Box-Cox Transformation

The Box-Cox Transformation is one method of transforming non-normal data, or data that can not be assumed normal, to meet a normal distribution and allow further capability analysis and hypothesis testing.

The term is named after statisticians George and David Cox which is a method that uses an exponent, Lambda, to transform the data. The value of Lambda is the power to which each data point is raised. Then a new (transformed) set of data is created and that transformed set of data is used in for statistical analysis. 

The tool is typically used in the ANALYZE phase of a DMAIC project.

Data Type Assumption:

  • Continuous X and Y.
  • Data does not contain negative numbers or zero.

When the data is not normally distributed, this could result in inaccuracies when calculating a z-score. This could result in an inaccurate representation of your process capability.

Control charts may depict a process that is more or less in control than in reality; and, when performing a hypothesis tests the results of your tests may not be accurate, especially as the data is less normal. 

Box-Cox Transformation using Minitab

The menus may change depending on the version of Minitab being used. However, the concept and general flow of the process will be similar. Use the 'Help' menu to advise on how to conduct this transformation using your version.

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