Some applications of weighing designs

Małgorzata Graczyk

Biometrical Letters (2013)

  • Volume: 50, Issue: 1, page 15-26
  • ISSN: 1896-3811

Abstract

top
The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.

How to cite

top

Małgorzata Graczyk. "Some applications of weighing designs." Biometrical Letters 50.1 (2013): 15-26. <http://eudml.org/doc/268796>.

@article{MałgorzataGraczyk2013,
abstract = {The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.},
author = {Małgorzata Graczyk},
journal = {Biometrical Letters},
keywords = {chemical balance weighing design; factorial design; spring balance weighing design},
language = {eng},
number = {1},
pages = {15-26},
title = {Some applications of weighing designs},
url = {http://eudml.org/doc/268796},
volume = {50},
year = {2013},
}

TY - JOUR
AU - Małgorzata Graczyk
TI - Some applications of weighing designs
JO - Biometrical Letters
PY - 2013
VL - 50
IS - 1
SP - 15
EP - 26
AB - The purpose of this paper is to apply results on weighing designs to the setting of 2m factorial designs. Using weighing designs, we give some proposals for experimental plans. Relevant counterexamples are indicated. Also the results of a simulation study on the existence of weighing designs are presented.
LA - eng
KW - chemical balance weighing design; factorial design; spring balance weighing design
UR - http://eudml.org/doc/268796
ER -

References

top
  1. Banerjee K.S. (1975): Weighing Designs for Chemistry, Medicine. Economics, Operations Research, Statistics. Marcel Dekker Inc., New York. Zbl0334.62030
  2. Banerjee T., Mukerjee R. (2008): Optimal factorial designs for cDNA microarray experiments. Ann. Appl. Statist. 2: 366-385.[WoS] Zbl1137.62074
  3. Beckman R.J. (1973). An application of multivariate weighing designs. Communication in Statistics 1(6): 561-565.[Crossref] Zbl0261.62052
  4. Box G.E., Hunter J.S., Hunter W.G. (2005). Statistics for Experimenters: Design, Innovation, and Discovery, 2nd Edition. Wiley. Zbl1082.62063
  5. Ceranka B., Graczyk M. (2001): Optimum chemical balance weighing designs under the restriction on weighings. Discussiones Mathematicae-Probability and Statistics 21: 111-120. Zbl1016.05009
  6. Ceranka B., Graczyk M. (2003): Optimum chemical balance weighing designs for v+1 objects. Kybernetika 39: 333-340. Zbl1248.62128
  7. Ceranka B., Katulska K. (1987a): The application of the theory of spring balance weighing design for experiments with mixtures (in Polish). Listy Biometryczne XXIV(1): 17-26. 
  8. Ceranka B., Katulska K. (1987b): The application of the optimum spring balance weighing designs (in Polish). Siedemnaste Colloquium Metodologiczne z Agro- Biometrii: 98-108. 
  9. Ceranka B., Katulska K. (1989): Application of the biased spring balance weighing theory to estimation of differences of line effects for legume content. Biometrical Journal 31: 103-110.[Crossref] Zbl0691.62070
  10. Ceranka B., Katulska K. (2001): A-optimal chemical balance weighing design with diagonal covariance matrix of errors. Moda 6, Advances in Model Oriented Design and Analysis, A.C. Atkinson, P. Hackl, W.G. Műller, eds., Physica-Verlag, Heidelberg, New York: 29-36. 
  11. Cheng C.S. (1980): Optimality of some weighing and n 2 fractional factorial designs. Annals of Statistics 8: 436-446.[WoS][Crossref] Zbl0425.62055
  12. Gawande B.N., Patkar A.Y. (1999): Application of factorial design for optimization of Cyclodextrin Glycosyltransferase production from Klebsiella pneumoniae pneumonaiae AS-22, Biotechnology and Bioengineering 64(2): 168-173.[Crossref] 
  13. Glonek G.F.V., Solomon P.J. (2004): Factorial and time course designs for cDNA microarray experiments. Biostatistics 5: 89-111.[Crossref][PubMed] Zbl1096.62077
  14. Graczyk M. (2009): Regular A-optimal design matrices X=(xij) xij=-1, 0, 1. Statistical Papers 50: 789-795.[WoS][Crossref] Zbl1247.62198
  15. Graczyk M. (2011): A-optimal biased spring balance design. Kybernetika 47: 893-901. Zbl1274.62495
  16. Graczyk M. (2012a): Notes about A-optimal spring balance weighing design. Journal of Statistical Planning and Inference 142: 781-784.[WoS] Zbl1232.62108
  17. Graczyk M. (2012b): A-optimal spring balance weighing design under some conditions. Communication in Statistics-Theory and Methods 41: 2386-2393 Zbl1271.62173
  18. Graczyk M. (2012c): Regular A-optimal spring balance weighing designs. Revstat 10(3): 1-11. 
  19. John P.W.M. (1971): Statistical Design and Analysis of Experiments. Macmillan, New York. Zbl0231.62089
  20. Katulska K. (1984): The application of the theory of weighing design for feeding mixtures investigations and in the geodesy (in Polish). Czternaste Colloquium Metodologiczne z Agro-Biometrii: 195-208. 
  21. Katulska K. (1989): Optimum biased spring balance weighing design. Statistics and Probability Letters 8: 267-271.[Crossref] Zbl0676.62058
  22. Kiefer J. (1974): General equivalence theory for optimum designs. The Annals of Statistics 2: 849-879.[Crossref] Zbl0291.62093
  23. Koukouvinos Ch. (1995): Optimal weighing designs and some new weighing matrices. Statistics and Probability Letters 25: 37-42.[Crossref] Zbl0838.62057
  24. Koukouvinos Ch., Seberry J. (1997): Weighing matrices and their applications. Journal of Statistical Planning and Inference 62: 91-101.[Crossref] Zbl0874.62084
  25. Montgomery D.C. (1991): Design and Analysis of Experiments. 3rd edition. John Wiley & Sons, New York. Zbl0747.62072
  26. Mukerjee R., Tang B. (2012): Optimal fractions of two-level factorials under a baseline parameterization. Biometrika 99(1): 71-84.[Crossref][WoS] Zbl1234.62113
  27. Pukelsheim F. (1993): Optimal Design of Experiment. John Wiley & Sons, New York. Zbl0834.62068
  28. Sathe Y.S., Shenoy R.G. (1990): Construction method for some A- and D- optimal weighing designs when N ≡ 3(mod4). Journal of Statistical Planning and Inference 24: 369-375.[Crossref] Zbl0731.62131
  29. Seta G., Mrówczyński M., Wachowiak H. (2000): Harmfulness and possibility of pollen beetle control with combined application of insecticides and foliar fertilisers (in Polish). Progress in Plant Protection/Postępy w Ochronie Roślin 40(2): 905-907. 
  30. Sloane N.J.A., Harwit M. (1976). Masks for Hadamard transform optics, and weighing designs. Applied Optics 15(1): 107-114.[PubMed][Crossref] 
  31. Yang Y.H., Speed T. (2002): Design issues for cDNA microarray experiments. Nature Genetics (Suppl.) 3: 579-588. 

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.