General Efficiency Balanced (GEB) Block Designs with Correlated Observations for Even Number of Treatments

Abstract

Abtsrcat Kiefer and Wynn (1981) developed optimality properties of 1st Order neighbor balanced designs. These neighbor balanced designs require a large number of blocks, specially, for even number of treatments. Construction of block designs for even number of treatments with correlated observations with lesser number of blocks is a challenge to researchers. In the present paper, an attempt has been made to construct efficient designs with even number of treatments in lesser number of blocks considering the observations, correlated of 1st order neighbors. The general efficiency balanced (GEB) block designs (Das and Ghosh, 1985 and Kageyama and Mukerjee, 1986) with correlated observations have been constructed for even number of treatments. The structure of the C-matrix of the design has been derived and the canonical efficiencies, A and D efficiencies of the resultant GEB designs are also obtained for different values of the correlation coefficient ρ (0 ≤ ρ ≤1).