powsign {EQUIVNONINF} R Documentation

## Nonconditional power of the UMPU sign test for equivalence and its nonrandomized counterpart

### Description

The program computes for each possible value of the number n_0 of zero observations the power conditional on N_0 = n_0 and averages these conditional power values with respect to the distribution of N_0. Equivalence is defined in terms of the logarithm of the ratio p_+/p_-, where p_+ and p_- denotes the probability of obtaining a positive and negative sign, respectively.

### Usage

``` powsign(alpha,n,eps1,eps2,poa)
```

### Arguments

 `alpha` significance level `n` sample size `eps1` absolute value of the lower limit of the hypothetical equivalence range for \log(p_+/p_-). `eps2` upper limit of the hypothetical equivalence range for \log(p_+/p_-). `poa` probability of a tie under the alternative of interest

### Value

 `alpha` significance level `n` sample size `eps1` absolute value of the lower limit of the hypothetical equivalence range for \log(p_+/p_-). `eps2` upper limit of the hypothetical equivalence range for \log(p_+/p_-). `poa` probability of a tie under the alternative of interest `POWNONRD` power of the nonrandomized version of the test against the alternative p_+ = p_- = (1-p_\circ)/2 `POW` power of the randomized UMPU test against the alternative p_+ = p_- = (1-p_\circ)/2

### Note

A special case of the test whose power is computed by this program, is the exact conditional equivalence test for the McNemar setting (cf. Wellek 2010, pp. 76-77).

### 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. 5.1.

### Examples

```
powsign(0.06580,50,0.847298,0.847298,0.26)
```

[Package EQUIVNONINF version 1.0.2 Index]