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Biometrika 2004 91(4):987-994; doi:10.1093/biomet/91.4.987
© 2004 by Biometrika Trust
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The distribution of the difference between two t-variates

Paul H. Garthwaite1 and John R. Crawford2

1 Department of Statistics, The Open University, Milton Keynes, MK15 9JA, U.K. p.h.garthwaite{at}open.ac.uk, 2 Department of Psychology, University of Aberdeen, Aberdeen AB24 2UB, U.K. j.crawford{at}abdn.ac.uk

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.

Key Words: Asymptotic t distribution; Bivariate t distribution; Dissociation; Standardised difference

Received June 2003. Revised April 2004.


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