Box-Cox formula
The Box-Cox transformation estimates lambda values that minimize the standard deviation of W, a standardized transformed variable. The transformation is given by the following formula:
where Yi is an original data value and λ is the parameter for the transformation.
Determining optimal λ
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.
Notation
| Term | Description |
|---|---|
| G | geometric mean of the original data |
Common λ values
The following table shows some commonly used λ values and their transformations.
| λ | Transformation |
|---|---|
| 2 |  |
| 0.5 |  |
| 0 |  |
| −0.5 |  |
| −1 |  |
