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

Abstract Experiments that involve nested structures may assign treatment conditions either to subgroups (such as classrooms) or individuals within subgroups (such as students). The design of such experiments requires knowledge of the intraclass correlation structure to compute the sample sizes necessary to achieve adequate power to detect the treatment effect. This study provides methods for computing power in three-level block randomized balanced designs (with two levels of nesting) where, for example, students are nested within classrooms and classrooms are nested within schools. 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 level-1, level-2, and level-3 units), and covariate effects (e.g., pretreatment measures). The methods are generalizable to quasi-experimental studies that examine group differences on an outcome.