The Power of the Test in Three-Level Designs

Field experiments that involve nested structures may assign treatment conditions either to entire groups (such as classrooms or schools), or individuals within groups (such as students). Since field experiments involve clustering, key aspects of their design include knowledge of the intraclass correlation structure and the sample sizes necessary to achieve adequate power to detect the treatment effect. This study provides methods for computing power in three-level designs, where for example, students are nested within classrooms and classrooms are nested within schools. The power computations take into account clustering effects at the classroom and at the school level, sample size effects (e.g., number of students, classrooms, and schools), and covariate effects (e.g., pre-treatment measures). The methods are generalizable to quasi-experimental studies that examine group differences in an outcome, or associations between predictors and outcomes.