Analyzing Simulation Experiments with Common Random Numbers

To analyze simulation runs which use the same random numbers, the blocking concept of experimental design is not needed. Instead, this paper applies a linear regression model with a nondiagonal covariance matrix. This covariance matrix does not need to have a specific pattern such as constant covariances. A simple example yields surprising results. The paper proposes a new framework for the error analysis. This framework consists of three factors (namely, common random numbers, replication, model validity), each with three levels.