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.

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.

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.

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.

scholarly journals Semiregular group divisible designs with dual properties

1992 ◽  
Vol 45 (1) ◽  
pp. 61-69
Author(s):  
Alan Rahilly
Keyword(s):  
Construction Method ◽  
Block Designs ◽  
Incomplete Block ◽  
Group Divisible Designs ◽  
Balanced Incomplete Block Designs ◽  
Group Divisible ◽  
Transversal Designs ◽  
Balanced Incomplete Block

A construction method for group divisible designs is employed to construct (i) infinitely many non-symmetric semiregular group divisible designs whose duals are semiregular group divisible designs, and (ii) infinitely many transversal designs whose duals are group divisible 3-associate designs. A construction method for affine α−resolvable balanced incomplete block designs is also given and illustrated.

A Note on Balanced Incomplete Block Designs

1954 ◽  
Vol 6 ◽  
pp. 341-346 ◽  
Author(s):  
D. A. Sprott
Keyword(s):  
Block Design ◽  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Balanced Incomplete Block Designs ◽  
Incomplete Block Design ◽  
Balanced Incomplete Block

A balanced incomplete block design is defined as an arrangement of v objects in b blocks, each block containing k objects all different, so that there are r blocks containing a given object and λ blocks containing any two given objects. Such designs have been studied for their combinatorial interest, as in (3), and also for their application to statistics, where the objects are usually varieties.

Sign in / Sign up

Export Citation Format

Share Document