randomization ? Given a certain budget for sampling and measuring, what is the optimal allocation of units? What is the required budget for obtaining a certain power on the test of no treatment effect ? In this article these questions will be dealt with for populations with two or three levels of nesting and contitmous outcomes. Multilevel models are used to model the relationship between experimental condition and the outcome variable. The estimator of the regressiot, coefficient associated with treatment condition, a parameter assumed to bej~Lred in this paper; is of main interest and should be estimated as efficiently as possible. Therefi)re, its variance is used as a criterion for optimizing the level of randomization attd the allocation of units.