Statistica Sinica 18(2008), 91-104

GENERAL RANKED SET SAMPLING FOR EFFICIENT

TREATMENT COMPARISONS

Zehua Chen$^1$, Jianbin Liu$^2$, Liang Shen$^1$ and You-Gan Wang$^3$

$^1$National University of Singapore, $^2$Zhejiang Sci-Tech University and

$^3$CSIRO Mathematical and Information Sciences

Abstract: 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.

Key words and phrases: Correlation, cost-effectiveness, ranked set sampling, relative precision, treatment comparison.