In this paper, we consider testing the location parameter with multilevel (or hierarchical) data. A general family of weighted test statistics are introduced. This family includes extensions to the case of multilevel data of familiar procedures like the t, the sign and the Wilcoxon signed-rank tests. Under mild assumptions, the test statistics have a null limiting normal distribution which facilitates their use. An investigation of the relative merits of selected members of the family of tests is achieved theoretically by deriving their relative asymptotic efficiency (ARE) and empirically via a simulation study. It is shown that the performance of a test depends on the clusters configura- tions and on the intracluster correlations. Explicit formulas for optimal weights and a discussion of the impact of omitting a level are provided for 2 and 3-level data. It is shown that using appropriate weights can greatly improve the performance of the tests.
Published December 2006 , 23 pages