bi2st {EQUIVNONINF} R Documentation

## Critical constants for the exact Fisher type UMPU test for equivalence of two binomial distributions with respect to the odds ratio

### 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

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 <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>

### References

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

### Examples

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


[Package EQUIVNONINF version 1.0.2 Index]