Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 78375, 14 pages
Comparison of two common estimators of the ratio of the means of independent normal variables in agricultural research
1Centre for Social Research and Evaluation, Ministry of Social Development, P.O. Box 1556, Wellington, New Zealand
2Department of Statistics, Macquarie University, NSW 2109, Australia
3Institute of Information Sciences and Technology, Massey University, Private Bag, Palmerston North 11 222, New Zealand
4Analytical Development, Fonterra Marketing & Innovation, Palmerston North 11029, New Zealand
Received 26 October 2005; Revised 24 May 2006; Accepted 5 June 2006
Copyright © 2006 C. G. Qiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper addresses the problem of estimating the ratio of the
means of independent normal variables in agricultural research.
The first part of the research examines the distributional
properties of the ratio of independent normal variables, both
theoretically and using simulation. The second part of the
research evaluates the relative merits of two common estimators of
the ratio of the means of independent normal variables in
agricultural research, an arithmetic average and a weighted
average, via simulation experiments using normal distributions.
The results are then tested using research data from rice breeding
multi-environment trials in Jilin Province, China, in 1994. These
data are used to demonstrate the diagnostic approach developed for
assessing the “safe” use of the arithmetic and the weighted
average methods for estimating the ratio of the means of
independent normal variables.