Journal of the Korean Statistical Society
- Volume 14 Issue 1
- /
- Pages.29-38
- /
- 1985
- /
- 1226-3192(pISSN)
- /
- 2005-2863(eISSN)
Cyclic Factorial Association Scheme Partially Balanced Incomplete Block Designs
Abstract
Cyclic Factorial Association Scheme (CFAS) for incomplete block designs in a factorial experiment is defined. It is a generalization of EGD/($2^n-1$)-PBIB designs defined by Hinkelmann (1964) or Binary Number Association Scheme (BNAS) named by Paik and Federer (1973). A property of PBIB designs having CFAS is investigated and it is shown that the structural matrix NN' of such designs has a pattern of multi-nested block circulant matrix. The generalized inverse of (rI-NN'/k) is obtained. Generalized Cyclic incomplete block designs for factorial experiments introduced by John (1973) are presented as the examples of CFAS-PBIB designs. Finally, the relationship between CFAS and BNAS in block designs is briefly discussed.
Keywords