Box-Cox Transformation

Definition of Box-Cox Transformation:

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In many industries, it is possible to find distributed data that does not follow the typical bell-shaped curve. In some instances, you will find that there is a much longer tail on the right side. This type of distribution follows the 80/20 rule, which states that roughly 80& of consequences come from 20% of causes. In order, to change this type of distribution into a much easier-to-work-with normal distribution, there is the Box-Cox Transformation method.

This method is useful in many fields such as biology, physics, marketing, manufacturing, and economics. Really, any area where there are instances of non-normal distribution can benefit from this tool.

Overview: What is Box-Cox Transformation?

Box-Cox Transformation is used for the transformation of non-normal dependent variables into a normal shape in order to make them easier to work with.

2 benefits and 2 drawbacks of Box-Cox Transformation

There are some clear benefits to a Box-Cox Transformation, but there are also some notable drawbacks. Let’s go through them both:


1. Testing

If your data is abnormal, running a Box-Cox Transformation allows you to run a greater variety of tests.

2. Better organization

Transformed data is generally easier to use for both humans and computers. Data quality is improved, which helps prevent null values, duplicates, and incompatible formats.


1. Negative values

One issue with Box-Cox Transformation is that it is ill-suited for use with negative values. The reason for this is that it requires raising negative values up a power, which leads to complex results.

2. The need for continuity in data

Another issue with Box-Cox Transformation is that the data you are using needs to be continuous.

Why is Box-Cox Transformation important to understand?

Box-Cox Transformation is important to understand for the following reasons:

Multiple regression analysis – Box-Cox Transformation is important to understand if you are going to be working with multiple regression analysis. It is the basic tool used with this type of analysis.

Standard deviation – It is important to understand the way that the Box-Cox method checks to see if you have the smallest deviation, so remember to look at your transformed data and check for normality using a tool such as Q-plot.

DMAIC – Having an understanding of Box-Cox Transformation is important for the Measure stage of DMAIC. During this stage, process capability studies are checked, and the first thing that is checked is whether or not data follows a normal distribution.

An industry example of Box-Cox Transformation

A manufacturing plant wanted to see the timeframe it took its workers on the assembly floor to put together a series of parts. A few workers put together the parts quickly and in close proximity timewise to one another, while the rest were spread out significantly. When looking at the data in a model, the data appeared non-normal, making it difficult to analyze it as thoroughly as hoped. To remedy this, the Box-Cox Transformation method was utilized in order to normalize the data, so that a lot more information could be gleaned from the exercise.

3 best practices when thinking about Box-Cox Transformation

Here are some practices to consider when it comes to using Box-Cox Transformation:

1. Use Box-Cox Transformation for calculating process capability with non-normal data

Calculating the process capability using non-normal data can give inaccurate results. Use the Box-Cox Transformation to transform the data to normal before working out the process capability.

2. It does not check for normality

Be advised that while this is a useful tool for transferring non-normal data into normalized data, it is not guaranteed that any data you put in is going to follow normality. Box-Cox Transformation does not check for normality.

3. Modified coefficients in a regression model

You need to be aware that when using Box-Cox Transformation in a regression model the coefficients will be modified. This is actually useful, in that it identifies the factors that are truly significant.

Frequently Asked Questions (FAQ) about Box-Cox Transformation

Who came up with Box-Cox Transformation?

Box-Cox Transformation is attributed to a collaboration between Sir David Cox and George Box in 1964. Cox was paying a visit to Box in Wisconsin, and they decided they should publish a paper together due to the similarity of their names.

How easy is it to use Box-Cox Transformation manually?

Working with Box-Cox Transformation manually can be complex and error-prone. It is recommended to generally utilize software whenever possible. For Six Sigma exams, you generally just need to understand how to transform the data as well as be able to substitute variables.

What kind of software do I need to use Box-Cox Transformation?

Minitab, Excel Analysis toolpack, or almost any other statistical software.

Normalizing the non-normal

Anytime there is a data set that appears to be non-normal but is positive values that run continuously, it is worth trying Box-Cox Transformation to make it easier to work with.

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