Search

AbstractMethod of constructing new and useful series of m-associate class partially balanced incomplete block (PBIB) designs, named as Generalized Extended Triangular (GET) designs, in m replications has been proposed along with an outline of analytical procedure. Triangular designs, one of the most popular and widely used class of PBIB(2) designs, and the extended triangular PBIB(3) designs form other two important particular cases of this generalized class of designs. To avoid the complexity involved in the construction methodology and to save time, an R package ‘‘GETdesigns’’ has been developed for the generation of the proposed designs. Further, these designs have been effectively used for obtaining mating designs and Latin hypercube designs. [ABSTRACT FROM AUTHOR]

For situations in multi-site varietal trials where the experimenters demand incomplete blocks with unequal sizes, minimum number of replications, or both, new series of incomplete block designs have been presented. The proposed designs are higher associate partially balanced incomplete block designs in two replications having flexible block sizes. These designs are affine resolvable and are optimal in the competing class of resolvable incomplete block designs. The underlying association schemes of these designs are defined. Further, they can be advantageously used for obtaining designs for various stages of breeding trials. An R-package developed for generating these designs has also been demonstrated. [ABSTRACT FROM AUTHOR]

AbstractA tri-hierarchical incomplete block (TriHIB) design is defined as an arrangement of v equi-replicated treatments in three levels of blocking such that each block of the first level contains m1 blocks of second level and that of second level contains m2 blocks of the third level. Every level of a TriHIB design, treated independently, is an incomplete block design (IBD) and ignoring any one level of blocking, results into a bi-hierarchical incomplete block (BiHIB) design. Here, two general methods of construction of TriHIB designs are proposed. In the first method, popular association schemes (viz., triangular, Latin square and rectangular) of partially balanced IBDs have been used for developing three series of designs with equal/unequal block sizes at higher levels of blocking. Second method yields another series of designs, through cyclic development of two initial sequences, with equal block sizes at first two levels and equal/unequal block sizes at the third level of blocking. A list of parameters of TriHIB designs for number of treatments up to 30 is presented, along with efficiency factors. Further, for easy accessibility and wider adaptability of these designs, an R package ‘Tri.Hierarchical.IBDs’ has been developed for the generation of the proposed designs. [ABSTRACT FROM AUTHOR]

Incomplete block designs bring out useful information from agricultural experimentation with high precision when there is a crunch in resources in terms of homogeneous blocks that can accommodate all the treatments. Balanced incomplete block designs or 2-designs are the most popular class of incomplete block designs. t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t≥2) occur together is a constant. In order to obtain tbalance, we may require large number of blocks and replications. Partially balanced t-designs are introduced for experimental situations where it is not possible to get balanced t-designs. Two series of such designs are obtained using cyclic development of initial block(s). Association of the proposed designs with t-packing designs are also demonstrated. [ABSTRACT FROM AUTHOR]

In agricultural, animal, fisheries and industrial experimentation under block design setup, systematic trend may affect the response under consideration. Although remote, these effects may still have high influence on response and hence should be incorporated in the model for proper model specification. Completely trend resistant block designs, also known as trend free block designs, are an important class of designs where the analysis can be done in usual manner as in case of normal block designs since trend effects and treatment effects are orthogonal. Literature is available on different aspects of trend resistant incomplete block designs mainly focusing on balanced incomplete block designs. This article deals with the construction of completely trend resistant Partially Balanced Incomplete Block (TR-PBIB) designs. Two methods of constructing such designs have been discussed. The information matrices for the class of designs developed have been derived and SAS code for the generation of the developed designs has also been provided. [ABSTRACT FROM AUTHOR]

Integrated farming system (IFS) approach is a powerful tool for ensuring the livelihood security of small and marginal farmers. The precision of IFS experiments can be enhanced using statistical and computational tools. Twopart designs are helpful in selecting the best possible components in IFS. They involve two groups of treatment arranged in incomplete blocks with respect to both groups, and the concurrence of treatment pairs within and between groups is constant. The fusion of two incomplete block designs in a systematic manner can yield two-part designs. Further, for situations where certain experimental units are not available, two-part structurally incomplete designs are proposed. [ABSTRACT FROM AUTHOR]

This paper describes the response surface model for mixed-level factors of the form 2n×3 where experimental units/plots experience the overlap effects from immediate left and right neighboring units. Conditions have been derived for the orthogonal estimation of the parameters of the model. A method of constructing mixed-level response surface designs of the form 2n×3 has been proposed. The designs developed satisfy the derived conditions of rotatability. Further, the method has been extended to the case of mixed-level rotatable designs of the form 2n×3n. An algorithm for the estimation of overlap effects has also been discussed, along with an illustration. [ABSTRACT FROM AUTHOR]

The use of an appropriate design is a very important aspect of agroforestry experimentation. Since different species of trees may interact spatially, plots in agroforestry could be connected through network of trees which would create non-directional adjacency effects on a plot. Hence, there is a need to take the "direct effect of trees" and "tree network effects" on the crop into account when designing an agroforestry experiment. Tree network effect refers to the influence a tree exerts on the surrounding plots as a result of adjacency of the plots. In this paper, a class of network designs incorporating effects of trees from adjacent plots has been obtained. The characterization properties of the designs have also been studied. The designs are found to be variance balanced for the estimation of direct as well as network effects of trees. They are also highly efficient designs, and hence, are recommended for agroforestry experimentation with multiple tree species and a single crop. [ABSTRACT FROM AUTHOR]