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# Box-Cox and Johnson Transformations

What do you do? You transform the data using either the Box-Cox transformation or the Johnson transformation.

## About the Box-Cox and Johnson Transformations and SPC for Excel

Having data that are normally distributed often simplifies your life. Many statistical tests are based on the assumption that your data are normally distributed. The calculation of Cpk (process capability) values require a normal distribution. If you data are not normally distributed, the first thing to try is to transform the data into a normal distribution using either the Box-Cox transformation or the Johnson transformation.

The Box-Cox transformation is Yλ where λ is value between -5 and 5. The procedure is designed to find the value of λ that minimizes the variation (standard deviation). For example, if λ = 2 minimizes the variation, then the data would be transformed as Y2. The Johnson transformation is more complex than the Box-Cox transformation. The Johnson transformation is chosen from three different functions by changing four parameters.

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