The Power of the Test for Treatment Effects in Three-Level Cluster Randomized Designs

Abstract Experiments that involve nested structures often assign entire groups (such as schools) to treatment conditions. Key aspects of the design of such experiments 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 cluster randomized balanced designs (with two levels of nesting), where, for example, students are nested within classrooms and classrooms are nested within schools and schools are assigned to treatments. The power computations take into account nesting effects at the second (classroom) and at the third (school) level, sample size effects (e.g., number of schools, classrooms, and individuals), and covariate effects (e.g., pretreatment measures). The methods are applicable to quasi-experimental studies that examine group differences in an outcome.