Testing statistical hypotheses of equivalence

Wellek (biostatistics, U. of Heidelberg, Germany) provides numerous solutions to the equivalence testing problems researchers in the medical field encounter as they seek to analyze real data sets. The initial chapters contain discussion of testing for noninferiority used in clinical trials. Each of the testing problems that follow are defined and illustrated with examples used in actual studies. Welleck has designed an accompanying website with numerous downloadable programs. It is a basic fact well known to every statistician that in any hypotheses testing problem there is an inherent logical asymmetry concerning the roles played by the two statements (traditionally termed null and alternative hypotheses) between which a decision shall be taken on the basis of the data collected in a suitable trial or experiment: Any valid testing procedure guarantees that the risk of deciding erroneously in favour of the alternative does not exceed some prespecified bound whereas the risk of taking a wrong decision in favour of the null hypothesis can typically be as high as 1 minus the significance level (i.e., 95% in the majority of practical applications).