bi1st {EQUIVNONINF}R Documentation

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 pp1p \le p_1 or pp2p \ge p_2 versus p1<p<p2p_1 < p < p_2, with pp denoting the parameter of a binomial distribution from which a single sample of size nn is available. In the output, one also finds the power against the alternative that the true value of pp falls on the midpoint of the hypothetical equivalence interval (p1,p2).(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 pp

P2

upper limit of the hypothetical equivalence range for pp

Value

alpha

significance level

n

sample size

P1

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

P2

upper limit of the hypothetical equivalence range for pp

C1

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

C2

right-hand limit of the critical interval for XX

GAM1

probability of rejecting the null hypothesis when it turns out that X=C1X=C_1

GAM2

probability of rejecting the null hypothesis for X=C2X=C_2

POWNONRD

Power of the nonrandomized version of the test against the alternative p=(p1+p2)/2p = (p_1+p_2)/2

POW

Power of the randomized UMP test against the alternative p=(p1+p2)/2p = (p_1+p_2)/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, §\S 4.3.

Examples

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

[Package EQUIVNONINF version 1.0.2 Index]