Multilevel Models II: Testing the Difference in Group Means in Two-Level Multisite Randomized Trials

Multilevel Models II: Testing the Difference in Group Means in Two-Level Multisite Randomized Trials

In contrast to randomizing clusters (Chapter 6), another choice with two-level designs is to randomize units within clusters. This essentially means that each cluster, or “site,” becomes its own small trial. This allows researchers to estimate how treatment effects vary across sites. So-called multisite randomized trials are also popular in social and health experiments (Raudenbush & Liu, 2000). In this chapter, we explore power analyses for these designs.

Suppose we have $j=\{1,2,\dots p\}$ treatments (in this volume, $p=2$), each with $i=\{1,2,\dots n\}$ units assigned to them within each cluster, and each set of units is assigned to ...