Random assignment to groups is the foundation for scientifically rigorous clinical trials. But assignment is challenging in group randomized trials when only a few units (schools) are assigned to each condition. In the DRSR project, we assigned 39 rural Pennsylvania and Ohio schools to three conditions (rural, classic, control). But even with 13 schools per condition, achieving pretest equivalence on important variables is not guaranteed. We collected data on six important school-level variables: rurality, number of grades in the school, enrollment per grade, percent white, percent receiving free/assisted lunch, and test scores. Key to our procedure was the inclusion of school-level drug use data, available for a subset of the schools. Also, key was that we handled the partial data with modern missing data techniques. We chose to create one composite stratifying variable based on the seven school-level variables available. Principal components analysis with the seven variables yielded two factors, which were averaged to form the composite inflate suppress (CIS) score which was the basis of stratification. The CIS score was broken into three strata within each state; schools were assigned at random to the three program conditions from within each stratum, within each state. Results showed that program group membership was unrelated to the CIS score, the two factors making up the CIS score, and the seven items making up the factors. Program group membership was not significantly related to pretest measures of drug use (alcohol, cigarettes, marijuana, chewing tobacco; smallest p>.15), thus verifying that pretest equivalence was achieved.
Graham, J.W., Pettigrew, J., Miller-Day, M., Krieger, J.L., Zhou, J, & Hecht, M.L. (2013). Random assignment of schools to groups in the Drug Resistance Strategies Rural Project: Some new methodological twists. Prevention Science, 15(4), 516-525. DOI 10.1007/s11121-013-0403-9