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Entropy 2016, 18(8), 291; doi:10.3390/e18080291

Indicators of Evidence for Bioequivalence

1
Département de Mathématiques, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland
2
Department of Mathematics and Statistics, La Trobe University, Melbourne 3086, Australia
Both authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editors: Julio Stern, Adriano Polpo and Kevin H. Knuth
Received: 29 May 2016 / Revised: 22 July 2016 / Accepted: 2 August 2016 / Published: 9 August 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
View Full-Text   |   Download PDF [806 KB, uploaded 9 August 2016]   |  

Abstract

Some equivalence tests are based on two one-sided tests, where in many applications the test statistics are approximately normal. We define and find evidence for equivalence in Z-tests and then one- and two-sample binomial tests as well as for t-tests. Multivariate equivalence tests are typically based on statistics with non-central chi-squared or non-central F distributions in which the non-centrality parameter λ is a measure of heterogeneity of several groups. Classical tests of the null λ λ 0 versus the equivalence alternative λ < λ 0 are available, but simple formulae for power functions are not. In these tests, the equivalence limit λ 0 is typically chosen by context. We provide extensions of classical variance stabilizing transformations for the non-central chi-squared and F distributions that are easy to implement and which lead to indicators of evidence for equivalence. Approximate power functions are also obtained via simple expressions for the expected evidence in these equivalence tests. View Full-Text
Keywords: evidence for alternatives; Kullback–Leibler divergence; sample size determination; two by two tables; two one-sided tests; variance stabilization evidence for alternatives; Kullback–Leibler divergence; sample size determination; two by two tables; two one-sided tests; variance stabilization
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Morgenthaler, S.; Staudte, R. Indicators of Evidence for Bioequivalence. Entropy 2016, 18, 291.

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