*Box-Cox Power Transformations*

## Box-Cox Power Transformations

Transform a data set with Box-Cox Power Transformations. Just enter a data set and p value or use preset values.
Instructions

- This tool lets you transform a data set by applying one or more Box-Cox Power Transformations. The research articles given in the References section cover this topic.
- To use the tool enter one data set value per line. End each line by hitting the
`Enter`

key so these are recognized as individual entries.
- To apply multiple transforms, check preset checkbox.
- To apply a single transform, uncheck preset checkbox and enter a p value (p ∈ [-2,+2]).
- To transform all the data to non-negative values, check the non-negatives checkbox. See next section.
- Submit or reset form as needed.

What is computed?

- The tool transforms a value, y, into a new one as
y* = ((y + c)^{p} - 1)/p

where usually p ∈ [-2, +2] and c offsets any negative or zero value.

- If min(y) > 0, the tool sets c = 0.
If min(y) ≤ 0, the tool sets c = 1 + |min(y)|.

- Therefore, the tool returns three possible transformation scenarios:

- if 0 < min(y) < 1, then min(y*) < 0
- if min(y) ≥ 1 then min(y*) ≥ 0
- if min(y) ≤ 0 then min(y*) = 0

where the first scenario returns negative values.

If you are working with data where 0 < min(y) < 1 and for some reason the transformed data must be non-negative, check the non-negative checkbox before submiting the form. This instructs the tool to set c = 2 + |min(y)| and min(y*) ≥ 0.

Who can use it?

- Statisticians, engineers, researchers, teachers, and students.

References

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