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.
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.
Term | Description |
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G | geometric mean of the original data |
λ | Transformation |
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2 | ![]() |
0.5 | ![]() |
0 | ![]() |
−0.5 | ![]() |
−1 | ![]() |