EQUIVNONINF (version 1.0.2)

bi2st: 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 \(X=C_2\)

References

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

Examples

# NOT RUN {
bi2st(.05,225,119,171, 2/3, 3/2)
# }