The distribution of the difference between two t-variates

P. H. Garthwaite, John Robertson Crawford

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)987-994
Number of pages7
Publication statusPublished - 2004


  • asymptotic t distribution
  • bivariate t distribution
  • dissociation
  • standardised difference


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