Description Usage Arguments Value Note Author(s) References Examples

The function computes the critical constants defining the uniformly most powerful
invariant test for the problem
*(ξ-η)/σ ≤ -\varepsilon_1* or *(ξ-η)/σ ≥ \varepsilon_2*
versus *-\varepsilon_1 < (ξ-η)/σ < \varepsilon_2*, with *ξ* and *η* denoting
the expected values of two normal distributions with common variance *σ^2* from which independent
samples are taken.
In addition, tt2st outputs the power against the null alternative *ξ = η*.

1 | ```
tt2st(m,n,alpha,eps1,eps2,tol,itmax)
``` |

`m` |
size of the sample from |

`n` |
size of the sample from |

`alpha` |
significance level |

`eps1` |
absolute value of the lower equivalence limit to |

`eps2` |
upper equivalence limit to |

`tol` |
tolerable deviation from |

`itmax` |
maximum number of iteration steps |

`m` |
size of the sample from |

`n` |
size of the sample from |

`alpha` |
significance level |

`eps1` |
absolute value of the lower equivalence limit to |

`eps2` |
upper equivalence limit to |

`IT` |
number of iteration steps performed until reaching the stopping criterion corresponding to TOL |

`C1` |
left-hand limit of the critical interval for the two-sample |

`C2` |
right-hand limit of the critical interval for the two-sample |

`ERR1` |
deviation of the rejection probability from |

`ERR2` |
deviation of the rejection probability from |

`POW0` |
power of the UMPI test against the alternative |

If the output value of ERR2 is NA, the deviation of the rejection probability at the right-hand
boundary of the hypothetical equivalence interval from *α* is smaller than the smallest
real number representable in R.

Stefan Wellek <stefan.wellek@zi-mannheim.de>

Peter Ziegler <peter.ziegler@zi-mannheim.de>

Wellek S: Testing statistical hypotheses of equivalence and noninferiority. Second edition.
Boca Raton: Chapman & Hall/CRC Press, 2010, *Par.* 6.1.

1 | ```
tt2st(12,12,0.05,0.50,1.00,1e-10,50)
``` |

```
Loading required package: BiasedUrn
m = 12 n = 12 alpha = 0.05 eps1 = 0.5 eps2 = 1 it = 25 c1 = 0.2797658 c2 = 0.9308834 ERR1 = 6.765859e-11 ERR2 = NA POW0 = 0.2101268
```

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