Some Comments on Gerechte Designs

Gerechte designs are row and column designs which have an additional blocking structure formed by spatially compact regions. In this paper, and a companion paper (B ailey et al. 1990) we consider the correct analysis of these designs. In this paper we discuss the purpose of gerechte designs, and we note that the regions are not orthogonal to the rows and columns. This means that the usual sums of squares for rows, columns and regions are not additive. We show how the correct analysis can be performed, either through the use of appropriate formulae, or by the use of a statistical package. In the companion paper we show that the correct analysis cannot be justified by a randomization argument, and we outline other developments in analysis and design that may be more satisfactory.     

Efficiency of 35-p Fractional Factorial Designs Determined Using Additional Information on the Spatial Variability of the Experimental Field

The paper presents estimates of the relative efficiency (RE) of the 3^5‐1 (V) and 3^5‐2 (III) fractional factorial designs. Three variants of each fractional design were generated from a one‐replicated 3⁵ full factorial design applied in field experiments with pea (Pisum sativum L.). Plant height and seed yield were determined in the study. Additional measurements of soil properties (pH, P, K, Mg) and plant traits determined on the alleys between experimental strips, sown with a single cultivar, were performed in regular nets of sampling points. Geostatistical methods were used to estimate the spatial variation of the experimental field. Information on spatial variation was included in the statistical analysis. It was found that in the 3^5‐1 (V) fractional designs most of the significant effects were the same as in the 3⁵ full factorial design. Information from these two types of design was similar, although there was a distinct tendency to higher values of the coefficient of determination R² for linear models of the 3^5‐1(V) designs. The 3^5‐2 (III) fractional designs were more variable in detecting significant effects. Generally, mean RE was higher in the 3^5‐2 (III) design than in the 3^5‐1 (V) design, but at the same time the standard error of the latter one was distinctly lower. It was also demonstrated that in agricultural field experiments factorial fractional designs are a very good alternative to full factorial designs as concerns the estimation of main and two‐factor interaction effects in the case of the 3^5‐1 (V) designs and main effects in that of the 3^5‐2 (III) designs. Even if the designs have a highly reduced number of treatments to be tested they are equally or more effective than the original 3⁵ design from which they were generated, provided that the generator is chosen very carefully and the spatial variation of the experimental field is considered in statistical analysis of the experimental data.     

Primary Comparison of Orthogonal and Homogenous Designs on Experimental Design and Optimization

Systematic studies are made on experimental design and optimization.The orthogonal array design(OAD) is equal to or better than the homogeneous/uniform design (HUD) in some principlal respects and that the homogeneous design (HUD) has its advantages,especially on the case with few experiments done.     

刍议东西方纪念性景观规划布局的特点

从纪念性景观的隶属、平面布局形式及空间序列组织手法等方面试分析比较东西方纪念性景观在规划布局上所呈现出的特点。     

Improving the precision of cotton performance trials conducted on highly variable soils of the southeastern USA coastal plain

Reliable agronomic and fibre quality data generated in Upland cotton (Gossypium hirsutum L.) cultivar performance trials are highly valuable. The most common strategy used to generate reliable performance trial data uses experimental design to minimize experimental error resulting from spatial variability. However, an alternative strategy uses a posteriori statistical procedures to account for spatial variability. In this study, the efficiency of the randomized complete block (RCB) design and nearest neighbour adjustment (NNA) were compared in a series of cotton performance trials conducted in the southeastern USA to identify the efficiency of each in minimizing experimental error for yield, yield components and fibre quality. In comparison to the RCB, relative efficiency of the NNA procedure varied amongst traits and trials. Results show that experimental analyses, depending on the trait and selection intensity employed, can affect cultivar or experimental line selections. Based on this study, we recommend researchers conducting cotton performance trials on variable soils consider using NNA or other spatial methods to improve trial precision.