
Accession Number : AD0678209
Title : THE THEORETICAL INVESTIGATION OF THE BLOCK DESIGNS.
Descriptive Note : Final rept.,
Corporate Author : NIHON UNIV TOKYO DEPT OF STATISTICS
Personal Author(s) : Ogawa,Junjiro
Report Date : JUN 1968
Pagination or Media Count : 46
Abstract : The report is divided into seven sections. A brief exposition of the incidence matrix of the balanced incomplete block (BIB) design is given in section 1. The HasseMinkowski pinvariant of the rational congruence is discussed in section 2. In section 3, the necessary condition for existence of a symmetrical BIB design is given in terms of the HasseMinkowski pinvariant as the prototype of the nonexistence proofs. In section 4, the properties of the association algebra of an association are presented with some examples of association schemes. Section 5 is devoted to the derivation of the necessary condition for existence of a regular and symmetrical partially balanced incomplete block (PBIB) design. The argument presented in section 5 is immediately carried over in section 6 to the derivation of the necessary condition for existence of a certain class of asymmetric PBIB designs. In section 7, the relationship algebra of a PBIB design is explained and some discussions of the nonexistence proofs in connection with the relationship algebra are presented. (Author)
Descriptors : (*COMBINATORIAL ANALYSIS, THEORY), EXPERIMENTAL DESIGN, MAPPING(TRANSFORMATIONS), SET THEORY, MATRICES(MATHEMATICS), THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE