bi2st {EQUIVNONINF}

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

References

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

Examples

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