Optimal Design in Multilevel Experiments
The presence of correlated responses complicates the analysis of data obtained from trials with nested data. The correct statistical model to analyze data from such experiments is the multilevel model, which explicitly takes nesting of subjects within groups into account by modeling random effects at the subjects and group level (Goldstein, 2003; Hox, 2002; Raudenbush & Bryk, 2002; Snijders & Bosker, 1999). Ignoring the nested data structure may result in type I or type II errors for the test on treatment effect, and consequently in incorrect conclusions with respect to the effectiveness of the experimental treatment condition. In addition, nesting of subjects within groups has implications for the calculation of the optimal design. Not only the total sample size needs to be calculated, but the optimal allocation of units as well. That is, should we sample many small groups or just a few large groups? Of course, a design with many groups and many subjects per group results in maximal statistical power, but is often not feasible because of limitations on the budget and on the number of subjects that are willing to participate in the trial.