American Journal of Theoretical and Applied Statistics
Volume 8, Issue 4, July 2019, Pages: 136-146
Received: Jun. 26, 2019;
Accepted: Aug. 1, 2019;
Published: Aug. 14, 2019
Views 230 Downloads 37
Léon Rob Verdooren, Danone Nutricia Research, Utrecht, The Netherlands
In Oil Palm Breeding trials the plots have palms at vertices of equilateral triangles with side length of 9 m. The plots consist of 6x6 = 36 palms, hence a plot is a rectangle of 46.8 x 54m. The number of tested varieties is 20 – 40, the experimental design needed is an incomplete block design, with usually 3 replications; the alpha-designs can give a connected incomplete block design. Current Oil Palm planting materials are DxP hybrid based on crossing selected dura palms (female parents) with pisifera palms (male parents) to produce tenera palms with thin shelled fruits. The crossing scheme of A dura and B pisifera is an incomplete diallel if he number of crossings C is smaller than A*B. To make a connected crossing scheme the alpha-design can be used. In the analysis of an oil palm breeding trial an additive model of the dura and pisifera effects is applied to estimate the general combining ability of the parents after removing the fixed replication effect and the random blocks within the replication effects. The analysis can be done with the package SAS or IBM SPSS Statistics with program Mixed; further with R and the R package lme4.
Léon Rob Verdooren,
Use of Alpha-Designs in Oil Palm Breeding Trials, American Journal of Theoretical and Applied Statistics.
Vol. 8, No. 4,
2019, pp. 136-146.
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Bechhofer, R. E. (1954): A single-sample multiple decision procedure for ranking means of normal populations with known variances. Ann. Math. Statist., 25, 16-39.
Caliński, T. (1971): On some desirable patterns in block designs, Biometrics, 27, 275–292.
Cochran, W. G. and Cox, G. M. (1957): Experimental Designs, second edition. John Wiley & Sons, New York, London, Sydney.
Corsten, L. C. A. (1958): Vectors, a tool in statistical regression theory. Thesis Landbouwhogeschool Wageningen, Veenman.
CycDesigN (2014): A package for the computer generation of Experimental Designs, http://www.vsni.co.uk/software/cycdesign/.
Gupta, S. S. (1965): On some multiple decision (selection and ranking) rules. Technometrics, 7, 225-245.
Kuiper, N. H. (1952): Variantie-analyse. Statistica, 6,149-194. An English translation of this Dutch article is published in 1983 as “Analysis of Variance”, Mededelingen van de Landbouwhogeschool te Wageningen, Nederland, 83 (10).
Laan, P. van der, Verdooren, L. R. (1989): Selection of Populations. An Overview and Some Recent Results. Biometrical Journal, 31, 383-420.
Patterson, H. D., Williams, E. R. (1976): A new class of resolvable incomplete block designs, Biometrika, 63, 83–92.
Patterson, H. D., Williams, E. R. and Hunter, E. A. (1978): Block designs for variety trials. Journal of Agricultural Science, Cambridge, 90, 395-400.
Patterson, H.. D, Silvey, V. (1980): Statutory and recommended list trials of crop varieties in the United Kingdom (with discussion). J R Stat Soc A, 143, 219–252.
Verdooren, Rob; Soh, Aik Chin and Roberts, Jeremy (2017): Field Experimentation, Chapter 12 in Soh, Aik Chin, Mayes, Sean and Roberts, Jeremy (editors): Oil Palm Breeding, Genetics and Genomics. Taylor & Francis Group, CRC Press, Boca Raton.
Williams, E. R. (1977): Iterative analysis of generalized lattice designs. Aust J Stat, 19, 39–42.
Stevens, W. L. (1948): Statistical analysis of a non-orthogonal tri-factorial experiment. Biometrika, 35, 346-367.