Description Usage Arguments Value Author(s) References Examples
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).
1  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 
lefthand limit of the critical interval for the observed number X of successes 
C2 
righthand 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 <[email protected]>
Peter Ziegler <[email protected]>
Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 4.3.
1  bi1st(.05,273,.65,.75)

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