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 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 <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, Par. 4.3.

### Examples

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

[Package EQUIVNONINF version 1.0.2 Index]