# Control treatments in designs with split units generated by Latin squares

Shinji Kuriki; Iwona Mejza; Kazuhiro Ozawa; Stanisław Mejza

Biometrical Letters (2014)

- Volume: 51, Issue: 2, page 125-142
- ISSN: 1896-3811

## Access Full Article

top## Abstract

top## How to cite

topShinji Kuriki, et al. "Control treatments in designs with split units generated by Latin squares." Biometrical Letters 51.2 (2014): 125-142. <http://eudml.org/doc/268761>.

@article{ShinjiKuriki2014,

abstract = {This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments using the considered designs, as well as possible arrangements of controls in the experiments.},

author = {Shinji Kuriki, Iwona Mejza, Kazuhiro Ozawa, Stanisław Mejza},

journal = {Biometrical Letters},

keywords = {Latin square; Youden square; split units; efficiency factors; merging treatment method; Incomplete split-plot design; General balance; Efficiency factors},

language = {eng},

number = {2},

pages = {125-142},

title = {Control treatments in designs with split units generated by Latin squares},

url = {http://eudml.org/doc/268761},

volume = {51},

year = {2014},

}

TY - JOUR

AU - Shinji Kuriki

AU - Iwona Mejza

AU - Kazuhiro Ozawa

AU - Stanisław Mejza

TI - Control treatments in designs with split units generated by Latin squares

JO - Biometrical Letters

PY - 2014

VL - 51

IS - 2

SP - 125

EP - 142

AB - This paper deals with two-factor experiments with split units. The whole plot treatments occur in a repeated Latin square, modified Latin square or Youden square, while subplot treatments occur in a block design within the whole plots. The statistical properties of the considered designs are examined. Special attention is paid to the case where one of the treatments is an individual control or an individual standard treatment. In addition, we give a brief overview of work on the design of experiments using the considered designs, as well as possible arrangements of controls in the experiments.

LA - eng

KW - Latin square; Youden square; split units; efficiency factors; merging treatment method; Incomplete split-plot design; General balance; Efficiency factors

UR - http://eudml.org/doc/268761

ER -

## References

top- Bailey R. (1995): General balance: artificial theory or practical relevance. Proc. of the International Conference on Linear Statistical Inference, LINSTAT’93, Mathematics and Applications. Vol. 306, Kluwer Academic Publishers, Dordrecht: 171-184. Zbl0813.62067
- Caliński T., Kageyama S. (2000): Block Designs: Randomizatiom Approach, Volume I: Analysis, Lecture Notes in Statistics, 150, Springer-Verlag, New York. Zbl0963.62071
- Caliński T., Kageyama S. (2003): Block Designs: Randomizatiom Approach, Volume II: Design, Lecture Notes in Statistics, 170, Springer-Verlag, New York. Zbl1108.62318
- Ceranka B., Mejza S. (1987): Merging of treatments in certain partially efficiency balanced block designs with two different numbers of replications. Calcutta Statist. Assoc. Bull. 36: 49-55. Zbl0715.62153
- Clatworthy W.H. (1973): Tables of Two-Associate-Class Partially Balanced Designs. NBS Applied Mathematics Series 63. Washington, D.C, USA. Zbl0289.05017
- Hering F., Mejza S. (2002): An incomplete split-block design generated by GDPBIBD(2)s. Journal of Statistical Planning and Inference 106: 125-134. Zbl1127.62394
- Houtman A.M., Speed T.P. (1983): Balance in designed experiments with orthogonal block structure. Ann. Statist., 11: 1069-1085. Zbl0566.62065
- Kachlicka D., Hering F., Mejza S. (2004): Control treatments in Youden Square with Split Units. Folia Fac. Sci. Nat. Univ. Masaryk. Brunensis, Mathematica 15: 137-144. Zbl1134.62352
- Kachlicka D., Mejza S. (1996): Repeated row-column designs with split units. Comp. Zbl0875.62385
- Statist. & Data Analysis 21: 293-305.
- Kachlicka D., Mejza S. (2003): Whole plot control treatments in Youden square with split units. Colloquium Biometryczne 33a: 77-84.
- Kachlicka D., Mejza S. (2006): Repeated Youden Square with Split Units generated by GDPBIBD(2). XVIIth. Summer School of Biometrics, "Current Trends in Biometrical Research", G. J. Mendel University of Agriculture and Forestry, Lednice, August 21 - 25. 2006. Eds. J. Hartmann i J. Michalek: 159-160.
- Kuriki S., Mejza S., Mejza I., Kachlicka D. (2009): Repeated Youden squares with subplot treatments in a proper incomplete block design. Biometrical Letters 46(2): 153-162. Zbl1292.62114
- Mejza I., Mejza S. (1996): Incomplete split plot designs generated by GDPBIBD(2). Calcutta Statist. Assoc. Bull. 46: 117-127. Zbl0907.62086
- Mejza S. (1992): On some aspects of general balance in designed experiments. Statistica, anno LII, 2: 263-278. Zbl0770.62060
- Mejza S., Kuriki S. (2013): Youden Square with Split Units. J.L. da Silva et al. (eds.), Advances in Regression, Survival Analysis, Extreme values, Markov Processes and Other Statistical Applications, Studies in Theoretical and Applied Statistics, DOI 10.1007/978-3-642-34904-1 1; Springer-Verlag Berlin Heidelberg: 3-10.[Crossref]
- Mejza S., Kuriki S. Kachlicka D. (2009). Repeated Youden Squares with subplot treatments in a group-divisible design. Journal of Statistics and Applications 4: 369-377. Zbl1292.62114
- Pearce S.C., Caliński T., Marshall T.F. de C. (1974): The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika 61: 449-460. Zbl0292.62052

## NotesEmbed ?

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