### 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 |
---|---|

Pages (from-to) | 383-394 |

Number of pages | 12 |

Journal | Communications in Statistics Part B: Simulation and Computation |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1981 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Statistics and Probability

### Cite this

*Communications in Statistics Part B: Simulation and Computation*,

*10*(4), 383-394. https://doi.org/10.1080/03610918108812216

**The rank transform in the two-sample location problem.** / Nath, Ravinder; Duran, B. S.

Research output: Contribution to journal › Article

*Communications in Statistics Part B: Simulation and Computation*, vol. 10, no. 4, pp. 383-394. https://doi.org/10.1080/03610918108812216

}

TY - JOUR

T1 - The rank transform in the two-sample location problem

AU - Nath, Ravinder

AU - Duran, B. S.

PY - 1981/1/1

Y1 - 1981/1/1

N2 - 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, TR, is a function of the Wilcoxon statistic. It is shown here that TR has approximately a t-distribution. The ARE of the TR -test is identical to that of the Wilcoxon test. A Monte Carlo study reveals that the TR-test is more robust, with regard to the significance level, than the t-test.

AB - 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, TR, is a function of the Wilcoxon statistic. It is shown here that TR has approximately a t-distribution. The ARE of the TR -test is identical to that of the Wilcoxon test. A Monte Carlo study reveals that the TR-test is more robust, with regard to the significance level, than the t-test.

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UR - http://www.scopus.com/inward/citedby.url?scp=0039874375&partnerID=8YFLogxK

U2 - 10.1080/03610918108812216

DO - 10.1080/03610918108812216

M3 - Article

VL - 10

SP - 383

EP - 394

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 4

ER -