bi1st: Critical constants and power of the UMP test for equivalence...

In EQUIVNONINF: Testing for Equivalence and Noninferiority

Description

The function computes the critical constants defining the uniformly most powerful (randomized) test for the problem p ≤ p_1 or p ≥ 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, Par. 4.3.

Examples

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

Example output

Loading required package: BiasedUrn
 alpha = 0.05    n = 273    P1 = 0.65    P2 = 0.75    C1 = 189    C2 = 194 
 gam1 = 0.3272078    gam2 = 0.3730956    POWNONRD = 0.2082461    POW = 0.2431317

EQUIVNONINF documentation built on July 12, 2021, 5:08 p.m.