Recently I am learning box-cox transformation. I know the transformation is to make data normal. And the formula for box-cox is:

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However, I am confused why when people get lambda, they will do the transformation follow this relationship:

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For example, if lambda equal to 2, then the transformation should be (x^2 -1)/2, not just x^2. Anyone can help me out? Thanks!

(My thinking is that the transformation is help us to get normality, so -1 and divided by a constant will not affect the normality. But if this is true, why do we need a -1 and divided by lambda in the boxcox formula?)

  • $\begingroup$ Although it is often stated that this transformation is intended to make data Normal, that is rarely the reason and it's not why it was invented. It is to make data more symmetrically distributed. There is no general basis to hope you can come any closer to Normality than that with just a single parameter of flexibility! $\endgroup$
    – whuber
    Aug 11, 2022 at 23:36