A unified terminology in block designs

Tadeusz Caliński; Sanpei Kageyama

Discussiones Mathematicae Probability and Statistics (2004)

  • Volume: 24, Issue: 1, page 127-145
  • ISSN: 1509-9423

Abstract

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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.

How to cite

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Tadeusz Caliński, and Sanpei Kageyama. "A unified terminology in block designs." Discussiones Mathematicae Probability and Statistics 24.1 (2004): 127-145. <http://eudml.org/doc/287711>.

@article{TadeuszCaliński2004,
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.},
author = {Tadeusz Caliński, Sanpei Kageyama},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {block design; PEB design; efficiency factor; basic contrast},
language = {eng},
number = {1},
pages = {127-145},
title = {A unified terminology in block designs},
url = {http://eudml.org/doc/287711},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Tadeusz Caliński
AU - Sanpei Kageyama
TI - A unified terminology in block designs
JO - Discussiones Mathematicae Probability and Statistics
PY - 2004
VL - 24
IS - 1
SP - 127
EP - 145
AB - 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.
LA - eng
KW - block design; PEB design; efficiency factor; basic contrast
UR - http://eudml.org/doc/287711
ER -

References

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