# bi2ste3: Determination of a maximally raised nominal significance... In EQUIVNONINF: Testing for Equivalence and Noninferiority

## Description

The objective is to raise the nominal significance level as far as possible without exceeding the target significance level in the nonrandomized version of the test. The approach goes back to R.D. Boschloo (1970) who used the same technique for reducing the conservatism of the traditional nonrandomized Fisher test for superiority.

## Usage

 `1` ```bi2ste3(m, n, eps, alpha, sw, tolrd, tol, maxh) ```

## Arguments

 `m` size of Sample 1 `n` size of Sample 2 `eps` noninferiority margin to the odds ratio \varrho, defined to be the maximum acceptable deviation of the true value of \varrho from unity `alpha` target significance level `sw` width of the search grid for determining the maximum of the rejection probability on the common boundary of the hypotheses `tolrd` horizontal distance from 0 and 1, respectively, of the left- and right-most boundary point to be included in the search grid `tol` upper bound to the absolute difference between size and target level below which the search for a corrected nominal level terminates `maxh` maximum number of interval-halving steps to be carried out in finding the maximally raised nominal level

## Details

It should be noted that, as the function of the nominal level, the size of the nonrandomized test is piecewise constant. Accordingly, there is a nondegenerate interval of "candidate" nominal levels serving the purpose. The limits of such an interval can be read from the output.

## Value

 `m` size of Sample 1 `n` size of Sample 2 `eps` noninferiority margin to the odds ratio \varrho, defined to be the maximum acceptable deviation of the true value of \varrho from unity `alpha` target significance level `sw` width of the search grid for determining the maximum of the rejection probability on the common boundary of the hypotheses `tolrd` horizontal distance from 0 and 1, respectively, of the left- and right-most boundary point to be included in the search grid `tol` upper bound to the absolute difference between size and target level below which the search for a corrected nominal level terminates `maxh` maximum number of interval-halving steps to be carried out in finding the maximally raised nominal level `ALPH_0` current trial value of the raised nominal level searched for `NHST` number of interval-halving steps performed up to now `SIZE` size of the critical region corresponding to alpha_0

## Author(s)

Stefan Wellek <[email protected]>
Peter Ziegler <[email protected]>

## References

Boschloo RD: Raised conditional level of significance for the 2 x 2- table when testing the equality of two probabilities. Statistica Neerlandica 24 (1970), 1-35.

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, \S6.6.2.

## Examples

 `1` ``` bi2ste3(50, 50, 1/3, 0.05, 0.05, 1e-10, 1e-8, 10) ```

EQUIVNONINF documentation built on Sept. 19, 2017, 5:06 p.m.