The Annals of Mathematical Statistics

On Partially Balanced Linked Block Designs

J. Roy and R. G. Laha

Full-text: Open access

Abstract

The computations in the analysis of any equireplicate design can be carried out very easily if the number of treatments common to any two blocks is constant. A design with this property is called a Linked Block (LB) design and was introduced by Youden [9]. It is well known that for a Balanced Incomplete Block (BIB) design to have a constant number of treatments in common between any two blocks, it is necessary and sufficient that it is symmetric, that is, the number of blocks is equal to the number of treatments. In this paper, necessary and sufficient conditions are derived for any design with a given treatment-structure matrix to be of the LB type and the results applied to Partially Balanced Incomplete Block (PBIB) designs. Finally a list is prepared of all LB designs in the class of two-associate PBIB designs enumerated by Bose, Shrikhande and Clatworthy [2].

Article information

Source
Ann. Math. Statist., Volume 28, Number 2 (1957), 488-493.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706977

Digital Object Identifier
doi:10.1214/aoms/1177706977

Mathematical Reviews number (MathSciNet)
MR88134

Zentralblatt MATH identifier
0081.36404

JSTOR
links.jstor.org

Citation

Roy, J.; Laha, R. G. On Partially Balanced Linked Block Designs. Ann. Math. Statist. 28 (1957), no. 2, 488--493. doi:10.1214/aoms/1177706977. https://projecteuclid.org/euclid.aoms/1177706977


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