Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Quantitative Economics


Economic Research Unit (ERU-Kolkata)


Rao, A. R. (ERU-Kolkata; ISI)

Abstract (Summary of the Work)

The use and importance, in Statistical Experimental, of Incomplete Block Designs, particularly, Balanced Incomplete Block (BIB) Designs, Doubly Balanced Incomplete Block (DBIB) Designs and Partially Balanced Inçomplete Block (PBIB) Designs are well known. Several combinational arrangements, including the incidence matrices of these Incomplete Block Designs and association matrices associated with PBIB Designs are known to be of use in Design of Experiments. In this thesis, we consider the construction problems pertaining to some of these combinational arrangements and take up the problem of construction of BIB, DBIB and FBIB Designs through them. The combinational arrangements studied in the thesis have, of course, other important uses besides their relevance in obtaining some BIB, DBIB and PBIB Design or proving the non-existence of some of them. But, it is the construction of Incomplete Block Designs that hns mostly prompted the author to study the construction of the combinational arrangements included in the thesis. A brief summary of the work undertaken in the thesis is provided below.Hadamard matrices always give rise to certain BIB and DBIB Designs. In Chapter 2, we give methods of construction of some infinity series of Hadamard matrices, based on orthogoal matrices with zero diagonal and + 1 elsewhere. The results proved are essentially generalizations and extensions of the results given by Williamson (1944, 47), Wallis (1969) and Turyn (1972 e).In Chapter 3, same results are proved regarding general Orthogonal Arrays (QAs) and Orthogonal Arrays of strength two and three. Bystematic methods are develoned for constructing QAs of strength 2 and 3 for different indices, with comparatively large number of constraints in most of the cases. Methods are also given for obtaining QA : II s of strength 2 of Rao (196 1a), when the aumber of levels, s is not a prime power. OAs and OA : s of strength 2 are utilised for the purpose of constructing series of BIB Designs, Group Divisible (GD) Designs and PBIB Designs with three associate classes. Some of the results of chapter 3 about the construction of BIB Designs through QAs and OA : s of strength 2 have been published (Mukhopadhyny, 1972 a).A Balanced Orthogoml Design (BOD) is a con binatorial arrangement first considered by Rao (1966). In Chapter 4, we give a method for constructing an infinite series of BOD's, given any odd prime power.


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