Box-Cox transformation

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 -10 to 10 for the factor with the lowest spread.

Uses

• Before transforming a data-set first look why the data is not normally distributed see What to do with not normally distributed Data
• All the data points must positive
• To find the optimum Box-Cox uses the STDEV and not looks for normality. So the result is not guaranteed the optimum value.
• Box-Cox transformation is only available in the Basic Statistics mode.
• In many cases it is better to use a rounded value instead of the optimum. Look to the table below.

commonly used exponents
	Y
-2
-1		inverse transformation
-0.5
0		logarithmic transformation
0.5		square root transformation
1		no transformation
2		quadratic 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

• Low resolution of the measurement
• Mixture of various distributions
• Sorted data
• Extreme values (outliers)

Formula to find optimum Lamda

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

Formula for transformation

Legend

s = STDEV
Geometric mean =

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

A before transformation	A after transformation

External links

• http://en.wikipedia.org/wiki/Power_transform
• http://www.isixsigma.com/tools-templates/normality/making-data-normal-using-box-cox-power-transformation/
• http://onlinestatbook.com/2/transformations/box-cox.html