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The distribution of the difference between two t-variates

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  • Paul H. Garthwaite
  • John R. Crawford

Abstract

In this paper, the difference between two correlated t variables is divided by a function of their sample correlation and the distribution of the resulting quantity is examined. Functions of the sample correlation are found for which this quantity is approximately pivotal and has a t distribution, asymptotically. Simulations show that the asymptotic results hold well for small sample sizes. The results yield a useful test for comparing the difference in standardised scores of an individual with those of a group of controls. The test assumes that sampling is from a bivariate normal distribution and robustness of the test to departure from normality is examined. Copyright 2004, Oxford University Press.

Suggested Citation

  • Paul H. Garthwaite & John R. Crawford, 2004. "The distribution of the difference between two t-variates," Biometrika, Biometrika Trust, vol. 91(4), pages 987-994, December.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:987-994
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.987
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