Testing Statistical Hypotheses of Equivalence Stefan Wellek (Central Institute of Mental Health, Mannheim, and University of Heidelberg, Germany)

Testing Statistical Hypotheses of Equivalence By Stefan Wellek (Central Institute of Mental Health, Mannheim, and University of Heidelberg, Germany)

Summary

Presents a comprehensive treatment of statistical equivalence testing. This title addresses a spectrum of specific, two-sided equivalence testing problems, from the one-sample problem with normally distributed observations of fixed known variance to problems involving various samples and multivariate data.

Testing Statistical Hypotheses of Equivalence by Stefan Wellek (Central Institute of Mental Health, Mannheim, and University of Heidelberg, Germany)

Equivalence testing has grown significantly in importance over the last two decades, especially as its relevance to a variety of applications has become understood. Yet published work on the general methodology remains scattered in specialists' journals, and for the most part, it focuses on the relatively narrow topic of bioequivalence assessment.

With a far broader perspective, Testing Statistical Hypotheses of Equivalence provides the first comprehensive treatment of statistical equivalence testing. The author addresses a spectrum of specific, two-sided equivalence testing problems, from the one-sample problem with normally distributed observations of fixed known variance to problems involving several samples and multivariate data. The treatment includes a concise review of basic mathematical results on optimal tests for equivalence, and the author makes available on the Internet a collection of computer programs that allow easy implementation of the methods presented.

In a field as complex and rich in potential applications as equivalence testing, Testing Statistical Hypotheses of Equivalence stands alone as a coherent reference that furnishes both the theoretical and practical tools needed for dealing with equivalence trials of any complexity and in any phase.

INTRODUCTION
Demonstration of Equivalence as a Basic Problem of Applied Statistics
Formalization of the Statistical Notion of Equivalence
Major Fields of Application of Equivalence Tests
Choosing the Main Distributional Parameter
Numerical Specification of the Limits of Equivalence
METHODS FOR ONE-SIDED EQUIVALENCE PROBLEMS
Objective of a One-Sided Equivalence Trial and Formulation of Hypotheses
Standard Solution for Location Parameter Families
Exact Two-Sample Tests for Binomial Distributions
GENERAL APPROACHES TO THE CONSTRUCTION OF TESTS FOR EQUIVALENCE IN THE STRICT SENSE
The Principle of Confidence Interval Inclusion
Bayesian Tests for Equivalence
The Classical Approach to Deriving Optimal Parametric Tests for Equivalence Hypotheses
Construction of Asymptotic Tests for Equivalence
EQUIVALENCE TESTS FOR SELECTED ONE-PARAMETER PROBLEMS
The One-Sample Problem with Normally Distributed Observations of Known Variance
Test for Equivalence of a Hazard Rate to Some Given Reference Value with Exponentially Distributed Survival Times
Testing for Equivalence of a Single Binomial Proportion to a Fixed Reference Success Probability
Confidence-Interval Inclusion Rules as Asymptotically UMP Tests for Equivalence
EQUIVALENCE TESTS FOR DESIGNS WITH PAIRED OBSERVATIONS
Sign Test for Equivalence
Equivalence Tests for the McNemar Setting
Paired t-Test for Equivalence
Signed Rank Test for Equivalence
A Generalization of the Signed Rank Test for Equivalence for Noncontinuous Data
EQUIVALENCE TESTS FOR TWO UNRELATED SAMPLES
Two-Sample t-Test for Equivalence
Mann-Whitney Test for Equivalence
A distribution-Free Two-Sample Equivalence Test Allowing for Arbitrary Patterns of Ties
Testing for Dispersion Equivalence of Two Gaussian Distributions
Equivalence Tests for Two Binomial Samples
Log-Rank Test for Equivalence of Two Survivor Functions
MULTI-SAMPLE TESTS FOR EQUIVALENCE
The Intersection-Union Principle as a General Solution to Multi-Sample Equivalence Problems
F-Test for Equivalence of k Normal Distributions
Modified Studentized Range Test for Equivalence
Testing for Dispersion Equivalence of More than Two Gaussian Distributions
A Nonparametric k-Sample Test for Equivalence
TESTS FOR ESTABLISHING GOODNESS OF FIT
Testing for Equivalence of a Single Multinomial Distribution with a
Fully Specified Reference Distribution
Testing for Approximate Collapsibility of Multiway Contingency Tables
Establishing Goodness of Fit of Linear Models for Normally Distributed Data
THE ASSESSMENT OF BIO-EQUIVALENCE
Introduction
Methods of Testing for Average Bioequivalence
Individual Bioequivalence: Criteria and Testing Procedures
Approaches to Defining and Establishing Population Bioequivalence
Bioequivalence Assessment as a Problem of Comparing Bivariate Distributions
APPENDIX
REFERENCES
INDEX

Testing Statistical Hypotheses of Equivalence Stefan Wellek (Central Institute of Mental Health, Mannheim, and University of Heidelberg, Germany)

Testing Statistical Hypotheses of Equivalence by Stefan Wellek (Central Institute of Mental Health, Mannheim, and University of Heidelberg, Germany)

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Testing Statistical Hypotheses of Equivalence by Stefan Wellek (Central Institute of Mental Health, Mannheim, and University of Heidelberg, Germany)

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