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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1050,
author = {Tadeusz Cali\'nski and Sanpei Kageyama},
title = {A unified terminology in block designs},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {24},
year = {2004},
pages = {127-145},
zbl = {1063.62107},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1050}
}
Tadeusz Caliński; Sanpei Kageyama. A unified terminology in block designs. Discussiones Mathematicae Probability and Statistics, Tome 24 (2004) pp. 127-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1050/
[000] [1] R.A. Bailey, H. Monod and J.P. Morgan, Construction and optimality of affine-resolvable designs, Biometrika 82 (1995), 187-200. | Zbl 0828.62061
[001] [2] T. Caliński, On some desirable patterns in block designs (with discussion), Biometrics 27 (1971), 275-292.
[002] [3] T. Caliński and S. Kageyama, Block designs: Their combinatorial and statistical properties, S. Ghosh and C.R. Rao (eds.), Handbook of Statistics, Volume 13: Design and Analysis of Experiments, Elsevier Science, Amsterdam (1996), 809-873. | Zbl 0912.62086
[003] [4] T. Caliński and S. Kageyama, Block Designs: A Randomization Approach, Volume I: Analysis, Lecture Notes in Statistics, Volume 150, Springer, New York 2000. | Zbl 0963.62071
[004] [5] T. Caliński and S. Kageyama, Block Designs: A Randomization Approach, Volume II: Design, Lecture Notes in Statistics, Volume 170, Springer, New York 2003. | Zbl 1108.62318
[005] [6] B. Ceranka and Z. Kaczmarek, Testing genetic parameters in the mixed model of triallel analysis, A.C. Atkinson, L. Pronzato and H.P. Wynn (eds.), MODA 5 - Advances in Model-Oriented Data Analysis and Experimental Design, Physica-Verlag, Heidelberg (1998), 177-185. | Zbl 0922.62114
[006] [7] B. Ceranka and S. Mejza, A new proposal for classification of block designs, Studia Scient. Mathematicarum Hungarica 15 (1980), 79-82. | Zbl 0504.62070
[007] [8] J.A. John, Cyclic Designs, Chapman and Hall, London 1987. | Zbl 0731.05001
[008] [9] R.M. Jones, On a property of incomplete blocks, J. Roy Statist. Soc. B 21 (1959), 172-179. | Zbl 0117.14308
[009] [10] H.D. Patterson and V. Silvey, Statutory and recommended list trials of crop varieties in the United Kingdom, J. Roy. Statist. Soc. Ser. A 143 (1980), 219-252.
[010] [11] S.C. Pearce, Supplemented balance, Biometrika 47 (1960), 263-271.
[011] [12] S.C. Pearce, T. Caliński and T.F. de C. Marshall, The basic contrasts of an experimental design with special reference to the analysis of data, Biometrika 61 (1974), 449-460. | Zbl 0292.62052
[012] [13] P.D. Puri and A.K. Nigam, On patterns of efficiency balanced designs, J. Roy. Statist. Soc. B 37 (1975), 457-458. | Zbl 0311.62048
[013] [14] P.D. Puri and A.K. Nigam, A note on efficiency balanced designs, Sankhy¯a B 37 (1975), 457-460. | Zbl 0364.62078
[014] [15] P.D. Puri and A.K. Nigam, Partially efficiency balanced designs, Commun. Statist. -Theor. Meth. A 6 (1977), 753-771. | Zbl 0363.62058
[015] [16] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, John Wiley, New York 1971.
[016] [17] G.M. Saha, On Calinski's patterns in block designs, Sankhy¯a B 38 (1976), 383-392. | Zbl 0409.62062
[017] [18] K.R. Shah, Use of inter-block information to obtain uniformly better estimates, Ann. Math. Statist. 35 (1964), 1064-1078. | Zbl 0229.62017
[018] [19] E.R. Williams, Efficiency-balanced designs, Biometrika 62 (1975), 686-689. | Zbl 0342.05009
[019] [20] F. Yates, Incomplete randomized blocks, Ann. Eugen. 7 (1936), 121-140.