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

摘要

This paper addresses the problem of estimating the ratio of themeans of independent normal variables in agricultural research.The first part of the research examines the distributionalproperties of the ratio of independent normal variables, boththeoretically and using simulation. The second part of theresearch evaluates the relative merits of two common estimators ofthe ratio of the means of independent normal variables inagricultural research, an arithmetic average and a weightedaverage, via simulation experiments using normal distributions.The results are then tested using research data from rice breedingmulti-environment trials in Jilin Province, China, in 1994. Thesedata are used to demonstrate the diagnostic approach developed forassessing the “safe” use of the arithmetic and the weightedaverage methods for estimating the ratio of the means ofindependent normal variables.