### Abstract

In the two-sample location problem, if the t-statistic is computed as a function of the ranks of the observations rather than the observations themselves, the resulting statistic, T_{R}, is a function of the Wilcoxon statistic. It is shown here that T_{R} has approximately a t-distribution. The ARE of the T_{R} -test is identical to that of the Wilcoxon test. A Monte Carlo study reveals that the T_{R}-test is more robust, with regard to the significance level, than the t-test.

Original language | English (US) |
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Pages (from-to) | 383-394 |

Number of pages | 12 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1981 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modeling and Simulation

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## Cite this

Nath, R., & Duran, B. S. (1981). The rank transform in the two-sample location problem.

*Communications in Statistics - Simulation and Computation*,*10*(4), 383-394. https://doi.org/10.1080/03610918108812216