A solution to dependency: using multilevel analysis to accommodate nested data Supplemental simulation and analysis

Simulations and analyses were conducted in R64 2.11.111 (R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2010)). In all simulations, a standardized (i.e., all variables have a mean of 0 and standard deviation of 1), two-level multilevel model was used, where individual observations i are nested within clusters j. To clarify the simulations, we use an example in which the individual observations are made on cells, and the clusters in which the cells are nested are mice. In our example, we wish to test whether cells from wild type (WT) and knockout (KO) mice differ with respect to a continuous and normally distributed characteristic of the cell, Y . Note that WT vs. KO (i.e., genotype) is our dichotomous experimental variable, X, and X only varies over, not within, mice (i.e., cells harvested from one mouse always have the same genotype). The multilevel model for the present example is given by: