Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 78375, 14 pages
doi:10.1155/JAMDS/2006/78375

Comparison of two common estimators of the ratio of the means of independent normal variables in agricultural research

C. G. Qiao,1 G. R. Wood,2 C. D. Lai,3 and D. W. Luo4

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.

Abstract

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.