scholarly journals Group Divisible Variance – Sum Third Order Rotatable Design through Balanced Incomplete Block Designs in Four Dimensions

2018 ◽  
pp. 1-9
Author(s):  
N. Chebet ◽  
M. Kosgei ◽  
G. Kerich
Keyword(s):  
Block Design ◽  
Block Designs ◽  
Incomplete Block ◽  
Third Order ◽  
Four Dimensions ◽  
Dimensional Group ◽  
Group Divisible ◽  
Origin Group ◽  
Balanced Incomplete Block ◽  
Rotatable Design

In the study of rotatable designs, the variance of the estimated response at a point is a function of the distance of that point from a particular origin. Group divisible Rotatable Designs have been evolved by imposing conditions on the levels of factors in a rotatable design. In Group Divisible Third Order Rotatable Designs (GDTORD), the v-factors are split into two groups of p and (v-p) factors such that the variance of a response estimated at a point equidistant from the centre of the designs is a function of the distances  and from a suitable origin for each group respectively. Where  and   denotes the distances of the projection of the points in each of the group from a suitable origin respectively. In this paper, a four dimensional Group Divisible Variance-Sum Third Order Rotatable Design is constructed using a balanced incomplete block design.  

Generalized Hadamard Matrices and Orthogonal Arrays of Strength Two

1964 ◽  
Vol 16 ◽  
pp. 736-740 ◽  
Author(s):  
S. S. Shrikhande
Keyword(s):  
Block Design ◽  
Orthogonal Arrays ◽  
Hadamard Matrices ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

The purpose of this note is to point out some connexions between generalized Hadamard matrices (4, 5) and various tactical configurations such as group divisible designs (3), affine resolvable balanced incomplete block designs (1), and orthogonal arrays of strength two (2). Some constructions for these arrays are also indicated.A balanced incomplete block design (BIBD) with parameters v, b, r, k, λ is an arrangement of v symbols called treatments into b subsets called blocks of k < v distinct treatments such that each treatment occurs in r blocks and any pair of treatments occurs in λ blocks.

scholarly journals GD PBIBD(2)s in incomplete split-plot × split-block type experiments

2006 ◽  
Vol 3 (1) ◽  
Author(s):  
Katarzyna Ambroży ◽  
Iwona Mejza
Keyword(s):  
Block Structure ◽  
Block Design ◽  
Block Type ◽  
Block Designs ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Split Plot ◽  
Randomization Scheme ◽  
Balanced Incomplete Block ◽  
Modeling Data

In this paper we present a method of designing a three-factor experiment with crossed and nested treatment structures. The design considered is called a split-plot × split-block design. A kind of design incomplete with respect to all three factors is examined. Additionally, we consider the usefulness of group divisible partially balanced incomplete block designs with two associate classes in planning such experiments. In modeling data obtained from them, we take into account the structure of experimental material and a four-step randomization scheme for the different kind of units. As regards the analysis of the obtained randomization model with seven strata, we adapt an approach typical of multistratum experiments with orthogonal block structure.

scholarly journals A note on matroids and block designs

1975 ◽  
Vol 20 (1) ◽  
pp. 54-58
Author(s):  
R. A. Main ◽  
D. J. A. Welsh
Keyword(s):  
Block Design ◽  
Regular Structure ◽  
Close Connection ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Incomplete Block Design ◽  
Combinatorial Geometries ◽  
Balanced Incomplete Block

The close connection between certain types of matroids or combinatorial geometries and block designs is well known. The relationships previously discussed have centred on the loose analogy between the blocks of a design and the hyperplanesor flats ot the matroid or geometry. The matroids which arise in this way have had in the main a very tight regular structure. Here we show that theclass of matroids whose bases are the blocks of a design ismuch wider — indeed from Theorem 6 below we obatain a metroid in a canonical way from any balanced incomplete block design in which no pair of blocks differ by exactly one element.

On Balanced Incomplete Block Designs with Large Number of Elements

1970 ◽  
Vol 22 (1) ◽  
pp. 61-65 ◽  
Author(s):  
Haim Hanani
Keyword(s):  
Block Design ◽  
Necessary Condition ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Balanced Incomplete Block Designs ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block ◽  
Image Position

A balanced incomplete block design (BIBD) B[k, λ; v] is an arrangement of v distinct elements into blocks each containing exactly k distinct elements such that each pair of elements occurs together in exactly λ blocks.The following is a well-known theorem [5, p. 248].THEOREM 1. A necessary condition for the existence of a BIBD B[k, λ,v] is that(1)It is also well known [5] that condition (1) is not sufficient for the existence of B[k, λ; v].There is an old conjecture that for any given k and λ condition (1) may be sufficient for the existence of a BIBD B[k, λ; v] if v is sufficiently large. It is attempted here to prove this conjecture in some specific cases.There is an old conjecture that for any given k and X condition (1) may be sufficient for the existence of a BIBD B[k, λ; v] if v is sufficiently large. It is attempted here to prove this conjecture in some specific cases.

8. Designs and geometry

2016 ◽  
pp. 123-139
Author(s):  
Robin Wilson
Keyword(s):  
Triple System ◽  
Block Design ◽  
Projective Planes ◽  
Latin Squares ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Orthogonal Latin Squares ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

Block designs are used when designing experiments in which varieties of a commodity are compared. ‘Designs and geometry’ introduces various types of block design, and then relates them to finite projective planes and orthogonal latin squares. A block design consists of a set of v varieties arranged into b blocks. If each block contains the same number k of varieties, each variety appears in the same number r of blocks, then for every block design we have v × r = b × k. A balanced incomplete-block design is when all pairs of varieties in a design are compared the same number of times. A triple system is when each block has three varieties.

On a Method of Construction of Balanced Incomplete Block Designs

1986 ◽  
Vol 35 (3-4) ◽  
pp. 157-160
Author(s):  
D. V. S. Sastry ◽  
R. H. Malgaonkar
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Group Divisible Designs ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Balanced Incomplete Block

This paper gives a method of construction of balanced incomplete block designs (BIBDs) and group divisible designs from the existing self complementary BIBDs.

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