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Exact theoretical distributions around the replicate results of a germination test

Published online by Cambridge University Press:  27 February 2019

Jean-Louis Laffont ,
Bonnie Hong ,
Bo-Jein Kuo  and
Kirk M. Remund
Jean-Louis Laffont*
Affiliation:
Pioneer Génétique SARL, 1131 Chemin de l'Enseigure, 31840 Aussonne, France
Bonnie Hong
Affiliation:
Corteva Agriscience, Agriculture Division of DowDuPont, 7300 NW 62nd Avenue, Johnston, IA 50131, USA
Bo-Jein Kuo
Affiliation:
Biostatistics Division, Department of Agronomy, National Chung Hsing University, 250 Kuo Kuang Road, Taichung, 40227, Taiwan, ROC
Kirk M. Remund
Affiliation:
Bayer Crop Science, 800 North Lindbergh Blvd, St Louis, Missouri 63167, USA
*
Author for correspondence: Jean-Louis Laffont, Email: jean-louis.laffont@pioneer.com
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Abstract

Many seed quality tests are conducted by first randomly assigning seeds into replicates of a given size. The replicate results are then used to check whether or not any problems occur in the realization of the test. The two main tools developed for this verification are the ratio of the observed variance of the replicate results to a theoretical variance and the tolerance for the range of the results. In this paper, we derive the theoretical distribution and its related properties of the sequence of numbers of seeds with a given quality attribute present in the replicates. From these theoretical results, we revisit the two quality checking tools widely used for the germination test. We show a precaution to be taken when relying on the variance ratio to check for under- or over-dispersion of the replicate results. This has led to the development of tables providing credible intervals of the variance ratio. The International Seed Testing Association tolerance tables for the range of the results are also compared with tolerances computed from the exact theoretical distribution of the range, leading us to recommend a revision of these tables.

Keywords

germinationover-dispersionpartitionsrangetolerancesunder-dispersionvariance ratio
Type
Research Paper
Information
Seed Science Research , Volume 29 , Issue 1 , March 2019 , pp. 64 - 72
Copyright
Copyright © Cambridge University Press 2019 

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