IDEAS home Printed from https://ideas.repec.org/a/taf/lstaxx/v44y2015i8p1621-1639.html
   My bibliography  Save this article

A Test of Non Null Hypothesis for Linear Trends in Proportions

Author

Listed:
  • Guolong Zhao

Abstract

Usual tests for trends stand under null hypothesis. This article presents a test of non null hypothesis for linear trends in proportions. A weighted least squares method is used to estimate the regression coefficient of proportions. A non null hypothesis is defined as its expectation equal to a prescribed regression coefficient margin. Its variance is used to construct an equation of basic relationship for linear trends in proportions along the asymptotic normal method. Then follow derivations for the sample size formula, the power function, and the test statistic. The expected power is obtained from the power function and the observed power is exhibited by Monte Carlo method. It reduces to the classical test for linear trends in proportions on setting the margin equal to zero. The agreement between the expected and the observed power is excellent. It is the non null hypothesis test matched with the classical test and can be applied to assess the clinical significance of trends among several proportions. By contrast, the classical test is restricted in testing the statistical significance. A set of data from a website is used to illustrate the methodology.

Suggested Citation

  • Guolong Zhao, 2015. "A Test of Non Null Hypothesis for Linear Trends in Proportions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(8), pages 1621-1639, April.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:8:p:1621-1639
    DOI: 10.1080/03610926.2013.776687
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03610926.2013.776687
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/03610926.2013.776687?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:lstaxx:v:44:y:2015:i:8:p:1621-1639. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/lsta .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.