Statistical Performance Analysis of Complete and Incomplete Block Designs: a Comparison of RCBD, Lattice Design and Alpha-Lattice Designs under SARI Field Conditions

Abstract

This study was conducted with the overall purpose of comparing the performance of commonly used incomplete block designs over that of the classical RCBD. Among the incomplete block designs, Lattice design and alpha lattice designs were employed. The compar ison was statistically done mainly based on mean square errors and their corresponding CVs for each design. For this purpose, three datasets obtained from SARI were analyzed using CRD, RCBD, lattice and alpha lattice designs. The results of the soybean variety trial data containing 8 treatments having two factors with 3 replications at five different locations were used to assess the performance of RCBD over CRD. The result showed that 31, 3, 53, and 13% precision increased with RCBD over CRD for four sites namely, Hawassa, Areka, Gofa and Bonga, respectively. The CV for CRD is 25.9, 19.2, 7.3 and 12.9% for the four sites above, respectively. While that of RCBD is 22.6, 18.8, 5.9 and 12.3% respectively. This again confirms that RCBD is more efficient than CRD under those tested sites. The implication of the insignificant block effect is there is no need of block for this site. The results of the maize variety trial data containing 25 treatments with 4 replications shown that 0.4, 6.2, 15.0, 0.1 and 10.3% prec ision increased with Lattice design over classical RCBD for the five research sites namely, Hawassa, Areka, Bonga, Jinka and Arba Minch sub Center, respectively. The CV for lattice design was 26.4, 20.9, 15.7, 21.7 and 18.9% for the above five sites, respectively. While that of the RCBD was 28.22, 25.0006, 21.8115, 26.291 and 20.5045%, respectively. This proves the increased efficiency of Lattice design over that of classical RCBD under SARI field condition. For the maize variety trial dataset containing 81 treatments with 3 replications, alpha lattice design is found to be more efficient than RCBD having relative efficiency of 18.8 %. The CV of alpha lattice design is 21.1% while that of RCBD 22.9%. The relative efficiencies of three datasets and their corresponding CVs respectively signify that the precision of experiment increased significantly using incomplete block designs instead of completely blocked designs mainly when the numbers of treatments are increased tremendously. Based on the results of this study, under SARI field setup, we conclude that RCBD is more efficient than CRD, lattice design and alpha lattice designs are more efficient than classical RCBD. In order to increase the precision of agricultural field experiments researchers are advised to use RCBD for small number of treatments; lattice and alpha lattice designs whenever there are large number of treatments taking into considerations the nature of field conditions.