bi1st {EQUIVNONINF} | R Documentation |
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).
bi1st(alpha,n,P1,P2)
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 |
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 |
Stefan Wellek <stefan.wellek@zi-mannheim.de>
Peter Ziegler <peter.ziegler@zi-mannheim.de>
Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 4.3.
bi1st(.05,273,.65,.75)