Evaluation of variance components from a group of experiments with multiple classifications

In conducting a replicated varietal yield trial, the experimenter usually is interested in obtaining the highest yielding variety or varieties from a group of varieties (or strains). A useful kind of information under such circumstances would be knowledge concerning the optimum allocation of replicates and varieties in any single experiment. Yates (23) and Perotti (12) have given a formula for determining the best combination of replicates and varieties in selecting the highest yielding variety or varieties from a simple randomized complete block design. For the more complex designs, formulas for determining the optimum allocation of varieties, replicates and locations (or years) would be useful

I.4 Screening Experimental Designs for Quantitative Trait Loci, Association Mapping, Genotype-by Environment Interaction, and Other Investigations

Crop breeding programs using conventional approaches, as well as new biotechnological tools, rely heavily on data resulting from the evaluation of genotypes in different environmental conditions (agronomic practices, locations, and years). Statistical methods used for designing field and laboratory trials and for analyzing the data originating from those trials need to be accurate and efficient. The statistical analysis of multi-environment trails (MET) is useful for assessing genotype × environment interaction (GEI), mapping quantitative trait loci (QTLs), and studying QTL × environment interaction (QEI). Large populations are required for scientific study of QEI, and for determining the association between molecular markers and quantitative trait variability. Therefore, appropriate control of local variability through efficient experimental design is of key importance. In this chapter we present and explain several classes of augmented designs useful for achieving control of variability and assessing genotype effects in a practical and efficient manner. A popular procedure for unreplicated designs is the one known as “systematically spaced checks.” Augmented designs contain “c” check or standard treatments replicated “r” times, and “n” new treatments or genotypes included once (usually) in the experiment

Pre-harvest sampling of soybeans for yield and quality

The route-sampling method of estimating crop production has been extended to soybeans in a preliminary survey which is reported here. In 1941, just prior to harvest, 67 fields in eight east central Illinois counties were sampled for yield, percent protein, percent oil and iodine number of the oil. Protein percent, oil percent and iodine number of the oil can be estimated satisfactorily, but estimating yield is more uncertain pending the accumulation of information on adjusting for harvesting losses and other factors which cause the sample average yield to be too large. The yield of seed per acre differed with the method of planting (width of rows), indicating for the season studied that soybeans should have been planted in rows about 2 feet apart. The iodine number of the oil was lower for fields with wide rows than for drilled fields. This was attributed to difference in date of planting rather than method of planting. It was concluded that two subsampling units should be taken per field and that the optimum size of subsampling unit is approximately 7 square feet. Other investigations have shown that after the pods are fully distended there is little or no change in yield or chemical composition, indicating that production and quality can be estimated well in advance of harvest

Punched card and calculating machine methods for analyzing lattice experiments including lattice squares and the cubic lattice

Punched card and calculating machine methods are given for analyzing data from lattice experiments. Numerical examples are worked out for the triple lattice, simple lattice, balanced lattice, lattice square with (k+1) / 2 replicates, lattice square with (k+1 ) replicates and cubic lattice designs. In addition, brief computational directions are given for the quadruple lattice, quintuple lattice and higher order lattices and for duplications of these designs. The use of the punched card machine method materially decreases the time and the chance for errors in making the computations, particularly when the total number of plots is more than about 150 or when more than one character is to be analyzed. The formulas given are appropriate for any k and for any number of repetitions of the basic plan for the simple lattice, triple lattice, quadruple lattice and higher order lattice designs and for the cubic lattice design and for any k for the lattice square with (k + 1)/2 replicates, lattice square with (k + 1) replicates and the balanced lattice designs

Sequential Design of Experiments

35 pages, 1 article*Sequential Design of Experiments* (Federer, Walter T.) 35 page

The Value of Summarizing Results from Individual Experiments

16 pages, 1 article*The Value of Summarizing Results from Individual Experiments* (Federer, Walter T.) 16 page

On Putting Statistical Theory into Practice

13 pages, 1 article*On Putting Statistical Theory into Practice* (Federer, Walter T.) 13 page

Complete Sets of F(n, n/s) Squares for s=p(k)

5 pages, 1 article*Complete Sets of F(n, n/s) Squares for s=p(k)* (Federer, Walter T.) 5 page