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Table of Contents
Testing Statistical Hypotheses of Equivalence
Stefan Wellek
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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






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