scholarly journals Resolvable block designs balanced for non-directional neighbour effects

2018 ◽  
Vol 33 (01) ◽  
Author(s):  
Akhilesh Jha ◽  
Cini Varghese ◽  
Seema Jaggi ◽  
Mohd Harun ◽  
Devendra Kumar
Keyword(s):  
Prime Power ◽  
Block Designs ◽  
Experimental Plot ◽  
Direct Effects ◽  
Neighbour Effects ◽  
Balanced Designs ◽  
Cultivable Land

When there is a constraint of cultivable land, experimental units are to be arranged side by side in compact blocks without gaps in between, the treatment applied to one experimental plot may affect the response on neighbouring plots besides the response to which it is applied. Neighbour-balanced designs, where in the allocation of treatments is such that every treatment occurs equally often with every other treatment as neighbours, can be advantageously used in such situations. These designs ensure that no treatment is unduly disadvantaged by its neighbours and also helps in estimating the neighbour effects besides the direct effects of treatments. Resolvable neighbour balanced designs are advisable if continuous area is not available for all replications. Methods for constructing a new series of resolvable block designs balanced for non-directional neighbour effects for prime or prime power of number of treatments (v) have been developed. The methods are discussed in detail along with appropriate examples in following section.

On a Class of Variance Balanced Designs Associated with GD Designs

1984 ◽  
Vol 33 (3-4) ◽  
pp. 187-190 ◽  
Author(s):  
G. G . Agarwal ◽  
Sanjay Kumar
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Balanced Designs ◽  
Balanced Incomplete Block ◽  
Block Sizes

In this paper variance balanced incomplete block designs have been constructed in unequal block sizes for situations when suitable BIB designs do not exist for a given number of treatments.

scholarly journals Interactions between plots in experiments with the splash-dispersed pathogen Rhynchosporium secalis on winter barley

1989 ◽  
Vol 112 (1) ◽  
pp. 97-114 ◽  
Author(s):  
J. F. Jenkyn ◽  
G. V. Dyke ◽  
O. J. Stedman ◽  
A. D. Todd
Keyword(s):  
Winter Barley ◽  
Alternative Methods ◽  
Rhynchosporium Secalis ◽  
Block Designs ◽  
Balanced Design ◽  
Leaf Blotch ◽  
Positional Variation ◽  
Neighbour Effects ◽  
Local Correlations ◽  
Randomized Block Designs

SummaryExperiments of balanced design in harvest years 1981 and 1982 were used to measure interactions between plots of winter barley with different amounts of leaf blotch, caused by the splash-dispersed pathogen Rhynchosporium secalis. On the appropriate transform scales (logarithms of counts and logits of percentages), the effects of extreme treatments on neighbouring plots were up to 30% of the effects of the same treatments on the plots to which they were applied. Powdery mildew (Erysiphe graminis f.sp. hordei) was commonly least severe in plots with most leaf blotch except soon after fungicide sprays had been applied which, although chosen to decrease leaf blotch, also had short-lived effects on mildew. Consequently, contrasts in mildew between differently treated plots changed sign during the season. The effects of the same treatments on neighbouring plots similarly changed with time but not necessarily in phase with their direct effects. Analyses of the rhynchosporium data that recognized the effects of neighbouring treatments typically had much smaller residual mean squares than analyses that ignored neighbour effects but assumed randomized block designs.Treatments had mostly small effects on grain yield but these data from two of the experiments showed marked positional variation. Individual plots yields from one of these experiments, testing five treatments, are quoted in the appendix so that they are available to others with an interest in alternative methods, such as nearest-neighbour models, to adjust for local correlations between plots.

Existence of simple BIBDs from a prime power difference family with minimum index

2019 ◽  
Vol 18 (09) ◽  
pp. 1950166
Author(s):  
Hsin-Min Sun
Keyword(s):  
Simple Formula ◽  
Prime Power ◽  
Block Designs ◽  
Incomplete Block ◽  
Difference Family ◽  
Balanced Incomplete Block Designs ◽  
Extensive Analysis ◽  
Power Difference ◽  
Balanced Incomplete Block ◽  
Minimum Index

We show that under certain technical conditions that simple [Formula: see text] balanced incomplete block designs (BIBDs) exist for all allowable values of [Formula: see text], where [Formula: see text] is an odd prime power. Our primary technique is to argue for the existence of difference families in finite fields, in the flavor of Wilson [J. Number Theory 4 (1972) 17–47]. We provide an extensive analysis in the cases, where [Formula: see text] and also for [Formula: see text].

