Minimal sufficient statistics for the partially balanced incomplete block (PBIB) design with two associate classes under an eisenhart model II

1962 ◽  
Vol 14 (1) ◽  
pp. 63-71 ◽  
Author(s):  
C. H. Kapadia
Keyword(s):  
Incomplete Block ◽  
Sufficient Statistics ◽  
Pbib Design ◽  
Balanced Incomplete Block

Non-Existence of Some Unsymmetrical Partially Balanced Incomplete Block Designs

1963 ◽  
Vol 15 ◽  
pp. 686-701 ◽  
Author(s):  
S. S. Shrikhande ◽  
D. Raghavarao ◽  
S. K. Tharthare
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Balanced Incomplete Block Designs ◽  
Pbib Design ◽  
Balanced Incomplete Block

A partially balanced incomplete block (PBIB) design with m-associate classes is defined by Bose and Shimamoto (4) as follows:(i) The experimental material is divided into b blocks of k units each, different treatments being applied to the units in the same block.(ii) There are v treatments each of which occurs in r blocks.(iii) There can be established a relation of association between any two treatments satisfying the following requirements.

Some Configurations in Finite Projective Spaces and Partially Balanced Incomplete Block Designs

1965 ◽  
Vol 17 ◽  
pp. 114-123 ◽  
Author(s):  
D. K. Ray-Chaudhuri
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Finite Projective Space ◽  
Block Designs ◽  
Incomplete Block ◽  
Finite Plane ◽  
Balanced Incomplete Block Designs ◽  
Pbib Design ◽  
Finite Projective Spaces ◽  
Balanced Incomplete Block

Using the methods developed in (2 and 3), in this paper we study some properties of the configuration of generators and points of a cone in an w-dimensional finite projective space. The configuration of secants and external points of a quadric in a finite plane of even characteristic is also studied. I t is shown that these configurations lead to several series of partially balanced incomplete block (PBIB) designs. PBIB designs are defined in Bose and Shimamoto (1). A PBIB design with m associate classes is an arrangement of v treatments in b blocks such that.

On the Evaluation of Some Expressions Concerning the PBIB Designs

1968 ◽  
Vol 11 (1) ◽  
pp. 107-114 ◽  
Author(s):  
Robert Cléroux
Keyword(s):  
Incomplete Block ◽  
Pbib Design ◽  
Associate Class ◽  
Balanced Incomplete Block

Consider a two associate class partially balanced incomplete block (PBIB) design [2] with parameters of the first kind t, b, r, λ,1 λ,2 n1, n2, and parameters of the second kind . Let the letters m, p, l, s represent treatments and define associates of treatment m, λmps = number of times the treatments m, p and s all occur together in the same block, λmpls = number of times the treatments m, p, l and s all occur together in the same block.

On the Construction of VB Designs

1998 ◽  
Vol 48 (1-2) ◽  
pp. 109-114
Author(s):  
C.C. Gujarathi ◽  
Pravender
Keyword(s):  
Analytical Study ◽  
Incomplete Block ◽  
Pbib Design ◽  
Variance Balance ◽  
Balanced Incomplete Block ◽  
The Given

This paper gives complete analytical study of suitability and non-availability of I-associate and II-associate designs of a given 2-class partially balanced incomplete block (2-PBIB) design in the construction of a variance balance (VB) design using the given 2-PBIB design.

Construction of Variance Balanced Designs through Triangular PBIB Designs

1995 ◽  
Vol 45 (1-2) ◽  
pp. 111-118 ◽  
Author(s):  
D.K. Ghosh ◽  
K. S. Joshi
Keyword(s):  
Block Design ◽  
Incomplete Block ◽  
Pbib Design ◽  
Group Divisible ◽  
Incomplete Block Design ◽  
Balanced Designs ◽  
Balanced Incomplete Block ◽  
The Given

Several authors have obtained variance balanced (VB) and ternary variance balanced ( V B) designs using balanced incomplete block (BIB) designs and group divisible (GD) designs. In the present investigation, another systematic methods have been developed for the construction of VB designs using A Triangular PBIB design and an incomplete block design where the blocks of the incomplete block design are formed by taking the second associate treatments of the given triangular PBIB design. Two Triangular PBIB designs. The methods of construction of VB designs are further illustrated by examples.

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