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Box-Cox transformation

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The Box-Cox transformation can be used to transform a non normal distributed data to a more normal distributed data-set. The Box-Cox procedure tries find the best exponent to transform the data int to a normal shape. All the data in the data-set will be raised with this factor. In order to do this the Box-Cox transformation search in a range form formula -10 to formula 10 for the factor with the lowest spread.

Uses

commonly used exponents
formula Y
-2 formula
-1 formulainverse transformation
-0.5 formula
0 formulalogarithmic transformation
0.5 formulasquare root transformation
1 formulano transformation
2 formulaquadratic transformation

When use a Box-Cox transformation

Use the transformation when the data is from a non normally continuous probability distribution (log-normal, weibull, F-distribution, Chi-square,...). The transformation is not a filter!
Use the Distribution fitting function Tools=>Distribution fitting to get a better understanding of the shape of the distribution.

Below is a summary of cases not suitable for the Box-Cox transformation

Formula to find optimum Lamda

formula
Develve searches for the smallest STDEV between a labda -10 till 10.

Formula for transformation

formula

Legend

s = STDEV
Geometric mean = formula

Example

To transform Column D select the Box-Cox transformation (Tools=>Box-Cox). Select data column to transform click Calculate. Select the output column if needed change or round the transformation lambda and click Transform. If Transform nominal and borders is selected the Nominal Max Tol. and Min Tol. will also be transformed.


Data file

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