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Educational research often studies subjects that are in naturally clusteredgroups of classrooms or schools. When designing a randomized experiment toevaluate an intervention directed at teachers, but with effects on teachers andtheir students, the power or anticipated variance for the treatment effectneeds to be examined at both levels. If the treatment is applied to clusters,power is usually reduced. At the same time, a cluster design decreases theprobability of contamination, and contamination can also reduce power to detecta treatment effect. Designs that are optimal at one level may be inefficientfor estimating the treatment effect at another level. In this paper we studythe efficiency of three designs and their ability to detect a treatment effect:randomize schools to treatment, randomize teachers within schools to treatment,and completely randomize teachers to treatment. The three designs are comparedfor both the teacher and student level within the mixed model framework, and asimulation study is conducted to compare expected treatment variances for thethree designs with various levels of correlation within and between clusters.We present a computer program that study designers can use to explore theanticipated variances of treatment effects under proposed experimental designsand settings.

Experimental designs for multiple-level responses, with application to a large-scale educational intervention