IDEAS home Printed from
   My bibliography  Save this article

Smooth extensions of Pearsons's product moment correlation and Spearman's rho


  • Rayner, J. C. W.
  • Best, D. J.


A smooth model for doubly ordered two-way contingency tables with no fixed marginals is given and the score test of the hypothesis of independence derived. For the saturated model the score statistic is the familiar Pearon's Xp2, and the first component is simply related to Pearson's product moment correlation. The higher-order components provide the promised extensions. They provide powerful direction tests and are easy to use and interpret, assessing if the bivariate moments of the data are consistent with what might be expected under the independence model. If ranks are used the score statistic is still Xp2, and the first component is simply related to Spearman's rho. The higher-order components again provide the promised extensions. In both cases the components permit an informative and close scrutiny of the data.

Suggested Citation

  • Rayner, J. C. W. & Best, D. J., 1996. "Smooth extensions of Pearsons's product moment correlation and Spearman's rho," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 171-177, October.
  • Handle: RePEc:eee:stapro:v:30:y:1996:i:2:p:171-177

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Burton, Robert M. & Dehling, Herold, 1990. "Large deviations for some weakly dependent random processes," Statistics & Probability Letters, Elsevier, vol. 9(5), pages 397-401, May.
    2. Li, Deli & Bhaskara Rao, M. & Wang, Xiangchen, 1992. "Complete convergence of moving average processes," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 111-114, May.
    3. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Eric Beh, 2004. "S-PLUS code for ordinal correspondence analysis," Computational Statistics, Springer, vol. 19(4), pages 593-612, December.


    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:eee:stapro:v:30:y:1996:i:2:p:171-177. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.