Journal of Statistical Theory and Practice

, Volume 9, Issue 3, pp 600–607 | Cite as

Establishing Practical Equivalence Between Three Treatments

  • Y. Lin
  • A. J. HayterEmail author
  • W. Liu


Consider a one-way layout with three treatments with unknown means μ1, μ2, and μ3, and a common unknown variance σ2. The practical equivalence of the three treatments can be concluded if the range of the three means is small in comparison to their standard deviation σ. This implies that the range Δ of the three reciprocal coefficients of variation μi/σ, 1 ≤ i ≤ 3, is less than a specified amount. In this article, it is shown how to construct an upper confidence bound for Δ for possibly unbalanced data sets. Small values of this upper bound allow practical equivalence to be established in an efficient manner. Examples of the implementation of this procedure are provided, and comparisons are made with other approaches. R code to implement the procedure is available.


Normal distribution One-way layout Equivalence Coefficient of variation Range Confidence interval Acceptance set Least favorable configuration 

AMS Subject Classification



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Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.School of ManagementFuzhou UniversityFuzhouChina
  2. 2.Department of Business Information and AnalyticsUniversity of DenverDenverUSA
  3. 3.S3RI and School of MathematicsUniversity of SouthamptonSouthamptonUK

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