ABSTRACT

Although the notions of equivalence and noninferiority have nowadays become part of standard terminology of applied statistics, the precise meaning of these terms is not self-explanatory. The first of them is used in statistics to denote a weak or, more adequately speaking, fuzzy form of an identity relation referring to the distribution(s) which underly the data under analysis. The fuzziness of equivalence hypotheses as considered in this book is induced by enlarging the null hypothesis of the traditional two-sided testing problem referring to the same statistical setting, through adding an “indifference zone” around the corresponding region (or point) in the parameter space. In other words, equivalence means here equality except for practically irrelevant deviations. Such an indifference zone is a basic and necessary ingredient of any kind of testing problem to be addressed in the planning and confirmatory analysis of a study, trial or experiment run with the objective of demonstrating equivalence. Admittedly, finding a consensus on how to specify that indifference zone concretely is far from easy in the majority of applications. However, it is an indispensable step without which the testing problem the experimenter proposes would make no statistical sense at all. The reason behind this fact whose proper understanding is an elementary prerequisite for a sensible use of the methods discussed in this book, will be made precise in § 1.5.