Description Usage Arguments Details Value Author(s) References Examples

Implementation of the paired-data analogue of the Mann-Whitney-Wilcoxon test for
equivalence of continuous distributions. The continuity assumption relates to the
intraindividual differences *D_i*. For details see Wellek S (2010) Testing statistical
hypotheses of equivalence and noninferiority. Second edition,*Par.* 5.4.

1 | ```
sgnrk(alpha,n,qpl1,qpl2,d)
``` |

`alpha` |
significance level |

`n` |
sample size |

`qpl1` |
lower equivalence limit |

`qpl2` |
upper equivalence limit |

`d` |
row vector with the intraindividual differences for all |

*q_+* is the probability of getting a positive sign of the so-called Walsh-average
of a pair of within-subject differences and can be viewed as a natural paired-observations
analogue of the Mann-Whitney functional *π_+ = P[X>Y]*.

`alpha` |
significance level |

`n` |
sample size |

`qpl1` |
lower equivalence limit |

`qpl2` |
upper equivalence limit |

`U_pl` |
observed value of the |

`SIGMAH` |
square root of the estimated asymtotic variance of |

`CRIT` |
upper critical bound to |

`REJ` |
indicator of a positive [=1] vs negative [=0] rejection decision to be taken with the data under analysis |

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.* 5.4.

1 2 3 |

```
Loading required package: BiasedUrn
alpha = 0.05 n = 20 qpl1_ = 0.2398 qpl2_ = 0.7602 U+ = 0.5526316 SIGMAH = 0.1207119 CRIT = 0.5435075 REJ = 1
```

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