Discussiones Mathematicae Probability and Statistics 24(1) (2004) 127-145

A UNIFIED TERMINOLOGY IN BLOCK DESIGNS

An Informative Classification

Tadeusz Caliński

Agricultural University of Poznań
60-637 Poznań, Poland

e-mail: calinski@au.poznan.pl

Sanpei Kageyama

Hiroshima University,
Higashi-Hiroshima 739-8524, Japan

e-mail: ksanpei@hiroshima-u.ac.jp

Abstract

Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB" itself is not much informative in a statistical sense. More information may be added to this term. In this paper, a unified terminology is suggested, aimed at giving more statistical meaning to the PEB designs, which may or may not be connected. The paper is essentially based on our recent books "BLOCK DESIGNS: A Randomization Approach", Springer Lecture Notes in Statistics, Vol. 150 (2000), Vol. 170 (2003), with some new additions.

Keywords: block design, PEB design, efficiency factor, basic contrast.

2000 Mathematics Subject Classification: 62K10.

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Received 22 December 2003