Equivalence hypothesis testing

In statistical applications, such as a comparison of two items, it is useful to know whether one item is equivalent to another. Similarly it is often desirable to know whether one item can act as a substitute for another. Applications of the concept of equivalence include blend and flavor modificati...

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Bibliographic Details
Published in:Food quality and preference 2010-04, Vol.21 (3), p.253-256
Main Authors: Ennis, Daniel M., Ennis, John M.
Format: Article
Language:English
Subjects:
Bioequivalence
Biological and medical sciences
blended foods
brand name products
drugs
Equivalence
flavor
food analysis
Food industries
food quality
Fundamental and applied biological sciences. Psychology
General aspects
generic drugs
Hypothesis testing
mathematical models
Methods of analysis, processing and quality control, regulation, standards
new methods
Noncentral chi-square
Noncentral F
null hypothesis
Power
TOST
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Summary:In statistical applications, such as a comparison of two items, it is useful to know whether one item is equivalent to another. Similarly it is often desirable to know whether one item can act as a substitute for another. Applications of the concept of equivalence include blend and flavor modifications of products, substitution of generic drugs for brand-name drugs, modifications of products in response to government regulations, or component substitutions with more healthful or lower cost components. In addition, some companies develop products that are direct substitutes for those of their competitors and make advertising claims concerning their equivalence. In a recent paper, Ennis and Ennis [Ennis, D. M., & Ennis, J. M. (2009). Hypothesis testing for equivalence based on symmetric open intervals. Communications in Statistics – Theory and Methods, 38(11), 1792–1803] used an open interval to define equivalence and provided exact and approximate methods for testing a null hypothesis of nonequivalence. In this paper, a discussion of this newly developed theory of equivalence testing is presented along with a comparison to existing methods such as the “two one-sided tests” (TOST) method. We provide numerical examples to illustrate this new theory and we demonstrate that although the TOST is a convenient approximation it is fundamentally inconsistent with the specification of the null hypothesis.
ISSN:0950-3293
1873-6343
DOI:10.1016/j.foodqual.2009.06.005