IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v27y2002i3p223-235.html
   My bibliography  Save this article

A New Maximum Likelihood Estimator for the Population Squared Multiple Correlation

Author

Listed:
  • Edward F. Alf Jr.
  • Richard G. Graf

Abstract

Using maximum likelihood estimation as described by R. A. Fisher (1912) , a new estimator for the population squared multiple correlation was developed. This estimator ( Ï circ; 2 (ML) ) was derived by examining all possible values of the population squared multiple correlation for a given sample size and number of predictors, and finding the one for which the observed sample value had the highest probability of occurring. The new estimator is shown to have greater accuracy than other estimators and to generate values that always fall within the parameter space. The utility of Ï circ; 2 (ML) in terms of providing the basis for the development of small sample significance tests is demonstrated. A Microsoft Excel workbook for computing Ï circ; 2 (ML) and its regions of nonsignificance and for computing a normal transformation for R 2 is offered.

Suggested Citation

  • Edward F. Alf Jr. & Richard G. Graf, 2002. "A New Maximum Likelihood Estimator for the Population Squared Multiple Correlation," Journal of Educational and Behavioral Statistics, , vol. 27(3), pages 223-235, September.
    • Handle: RePEc:sae:jedbes:v:27:y:2002:i:3:p:223-235
    DOI: 10.3102/10769986027003223
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/10769986027003223
    Download Restriction: no
    File URL: https://libkey.io/10.3102/10769986027003223?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
    ---><---

    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:sae:jedbes:v:27:y:2002:i:3:p:223-235. 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: SAGE Publications (email available below). General contact details of provider: .

    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.