Testing for equivalence in k sample models Apl. Prof. Dr. Helmut Finner Deutsches Diabetes-Zentrum Institut für Biometrie und Epidemiologie Abstract
Hodges
and Lehmann (1954) proposed to distinguish between statistical and
material significance in hypotheses testing. They discussed several
testing problems where the hypotheses are defined in terms of certain
threshold values. Among others, they derived a new test related to
Student's t-test in terms of a complicated two-dimensional rejection
region. Many years later, their method was adopted for the construction
of a test for equivalence of two normal means. A good source for
two-sample equivalence tests is Wellek (2003).
In this talk we are concerned with the more advanced problem of establishing equivalence of treatment means in k sample models, where equivalence is defined in terms of a threshold value. We give a review of developments in this field. Besides the problem of establishing equivalence between all treatment means we consider the problem of selecting treatments which are equivalent to the best treatment. We reformulate the original selection problem as a multiple testing problem and propose some step-down and step-up procedures which can be constructed by applying the closure principle and partitioning principles. The new step-down procedure provides a uniform improvement over procedures currently in use. References
Giani,
G. and Finner, H. (1991). Some general results on least favourable
parameter configurations with
special reference to equivalence testing and the range statistic. J.
Statist. Planning Inf. 28, 33-47.
Finner, H. and Strassburger, K. (2006). On delta-equivalence with the best in k-sample models. J. Am. Statist. Assoc. 101, 737-74. Finner, H. & Strassburger, K. (2002). The partitioning principle: A powerful tool in multiple decision theory. Ann. Statist. 30, 1194 -1213. Hodges, J. L. and Lehmann, E. L. (1954). Testing the approximate validity of statistical hypotheses. J. R. Stat. Soc., B 16, 261-268. Wellek, S. (2003). Testing statistical hypotheses of equivalence. Boca Raton, Chapman and Hall. |