Balanced Assignment of Experimental Units in the Analysis of Covariance through Optimization

In a designed experiment with covariates, experimental units are typically assigned to treatments randomly and analysis of covariance is used to account for the covariate. In cases where the covariate is known beforehand, the possibility exists to assign experimental units systematically to achieve a ”balanced” covariate distribution in each treatment. This balance can be accomplished by solving a multi-criteria number partitioning problem. We discuss approximate methods for solving this NP hard optimization problem and present simulation results quantifying increases in the power of the statistical test for differences in treatment means.