Methods of adjustment for two-dimensional spatial heterogeneity of grain yield were investigated for 224 UK cereal trials. The methods used row and column ‘block’ analysis of plot yields and neighbour analysis based on first differences of plot yields. In 36% of trial analyses for block models and 30% for neighbour models the average variance of variety differences was reduced by more than 10% compared with the better of the one-dimensional row or column models. Compared with complete blocks, 2-D block analysis had a mean efficiency of 153% whereas the conventional 1-D block analysis (by rows) had a mean efficiency of 127%. Similarly, 2-D neighbour analysis had a mean efficiency of 159% whereas the 1-D analysis had a mean efficiency of 137%. Recently, general statistical methods have been developed for two-dimensional design and analysis; their wider use should lead to major gains in the precision of variety trials.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0021859600067253

Statistical analysis of two-dimensional variation in variety yield trials

Analysis of 33 varieties of three sorghum (Sorghum spp.) species cultivated in China showed that sudangrass (Sorghum sudanense Stapf) and sorghum–sudangrass hybrid [Sorghum bicolor (L.) Moench × S. sudanense] samples had higher concentrations of phenolic compounds (including total soluble phenol, proanthocyanidin, flavan-4-ols, anthocyanins, and five phenolic acids) than sorghum (S. bicolor) samples. In addition, the phenolic compounds were distributed extensively in the grain morphological fractions (including glumes, spikelets, caryopsis, endosperm, and embryo) of sudangrass and sorghum–sudangrass hybrid samples; however, they were mainly present in the glumes of sorghum except for total soluble phenol. The results indicated that sudangrass and sorghum–sudangrass hybrid samples in this study would be good sources of useful phenolic compounds such as anthocyanin (6.93 mg g−1 and 4.72 mg g−1) and proanthocyanidin (10.37 mg g−1 and 8.16 mg g−1) compared with sorghum samples (2.97 mg g−1 and 0.18 mg g−1 for anthocyanin and proanthocyanidin, respectively). Sudangrass and sorghum–sudangrass hybrid samples had higher antioxidant activities of 2,2¢-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) (ABTS) and 1,1-diphenyl-2-picrylhydrazyl radical (DPPH) (230 and 108 μmol trolox equivalents [TE] g−1 for sudangrass; 258.5 and 130.3 μmol TE g−1 for sorghum–sudangrass hybrid) than sorghum samples (202.5 and 39.5 μmol TE g−1 for ABTS and DPPH, respectively). Thus, the sudangrass and sorghum–sudangrass hybrid samples in this study represented better commercial resources for nutritional and pharmaceutical purposes than sorghum samples because of higher antioxidant activities.

Multienvironment Quantitative Trait Loci Mapping and Consistency across Environments of Resistance Mechanisms to Ferrous Iron Toxicity in Rice

SUMMARY Pseudofactors are an inherently simple device to aid the construction and analysis of designed experiments. Although they were introduced over 50 years ago, they still puzzle many statisticians. After a historical introduction a worked example is used to demonstrate how pseudofactors are used to construct the design, to obtain the analysis-of-variance table and table of means and to calculate standard errors of contrasts. Then the algebraic and algorithmic roles of pseudofactors are explained and reviewed, with particular emphasis on Genstat. Finally, a section on standard designs shows how pseudofactors may be used to construct more efficient designs, and to give simpler or better analyses, than those recommended in the current literature.

Pseudofactors: Normal Use to Improve Design and Facilitate Analysis

We consider nested row-column designs where each of the row and column component designs is specified. For the case that each of the component designs has second-order balance, we define such a nested row-column design to be special if it is generally balanced, with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components. We show that if any special row-column design exists then it is A-optimal over all nested row-column designs with the given components.

Optimal nested row-column designs with specified components

viii ABBREVIATIONS AND MAIN NOTATION x Chapter

Variance-distance relationships in agricultural field plot experiments

On donne une definition generale et on donne une approche unifiee a l'analyse d'une classe restreinte de tels plans

D. Ratcliff

Papers

The analysis of lattice square designs