Term | Description |
---|---|

D | Difference |

Test mean |

Term | Description |
---|---|

s | Standard deviation of the observations |

n | Number of observations |

Let *k*_{1}and *k*_{2} be the values that you specify for the lower limit and the upper limit, respectively. By default, the lower equivalence limit, *δ*_{1} , is given by:
and the upper equivalence limit, *δ*_{2}, is given by:

However, if you select the option to multiply your limits by the target value, then the limits are given by:
Term | Description |
---|---|

v | Degrees of freedom |

n | Number of observations |

By default, Minitab uses the following formula to calculate the 100(1 – α)% confidence interval (CI) for the difference:

CI = [min(*C, D _{l}*), max(

where:

If you select the option to use the 100(1 – 2 α)% CI, then the CI is given by the following formula:

CI = [*D _{l}, D_{u}*]

For a hypotheses of Test mean > target, or Test mean - target > lower limit, the 100(1 – α)% lower bound is equal to *D _{L}*.

For a hypothesis of Test mean < target, or Test mean - target < upper limit, the 100(1 – α)% upper bound is equal to *D _{U}*.

Term | Description |
---|---|

D | Difference between the mean of the test sample and the target value |

SE | Standard error |

δ_{1} | Lower equivalence limit |

δ_{2} | Upper equivalence limit |

v | Degrees of freedom |

α | Significance level for the test |

t_{1 – α, v} | Upper 1 – α critical value for a t-distribution with v degrees of freedom |

Let *t *_{1} be the t-value for the hypothesis, , and let *t *_{2} be the t-value for the hypothesis, , where is the difference between the mean of the test population and the target value. By default, the t-values are calculated as follows:

For a hypothesis of Test mean > target, *δ*_{1}= 0.

For a hypothesis of Test mean < target, *δ*_{2}= 0.

Term | Description |
---|---|

D | Difference between the mean of the test sample and the target value |

SE | Standard error of the difference |

δ_{1} | Lower equivalence limit |

δ_{2} | Upper equivalence limit |

The probability, P_{H0}, for each null hypothesis (H_{0}) is given by the following:

H_{0} |
P-Value |
---|---|

Term | Description |
---|---|

Unknown difference between the mean of the test population and the target value | |

δ_{1} | Lower equivalence limit |

δ_{2} | Upper equivalence limit |

v | Degrees of freedom |

T | t distribution with v degrees of freedom |

t_{1} | The t-value for the hypothesis |

t_{2} | The t- value for the hypothesis |

For information on how the t-values are calculated, see the section on t-values.