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Exact tests of equivalence and efficacy with a non-zero lower bound for comparative studies by I. S. F. Chan,Statistics in Medicine,17, 1403-1413 (1998) by Joachim Röhmel; Ulrich Mansmann is a Mathematics article available to read on EtoBox.

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Chan considered exact non-asymptotical tests based on two types of asymptotical test statistics Z #/ and Z #$ for the classical and non-classical null hypotheses. A lot of material on exact non-asymptotical tests for two independent binomially distributed variables has been published for the classical null hypothesis H : P !P \*0. Little is known, however, for shifted null hypotheses such as H : P !P \* . We agree with the author that there is some need to develop exact tests, because the true levels of the usual asymptotical tests are quite unsatisfactory, in particular for small to medium sample sizes. We have, however, some problems with his paper. For "xed \* and the resulting statistic Z\*"Z #/ ( \*), the author de"nes the p-value through max Pr(Z\*)Z\* "P3D) where the domain of P is the interval D"[0, 1! \*]. According to the author's formula (1), this interval is only the boundary of the null space. For a valid p-value the search for the maximum must therefore be extended over the whole null space. This could be done, for example, by investigating p( )"max Pr(Z\*)Z\* "P3[0, 1 ! ]) as a function of , 1\* \* \*. The procedure proposed by Chan would be a valid procedure if p( )

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Author

Joachim Röhmel; Ulrich Mansmann

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 0277-6715)

Published

1999

Language

EN

Field

Mathematics (Physical Sciences)