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Optimal sample size for estimating the proportion of transgenic plants using the Dorfman model with a random confidence interval

Published online by Cambridge University Press:  22 March 2011

Osval Antonio Montesinos-López ,
Abelardo Montesinos-López ,
José Crossa ,
Kent Eskridge  and
Ricardo A. Sáenz
Osval Antonio Montesinos-López*
Affiliation:
Facultad de Telemática, Universidad de Colima, Bernal Díaz del Castillo No. 340, Col. Villas San Sebastián, C.P. 28045, Colima, Colima, México
Abelardo Montesinos-López
Affiliation:
Departamento de Estadística, Centro de Investigación en Matemáticas (CIMAT), Guanajuato, Guanajuato, México
José Crossa
Affiliation:
Biometrics and Statistics Unit of the Crop Informatics Laboratory (CRIL) of the Maize and Wheat Improvement Center (CIMMYT), Apdo. Postal 6-641, Mexico, D.F., Mexico
Kent Eskridge
Affiliation:
Department of Statistics, University of Nebraska, Lincoln, Nebraska, USA
Ricardo A. Sáenz
Affiliation:
CUICBAS, Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, México28040
*
*Correspondence Email: [email protected]
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Abstract

Group testing is a procedure in which groups that contain several units (plants) are analysed without having to inspect individual plants, with the purpose of estimating the prevalence of genetically modified plants (adventitious presence of unwanted transgenic plants, AP) in a population at a low cost, without losing precision. When pool (group) testing is used to estimate the proportion of AP (p), there are several procedures that can be used for computing the confidence interval (CI); however, they usually do not ensure precision in the estimation of p. This research proposes a formula for determining the required number of pools (g), given a pool size (k), for estimating the proportion of AP plants using the Dorfman model. The proposed formula ensures precision in the estimated proportion of AP because it guarantees that the width (W) of the CI will be equal to, or narrower than, the desired width (ω), with a probability of γ. This probability accounts for the stochastic nature of the sample variance of p. We give examples to show how to use the proposed sample-size formula. Simulated data were created and tables are presented showing the different scenarios that a researcher may encounter. The Monte Carlo method was used to study the coverage and the level of assurance achieved by the proposed sample sizes. An R program that reproduces the results in the tables and makes it easy for the researcher to create other scenarios is given in the Appendix.

Keywords

adventitious presence of transgenic plantsconfidence intervaldesired widthgroup testingpool sampling
Type
Research Article
Information
Seed Science Research , Volume 21 , Issue 3 , September 2011 , pp. 235 - 245
Copyright
Copyright © Cambridge University Press 2011

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