On testing the equivalence of treatments using the measure of range

Hubert J. Chen, Miin-Jye Wen, Chia Jui Chuang

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)603-614
Number of pages12
JournalComputational Statistics and Data Analysis
Volume55
Issue number1
DOIs
Publication statusPublished - 2011 Jan 1

Fingerprint

Least Favorable Configuration
Equivalence
Testing
Range of data
Standardization
Critical value
Sample Size
Two-stage Sampling
Sampling
Unknown
Null hypothesis
Tables
Experiments
Alternatives
Demonstrate
Experiment

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

@article{79f4ebea43ec4537a50e554edf4f21df,
title = "On testing the equivalence of treatments using the measure of range",
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.",
author = "Chen, {Hubert J.} and Miin-Jye Wen and Chuang, {Chia Jui}",
year = "2011",
month = "1",
day = "1",
doi = "10.1016/j.csda.2010.06.002",
language = "English",
volume = "55",
pages = "603--614",
journal = "Computational Statistics and Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",
number = "1",

}

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

In: Computational Statistics and Data Analysis, Vol. 55, No. 1, 01.01.2011, p. 603-614.

Research output: Contribution to journalArticle

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 -