Type ICCx(ICCy) ρxz (ρyz) N   TypeI error Mean Variance Mean Variance Mean Variance 1 0.67 0.305 100 theoretical 0.391 0.0163 0.391 0.0162 0 0.0095 0.05         empirical 0.395 0.0177 0.398 0.0178 -0.002 0.0103 0.061   0.67 0.305 400 theoretical 0.391 0.0041 0.391 0.0041 0 0.0024 0.05         empirical 0.392 0.0041 0.393 0.0042 -0.001 0.0023 0.045   0.67 0.5 100 theoretical 0.71 0.0212 0.71 0.0212 0 0.0146 0.05         empirical 0.72 0.0229 0.723 0.0233 -0.003 0.0161 0.058   0.67 0.5 400 theoretical 0.71 0.0053 0.71 0.0053 0 0.0036 0.05         empirical 0.712 0.0053 0.714 0.0055 -0.001 0.0036 0.044 2 0.67 0.305 100 theoretical 0.391 0.0166 0.391 0.0168 0 0.01 0.05         empirical 0.395 0.0183 0.398 0.018 -0.003 0.0106 0.051   0.67 0.305 400 theoretical 0.391 0.0042 0.391 0.0042 0 0.0025 0.05         empirical 0.394 0.0042 0.393 0.0041 0.001 0.0026 0.048   0.67 0.5 100 theoretical 0.71 0.0226 0.71 0.0222 0 0.0167 0.05         empirical 0.724 0.027 0.728 0.0269 -0.004 0.0201 0.039   0.67 0.5 400 theoretical 0.71 0.0056 0.71 0.0056 0 0.004 0.05         empirical 0.715 0.0058 0.713 0.0057 0.002 0.0044 0.048

Theoretical variance estimates are medians over 4000 simulated samples; Type 1 simulations assume that ICCx, ICCy are known; Type 2 simulations estimates ICCx, ICCy, from the sample data; for both Type 1 and Type 2 simulations, the underlying ICCx, ICCy are provided in the 2nd column of the table. Simulation results are based on 4000 simulations.

Table 2: Simulation results for the test procedure in (5) and (6).