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

top
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

top

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

top
  1. [1] R.A. Bailey, H. Monod and J.P. Morgan, Construction and optimality of affine-resolvable designs, Biometrika 82 (1995), 187-200. Zbl0828.62061
  2. [2] T. Caliński, On some desirable patterns in block designs (with discussion), Biometrics 27 (1971), 275-292. 
  3. [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. Zbl0912.62086
  4. [4] T. Caliński and S. Kageyama, Block Designs: A Randomization Approach, Volume I: Analysis, Lecture Notes in Statistics, Volume 150, Springer, New York 2000. Zbl0963.62071
  5. [5] T. Caliński and S. Kageyama, Block Designs: A Randomization Approach, Volume II: Design, Lecture Notes in Statistics, Volume 170, Springer, New York 2003. Zbl1108.62318
  6. [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. Zbl0922.62114
  7. [7] B. Ceranka and S. Mejza, A new proposal for classification of block designs, Studia Scient. Mathematicarum Hungarica 15 (1980), 79-82. Zbl0504.62070
  8. [8] J.A. John, Cyclic Designs, Chapman and Hall, London 1987. Zbl0731.05001
  9. [9] R.M. Jones, On a property of incomplete blocks, J. Roy Statist. Soc. B 21 (1959), 172-179. Zbl0117.14308
  10. [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. 
  11. [11] S.C. Pearce, Supplemented balance, Biometrika 47 (1960), 263-271. 
  12. [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. Zbl0292.62052
  13. [13] P.D. Puri and A.K. Nigam, On patterns of efficiency balanced designs, J. Roy. Statist. Soc. B 37 (1975), 457-458. Zbl0311.62048
  14. [14] P.D. Puri and A.K. Nigam, A note on efficiency balanced designs, Sankhy¯a B 37 (1975), 457-460. Zbl0364.62078
  15. [15] P.D. Puri and A.K. Nigam, Partially efficiency balanced designs, Commun. Statist. -Theor. Meth. A 6 (1977), 753-771. Zbl0363.62058
  16. [16] D. Raghavarao, Constructions and Combinatorial Problems in Design of Experiments, John Wiley, New York 1971. 
  17. [17] G.M. Saha, On Calinski's patterns in block designs, Sankhy¯a B 38 (1976), 383-392. Zbl0409.62062
  18. [18] K.R. Shah, Use of inter-block information to obtain uniformly better estimates, Ann. Math. Statist. 35 (1964), 1064-1078. Zbl0229.62017
  19. [19] E.R. Williams, Efficiency-balanced designs, Biometrika 62 (1975), 686-689. Zbl0342.05009
  20. [20] F. Yates, Incomplete randomized blocks, Ann. Eugen. 7 (1936), 121-140. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.