The Box-Cox transformation is given by the following formula:
where Yi is an original data value and λ is the parameter for the transformation.
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 Zi 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.
|G||geometric mean of the original data|