Discussiones Mathematicae Probability and Statistics 23(1) (2003) 45-68

SOME CONSTRUCTIONS OF NESTED BALANCED EQUIREPLICATE BLOCK DESIGNS

Shivani  Rai, Shakti  Banerjee

Devi Ahilya University,
Indore-452001, India
e-mail: shivanirai@rediffmail.com
e-mail:
shaktibn@yahoo.com

Sanpei  Kageyama

Hiroshima University
Higashi-Hiroshima 739-8524, Japan
e-mail: ksanpei@hiroshima-u.ac.jp

Abstract

Various methods of constructing nested ternary and quaternary efficiency balanced and variance balanced designs are proposed by applying some repetitions of treatments in all possible pairs of treatments. In these designs sub-blocks and super-blocks may form different p-ary designs, where sub-blocks have higher efficiency as compared to super-blocks, i.e., any two elementary treatment contrasts in the sub-blocks can be measured with higher efficiency than any two elementary contrasts in the super-block structure. A comparison is shown in Table 1.

Keywords: Balanced incomplete block (BIB) design; efficiency balanced (EB) design; variance balanced (VB) design; efficiency balanced ternary (EBT); variance balanced ternary (VBT); efficiency balanced quaternary (EBQ); variance balanced quaternary (VBQ).

2000 Mathematics Subject Classification: Primary 62K10; Secondary 62K05, 05B05.

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Received 15 December 2002