• Login
    View Item 
    •   Home
    • Massey Documents by Type
    • Theses and Dissertations
    • View Item
    •   Home
    • Massey Documents by Type
    • Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Ratio estimators in agricultural research : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University, Palmerston North, New Zealand

    Icon
    View/Open Full Text
    01_front.pdf (2.406Mb)
    02_whole.pdf (11.65Mb)
    Export to EndNote
    Abstract
    This thesis addresses the problem of estimating the ratio of quantitative variables from several independent samples in agricultural research. The first part is concerned with estimating a binomial proportion, the ratio of discrete counts, from several independent samples under the assumption that there is a single underlying binomial proportion p in the population of interest. The distributions and properties of two linear estimators, a weighted average and an arithmetic average, are derived and merits of the approaches discussed. They are both unbiased estimators of the population proportion, with the weighted average having lower variability than the arithmetic average. These findings are obtained through a first principles analysis, with a geometrical interpretation presented. This variability result is also a consequence of the Rao-Blackwell theorem, a well-known result in the theory of statistical inference. Both estimators are used in the literature but we conclude that the weighted average estimate should always be used when the sample sizes are unequal. These results are illustrated by a simulation experiment and are validated using survey data in the study of lodging percentage of sunflower cultivar, Improved Peredovic, in Jilin Province, China in 1994. The second part of the research addresses the problem of estimating the ratio μͯ / μ, of the means of continuous variables in agricultural research. The distributional properties of the ratio X/Y of independent normal variables are examined, both theoretically and using simulation. The results show that the moments of the ratio do not exist in general. The moments exist, however, for a punctured normal distribution of the denominator variable if we only sample points for which | Y |>ε, ε being a small positive quantity. We draw out the practical rule-of-thumb that the ratio of two independent normal variables can be used to estimate μͯ / μ, when the coefficient of variation of the denominator variable is sufficiently small (less than or equal to 0.2). Lastly the thesis evaluates the relative merits of two common estimators of the ratio of the means of continuous variables in agricultural research, an arithmetic average and a weighted average, via simulation experiments using normal distributions. In the first simulation, the ratio and common coefficient of variation are changed while the sample size is kept moderately large. In the second simulation, the ratio and sample size are changed while the coefficient of variation is held constant. Results show that the weighted average always provides a better estimate of the true ratio and has lower variability than the arithmetic average. It is recommended that the weighted average be used for estimating the ratio from several pairs of observations. These results are tested using research data from rice breeding multi-environment trials in Jilin Province, China in 1995 and 1996. These data are used to demonstrate the diagnostic approach developed for assessing the 'safety' use of the arithmetic and the weighted average methods for estimating the ratio of the means of independent normal variables.
    Date
    2002
    Author
    Qiao, Chun Gui
    Rights
    The Author
    Publisher
    Massey University
    URI
    http://hdl.handle.net/10179/13491
    Collections
    • Theses and Dissertations
    Metadata
    Show full item record

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1
     

     

    Tweets by @Massey_Research
    Information PagesContent PolicyDepositing content to MROCopyright and Access InformationDeposit LicenseDeposit License SummaryTheses FAQFile FormatsDoctoral Thesis Deposit

    Browse

    All of MROCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister

    Statistics

    View Usage Statistics

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1