Find definitions and interpretation guidance for every transformation that is provided with individual distribution identification.

If you include the Box-Cox transformation when you perform individual distribution identification, Minitab reports the value of lambda (λ) used in the transformation.

The Box-Cox transformation estimates a lambda value, as shown below, which minimizes the standard deviation of a standardized transformed variable. The resulting transformation is Y^{λ} when λ ҂ 0 and ln Y when λ = 0.

This method searches through many types of transformations. The following table shows some common transformations, where Y' is the transform of the data Y:

Lambda (λ) value | Transformation |
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If you include the Johnson transformation when you perform individual distribution identification, Minitab reports the function used to transform the data. For example, suppose the Johnson transformation function is 0.762475 + 0.870902 × Ln(( X – 46.3174)/(59.6770 – X)). If the original data value for X is 50, then the transformed value of 50 is calculated as 0.762475 + 0.870902 × Ln((50 – 46.3174)/(59.6770 – 50)), which equals –0.07893.

For more information on the algorithm that Minitab uses to define the Johnson transformation function, go to Methods and formulas for transformations in Individual Distribution Identification.