IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i1d10.1007_s00362-017-0924-6.html
   My bibliography  Save this article

Following K. Pearson to test the general linear hypothesis

Author

Listed:
  • Lynn Roy LaMotte

    (School of Public Health)

Abstract

The numerator sum of squares in the conventional F-statistic for testing a linear hypothesis in a general linear model can be viewed as following the heuristic that K. Pearson used in his seminal 1900 paper. That is, find a statistic $$\varvec{U}$$U that has expected value $$\varvec{0}$$0 under the null hypothesis and form from it $$\varvec{U}^{\prime }[\mathrm {Var}(\varvec{U})]^{-1}\varvec{U}$$U′[Var(U)]-1U, which, if $$\varvec{U}$$U is approximately normal, can be approximated as a chi-squared random variable. The class considered here comprises all such statistics based on linear statistics that have expected value $$\varvec{0}$$0 under the null hypothesis. Dominance relations among this class in terms of power are examined, and a complete subclass is described.

Suggested Citation

  • Lynn Roy LaMotte, 2020. "Following K. Pearson to test the general linear hypothesis," Statistical Papers, Springer, vol. 61(1), pages 71-83, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0924-6
    DOI: 10.1007/s00362-017-0924-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0924-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-017-0924-6?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

    Keywords

    Power; F-tests; Linear models;
    All these keywords.

    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:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0924-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.