### 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.

Original language | English |
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Pages (from-to) | 987-994 |

Number of pages | 7 |

Journal | Biometrika |

Volume | 91 |

DOIs | |

Publication status | Published - 2004 |

### Keywords

- asymptotic t distribution
- bivariate t distribution
- dissociation
- standardised difference
- SAMPLES
- SCORE

## Cite this

*Biometrika*,

*91*, 987-994. https://doi.org/10.1093/biomet/91.4.987