Standard Errors and Sample Sizes for Two-Level Research

The hierarchical linear model approach to a two-level design is considered, some variables at the lower level having fixed and others having random regression coefficients. An approximation is derived to the covariance matrix of the estimators of the fixed regression coefficients (for variables at the lower and the higher level) under the assumption that the sample sizes at either level are large enough. This covariance matrix is expressed as a function of parameters occurring in the model. If a research planner can make a reasonable guess as to these parameters, this approximation can be used as a guide to the choice of sample sizes at either level.