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Testing Equivalence Simultaneously for Location and Dispersion of two Normally Distributed Populations
Author(s) -
Bauer Peter,
Bauer Michael M.
Publication year - 1994
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710360602
Subject(s) - equivalence (formal languages) , mathematics , sample size determination , heteroscedasticity , statistics , type i and type ii errors , population , statistical hypothesis testing , statistical power , demography , discrete mathematics , sociology
In clinical trials with an active control usually therapeutical equivalence of a new treatment is investigated by looking at a location parameter of the distributions of the primary efficacy variable. But even if the location parameters are close to each other existing differences in variability may be connected with different risks for under or over treatment in an individual patient. Assuming normally distributed responses a multiple test procedure applying two shifted one‐sided t ‐tests for the mean and accordingly two one‐sided F ‐tests for the variances is proposed. Equivalence in location and variability is established if all four tests lead to a rejection at the (one‐sided) level α. A conservative procedure “correcting” the t ‐tests for heteroscedasticity is derived. The choice of a design in terms of the global level α, the global power, the relevant deviations in the population means and variances, as well as the sample size is outlined. Numerical calculations of the actual level and power for the proposed designs show, that for balanced sample sizes the classical uncorrected one‐sided t ‐tests can be used safely without exaggerating the global type I error probability. Finally an example is given.