Select the method or formula of your choice.

This topic describes how power is calculated when you select Test mean - reference mean (Difference) in Hypothesis about.

Let *t _{α,v}* be the upper

For the alternative hypothesis of Test mean > reference mean or Test mean - reference mean > lower limit, the power is given by:

For the alternative hypothesis of Test mean < reference mean or Test mean - reference mean < upper limit, the power is given by:

where CDF(*x*; *v*, *λ*) is the cumulative distribution function, evaluated at *x*, for a noncentral t-distribution with noncentrality parameter, *λ*, and *v* degrees of freedom.

The degrees of freedom, *v*, is given by:

The noncentrality parameter that corresponds to the lower equivalence limit is denoted as *λ*_{1}, and is given by:

where *σ* is the standard deviation of the differences between paired observations.

For the alternative hypothesis of Test mean > reference mean, *δ*_{1} = 0.

The noncentrality parameter that corresponds to the upper equivalence limit is denoted as *λ*_{2}, and is given by the following formula:

For the alternative hypothesis of Test mean < reference mean, *δ*_{2} = 0.

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

α | significance level for the test |

D | mean of the test population minus the mean of the reference population |

δ_{1} | lower equivalence limit |

δ_{2} | upper equivalence limit |

n | sample size |

σ | standard deviation of the differences between paired observations |

This topic describes how power is calculated when you select Test mean / reference mean (Ratio, by log transformation) in Hypothesis about.
### Power

### Degrees of freedom

### Noncentrality parameters

Let* t _{α,v}* be the upper

For the alternative hypothesis of Test mean / reference mean > lower limit, the power is given by:

For the alternative hypothesis of Test mean / reference mean < upper limit, the power is given by:

where CDF( *x*; *v*, *λ*) is the cumulative distribution function, evaluated at *x*, for a noncentral t-distribution with noncentrality parameter, *λ*, and *v* degrees of freedom.

The degrees of freedom, *v*, is given by:

The noncentrality parameter that corresponds to the lower equivalence limit is denoted as *λ*_{1}, and is given by:

where *σ* is the standard deviation of the log-transformed differences between paired observations.

The noncentrality parameter that corresponds to the upper equivalence limit is denoted as *λ*_{2}, and is given by:

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

α | significance level for the test |

ρ | ratio of the test population mean to the reference population mean |

δ_{1} | lower equivalence limit |

δ_{2} | upper equivalence limit |

n | sample size |

σ | standard deviation of the log-transformed differences between paired observations |

If you provide values for power and the difference (or ratio), Minitab calculates the sample size. Minitab uses the appropriate power formula and an iterative algorithm to identify the smallest sample size, *n*, for which the power is greater than or equal to the specified value. The actual power for *n* is likely to be greater than the specified power. This is because *n* must be a discrete integer value, and no value *n* is likely to yield exactly the specified power value.

If you provide values for power and sample size, Minitab calculates values for the difference. Minitab uses the appropriate power formula and an iterative algorithm to identify the largest and/or smallest difference for which the power is greater than or equal to the specified value.

If you provide values for power and sample size, Minitab calculates values for the ratio. Minitab uses the appropriate power formula and an iterative algorithm to identify the largest and/or smallest ratio for which the power is greater than or equal to the specified value.