bi2ste3 {EQUIVNONINF}

Determination of a maximally raised nominal significance level for the nonrandomized version of the exact Fisher type test for 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

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 <[e-mail]>
Peter Ziegler <[e-mail]>

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

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