### Abstract

A studentized range test is proposed to test the hypothesis of average equivalence of treat- ments in terms of the distance between means against the alternative hypothesis of in- equivalence. A least favorable configuration (LFC) of means to guarantee the maximum level at a null hypothesis and a LFC of means to guarantee the minimum power at an al- ternative hypothesis are obtained. The level and power of the test are fully independent of the unknown means and variances. For a given level and a given power, the critical value and the required sample size for an experiment can be simultaneously determined, and the tables of critical values and sample sizes are provided for practitioners. A real numeri- cal example to demonstrate the use of the test procedure is provided. In situations where the common population variance is unknown and the equivalence is the actual distance be- tween means without standardization, a two-stage sampling procedure can be employed to find these solutions. It proves to be a quite feasible solution for practitioners.

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

Pages (from-to) | 603-614 |

Number of pages | 12 |

Journal | Computational Statistics and Data Analysis |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Computational Statistics and Data Analysis*,

*55*(1), 603-614. https://doi.org/10.1016/j.csda.2010.06.002

}

*Computational Statistics and Data Analysis*, vol. 55, no. 1, pp. 603-614. https://doi.org/10.1016/j.csda.2010.06.002

**On testing the equivalence of treatments using the measure of range.** / Chen, Hubert J.; Wen, Miin-Jye; Chuang, Chia Jui.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On testing the equivalence of treatments using the measure of range

AU - Chen, Hubert J.

AU - Wen, Miin-Jye

AU - Chuang, Chia Jui

PY - 2011/1/1

Y1 - 2011/1/1

N2 - A studentized range test is proposed to test the hypothesis of average equivalence of treat- ments in terms of the distance between means against the alternative hypothesis of in- equivalence. A least favorable configuration (LFC) of means to guarantee the maximum level at a null hypothesis and a LFC of means to guarantee the minimum power at an al- ternative hypothesis are obtained. The level and power of the test are fully independent of the unknown means and variances. For a given level and a given power, the critical value and the required sample size for an experiment can be simultaneously determined, and the tables of critical values and sample sizes are provided for practitioners. A real numeri- cal example to demonstrate the use of the test procedure is provided. In situations where the common population variance is unknown and the equivalence is the actual distance be- tween means without standardization, a two-stage sampling procedure can be employed to find these solutions. It proves to be a quite feasible solution for practitioners.

AB - A studentized range test is proposed to test the hypothesis of average equivalence of treat- ments in terms of the distance between means against the alternative hypothesis of in- equivalence. A least favorable configuration (LFC) of means to guarantee the maximum level at a null hypothesis and a LFC of means to guarantee the minimum power at an al- ternative hypothesis are obtained. The level and power of the test are fully independent of the unknown means and variances. For a given level and a given power, the critical value and the required sample size for an experiment can be simultaneously determined, and the tables of critical values and sample sizes are provided for practitioners. A real numeri- cal example to demonstrate the use of the test procedure is provided. In situations where the common population variance is unknown and the equivalence is the actual distance be- tween means without standardization, a two-stage sampling procedure can be employed to find these solutions. It proves to be a quite feasible solution for practitioners.

UR - http://www.scopus.com/inward/record.url?scp=77958038357&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958038357&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2010.06.002

DO - 10.1016/j.csda.2010.06.002

M3 - Article

VL - 55

SP - 603

EP - 614

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 1

ER -