The Box-Cox transformation is given by the following formula:

where *Y _{i}* is an original data value and

The following table shows some commonly used *λ* values and their transformations.

λ | Transformation |
---|---|

2 | |

0.5 | |

0 | |

−0.5 | |

−1 |

Optimal *λ* is the value between −5 and 5 that minimizes the standard deviation (*σ*) of the transformed data. In order to accurately compare *σ* for different values of *λ*, Minitab calculates standardized transformed values *Z _{i}* for this comparison, according to the following formula:

To estimate *σ* for subgroups data, Minitab uses the unbiased estimate of the pooled standard deviation. To estimate *σ* for individuals data, Minitab uses the unbiased estimate of the average moving range.

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

G | geometric mean of the original data |