The purpose of this paper is to demonstrate in detail how the Empirical Bayes (EB) statistical estimation strategy can be applied to an important class of educational research contexts. EB methods are tailored specifically to the analysis of data with a hierarchical structure. For instance, investigators may be interested in discovering how effects within schools (e.g., the relationship between student social class and achievement) vary as a function of differences between schools (e.g., policies and practices). Similarly, meta-analysts often wish to find out how differences between experimental and control groups within studies vary as a function of differences between studies (e.g., how treatments are implemented). Developmental psychologists care about how children's intellectual growth rates vary as a function of different pre-school experiences. In each case parameters at one level (within schools, within studies, and within children) vary as a function of parameters at another level (between schools, between studies, between children). This paper explains how the EB strategy works when the central goal of an investigation is to estimate the second level parameters (i.e., the between-group parameters), and an important ancillary goal is to assess the adequacy of a hierarchical linear model for fitting such hierarchical data. (Author)