General Ranked Set Sampling for Efficient Treatment Comparisons

In treatment comparison experiments, the treatment responses are often correlated with some concomitant variables which can be measured before or at the beginning of the experiments. In this article, we propose schemes for the assignment of experimental units that may greatly improve the efficiency of the comparison in such situations. The proposed schemes are based on general ranked set sampling. The relative efficiency and cost-effectiveness of the proposed schemes are studied and compared. It is found that some proposed schemes are always more efficient than the traditional simple random assignment scheme when the total cost is the same. Numerical studies show promising results using the proposed schemes.