ABSTRACT
Spatial variability in fields is a universal phenomenon that affects the detection of treatment differences in agricultural experiments by inflat ing the estimated experimental error variance. This dilemma confronts all researchers who conduct field experiments. They meet this problem by using an appropriate design and layout of the experiment and by us ing improved statistical methodology for statistical analyses. Owing to the large numbers of genotypes involved in plant-breeding programs, small plots are the rule. The smallest unit of area allotted to one geno type or treatment is denoted as an experimental unit. This has been called a plot (also called a plat in older literature). The arrangement of the experimental units in an experiment is known as the experiment de sign (ED), and the selection of the treatments (genotypes) to be included in the experiment is known as a treatment design. Starting with Sir Ron ald A. Fisher’s three design principles of blocking, randomization, and replication, many types of EDs have evolved and are still evolving to meet the various situations encountered by researchers. Randomization is necessary to obtain an unbiased estimate of the error variance. Many types of EDs such as a completely randomized experiment design, ran domized complete-block experiment design (RCBD), split-plot experi ment design, split-block experiment design, incomplete block (lattice) experiment design (IBD), Latin square ED, Youden ED, lattice square and lattice rectangle EDs, cross-over EDs, etc., have been described and used in published literature. Lattice (incomplete block) and lattice square (resolvable row-column) experiment designs are popular de signs for plant-breeding evaluation trials. When the incomplete block and lattice square experiment designs were introduced in the 1930s and 1940s, experimental data were analyzed on simple desk calculators. Consequently, the emphasis was on obtaining designs easy to construct and simple to analyze. The use of catalogued lattices and lattice squares, such as may be found in Cochran and Cox (1957) and Federer (1955), e.g., is limited because of the wide variety of numbers of genotypes oc curring in practice. This limitation has been lifted as a result of develop ments such as Patterson and Williams (1976), e.g., who devised the resolvable (the incomplete blocks form a complete block or replicate for
the set of v genotypes) incomplete block designs called alpha designs. A main advantage of alpha designs over the traditional lattices is their flexibility to accommodate any number of genotypes in any number of replicates and to be able to have incomplete blocks of different sizes. When the field layout is in a row-column shape, either for the entire ex periment or within each complete block, EDs for any number of geno types and replicates can be developed (Nguyen and Williams, 1993; John and Williams, 1995; Federer, 1998b) that control variability in two directions. The row-column EDs have two block components, i.e., blocks in rows and blocks in columns either for the whole experimental area or for each complete block (resolvable row-column EDs). Like wise, several software packages are available for obtaining randomized plans of these designs for various numbers of genotypes and replicates. When the entire experiment is laid out in a row-column arrangement, it may be desirable to assure that genotypes do not occur more often than once in a row or a column of the experiment. The so-called “latinized designs” accomplish this. Also, it may be desirable to restrict random ization of genotypes in such a way that certain groups of genotypes do not occur together so that genotypic interference can be avoided. Latinized alpha lattice and row-column designs as well as neighbor-restricted de signs can be generated using the software package Alpha+ (1996).
