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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

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    Cited by:

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


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