### Abstract

The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.

Original language | English |
---|---|

Pages (from-to) | 1437-1455 |

Number of pages | 19 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 10 |

Issue number | 14 |

DOIs | |

State | Published - Jan 1 1981 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*10*(14), 1437-1455. https://doi.org/10.1080/03610928108828125

**A Generalization of the Rank Transform in the Two-Sample Location Problem.** / Nath, Ravinder; Duran, B. S.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 10, no. 14, pp. 1437-1455. https://doi.org/10.1080/03610928108828125

}

TY - JOUR

T1 - A Generalization of 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 - The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.

AB - The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.

UR - http://www.scopus.com/inward/record.url?scp=84948243996&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84948243996&partnerID=8YFLogxK

U2 - 10.1080/03610928108828125

DO - 10.1080/03610928108828125

M3 - Article

AN - SCOPUS:84948243996

VL - 10

SP - 1437

EP - 1455

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 14

ER -