# bi2st: Critical constants for the exact Fisher type UMPU test for... In EQUIVNONINF: Testing for Equivalence and Noninferiority

## Description

The function computes the critical constants defining the uniformly most powerful unbiased test for equivalence of two binomial distributions with parameters p_1 and p_2 in terms of the odds ratio. Like the ordinary Fisher type test of the null hypothesis p_1 = p_2, the test is conditional on the total number S of successes in the pooled sample.

## Usage

 1 bi2st(alpha,m,n,s,rho1,rho2) 

## Arguments

 alpha significance level m size of Sample 1 n size of Sample 2 s observed total count of successes rho1 lower limit of the hypothetical equivalence range for the odds ratio \varrho = \frac{p_1(1-p_2)}{p_2(1-p_1)} rho2 upper limit of the hypothetical equivalence range for \varrho

## Value

 alpha significance level m size of Sample 1 n size of Sample 2 s observed total count of successes rho1 lower limit of the hypothetical equivalence range for the odds ratio \varrho = \frac{p_1(1-p_2)}{p_2(1-p_1)} rho2 upper limit of the hypothetical equivalence range for \varrho C1 left-hand limit of the critical interval for the number X of successes observed in Sample 1 C2 right-hand limit of the critical interval for X GAM1 probability of rejecting the null hypothesis when it turns out that X=C_1 GAM2 probability of rejecting the null hypothesis for X=C_2

## Author(s)

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

## References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 6.6.4.

## Examples

 1 bi2st(.05,225,119,171, 2/3, 3/2) 

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