Establishing Practical Equivalence Between Three Treatments
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.
KeywordsNormal distribution One-way layout Equivalence Coefficient of variation Range Confidence interval Acceptance set Least favorable configuration
AMS Subject Classification62J10
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