Merging of Treatments in Certain Partially Efficiency Balanced Block Designs with Two Different Numbers of Replications

1987 ◽  
Vol 36 (1-2) ◽  
pp. 49-56 ◽  
Author(s):  
B. Ceranka ◽  
S. Mejza
Keyword(s):  
Point Of View ◽  
Block Designs ◽  
Balanced Designs

A procedure of construction merging treatments in balanced block designs with two different numbers of replications (an alternative name of inter-and intra-group balanced designs) is considered from the point of view of the concept of partially efficiency balanced block designs. It is proved that the designs considered belong to block designs with at most three efficiency classes.

Experimental Designs Balanced for the Estimation of Residual Effects of Treatments

1949 ◽  
Vol 2 (2) ◽  
pp. 149 ◽  
Author(s):  
EJ Williams
Keyword(s):  
Residual Effect ◽  
Latin Squares ◽  
Experimental Designs ◽  
Residual Effects ◽  
Direct Effects ◽  
Balanced Design ◽  
Orthogonal Latin Squares ◽  
Mutually Orthogonal Latin Squares ◽  
Wide Applicability ◽  
Balanced Designs

Where an experiment can be carried out by applying different treatments in succession to the same unit of experimental material, accurate comparisons can be made between the effects of different treatments. To allow for the residual effect of previous treatments on the result obtained for any given treatment, it is desirable to adjust the results for such effects. Methods of constructing balanced designs for the estimation of these residual effects are described in this paper, and are summarized as follows. Designs balanced for effect of single preceding treatment: When n, the number of treatments, is even, a balanced design is possible with n replications ; when n is odd, 2n replications are required.Designs balanced for the effects of any number of preceding treatments, ignoring the interaction of residual effects: When n is a prime or a power of a prime, a balanced design is possible in n(n-1) replications, which may be set out as a set of n-1 mutually orthogonal Latin squares, with the same first columns. Designs which are not expressible as mutually orthogonal Latin squares are also possible. Designs balanced for the effect of the two preceding treatments and their interactions : A design can be developed from a set of n-l mutually orthogonal Latin squares obeying certain restrictions. The method of analysis of designs of this type is set out in detail, together with a numerical example. Direct effects of treatments are shown to be only slightly confounded, the maximum confounding being 4 per cent., when there are three treatments. These designs have wide applicability wherever successive treatments can be applied to the same unit of experimental material.

scholarly journals Applying Balanced Generalized Weighing Matrices to Construct Block Designs

10.37236/1556 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Yury J. Ionin
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Block Designs ◽  
Weighing Matrices ◽  
Symmetric Designs

Balanced generalized weighing matrices are applied for constructing a family of symmetric designs with parameters $(1+qr(r^{m+1}-1)/(r-1),r^{m},r^{m-1}(r-1)/q)$, where $m$ is any positive integer and $q$ and $r=(q^{d}-1)/(q-1)$ are prime powers, and a family of non-embeddable quasi-residual $2-((r+1)(r^{m+1}-1)/(r-1),r^{m}(r+1)/2,r^{m}(r-1)/2)$ designs, where $m$ is any positive integer and $r=2^{d}-1$, $3\cdot 2^{d}-1$ or $5\cdot 2^{d}-1$ is a prime power, $r\geq 11$.

Optimality of neighbour balanced designs when neighbour effects are neglected

1997 ◽  
Vol 64 (2) ◽  
pp. 353-367 ◽  
Author(s):  
Jean-Marc Azaïs ◽  
Pierre Druilhet
Keyword(s):  
Neighbour Effects ◽  
Balanced Designs

A Note on Partially Efficiency Balanced Designs

1980 ◽  
Vol 29 (3-4) ◽  
pp. 185-190 ◽  
Author(s):  
Satyabrata Pal
Keyword(s):  
General Class ◽  
Block Designs ◽  
Balanced Designs ◽  
Definition Of

In this note we modify the definition of Partially Efficiency Balanced (PEB) designs as given by Puri et al (1977 a) and show that the PEB designs constitute the most general class which includes any conceivable design in the class of block designs.

Complete Block Designs. II Analysis of Partially Balanced Designs

1977 ◽  
Vol 19 (6) ◽  
pp. 455-461
Author(s):  
G. Herrendörfer ◽  
D. Rasch
Keyword(s):  
Block Designs ◽  
Balanced Designs
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