bi1st {EQUIVNONINF}

Critical constants and power of the UMP test for equivalence of a single binomial proportion to some given reference value

Description

The function computes the critical constants defining the uniformly most powerful (randomized) test for the problem p \le p_1 or p \ge p_2 versus p_1 < p < p_2, with p denoting the parameter of a binomial distribution from which a single sample of size n is available. In the output, one also finds the power against the alternative that the true value of p falls on the midpoint of the hypothetical equivalence interval (p_1 , p_2).

Usage

bi1st(alpha,n,P1,P2)

Arguments

alpha

significance level

n

sample size

P1

lower limit of the hypothetical equivalence range for the binomial parameter p

P2

upper limit of the hypothetical equivalence range for p

Value

alpha

significance level

n

sample size

P1

lower limit of the hypothetical equivalence range for the binomial parameter p

P2

upper limit of the hypothetical equivalence range for p

C1

left-hand limit of the critical interval for the observed number X of successes

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

POWNONRD

Power of the nonrandomized version of the test against the alternative p = (p_1+p_2)/2

POW

Power of the randomized UMP test against the alternative p = (p_1+p_2)/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 4.3.

Examples

bi1st(.05,273,.65,.75)