Garthwaite, Paul H. and Crawford, John R.
The distribution of the difference between two t-variates and application to a test for dissociations.
Biometrika, 91(4) pp. 987–994.
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.
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