# 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

 `1` ```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 <[email protected]>
Peter Ziegler <[email protected]>

## References

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition. Boca Raton: Chapman & Hall/CRC Press, 2010, Par. 4.3.

## Examples

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

EQUIVNONINF documentation built on Sept. 19, 2017, 5:06 p.m.