A unified method for determining the sample size needed for evaluation of mean differences in hierarchical research designs

Abstract

Hierarchical data sets arise when data for individuals (e.g., students, clients, or citizens) are nested within various groups (e.g., classes, hospitals, or regions), and often appear in social science research. For such data, a hierarchical linear model, which considers the dependent structure of individuals' data within the same groups, is useful. In the present research, we derived formulas in order to evaluate the sample size needed for research designs with hierarchical data, focusing on the mean difference between 2 groups for cases of both multisite randomized trials (MRTs) and cluster randomized trials (CRTs). These formulas were derived in light of both statistical power and the confidence interval of the effect size. Additionally, for practical purposes, numerical tables were constructed that could easily be used to determine the sample size needed. The numerical tables for multisite randomized trials can also be used for paired designs, such as repeated measures designs and randomized block designs.