Constructing a More Powerful Test in Three-Level Cluster Randomized Designs (WP-07-15)
Experiments that involve nested structures may assign treatment conditions either to entire groups (such as schools), or subgroups (such as classrooms) or individuals (such as students). A key aspect of the design of such experiments includes knowledge of the intraclass correlation structure. This study provides methods for constructing a test for the treatment effect that is more powerful than the typical test based on level-3 unit means in three-level cluster randomized designs (with two levels of nesting). When the intraclass correlation structure at the second and third level is known the proposed test provides higher estimates of power because it preserves the degrees of freedom associated with the number of level-2 and level-1 units. The advantage in power estimates is more pronounced when the number of level-3 units is small.